Publications

Abstract: We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band-limited signal such that the Fourier transform (FT) of a signal can be exactly computed from its samples. Our figure of merit is the sampling efficiency, which is defined as a ratio of the degrees of freedom required to represent a band-limited signal in harmonic domain to the number of samples required to accurately compute the FT. The proposed sampling scheme is asymptotically as efficient as the most efficient scheme developed very recently. For the computation of FT and inverse FT, we also develop fast algorithms of complexity similar to the complexity attained by the fast algorithms for the existing sampling schemes. The developed algorithms are stable, accurate and do not have any pre-computation requirements. We also analyse the computation time and numerical accuracy of the proposed algorithms and show, through numerical experiments, that the proposed Fourier transforms are accurate with errors on the order of numerical precision.

Abstract: This paper presents a novel sampling scheme on the sphere for obtaining head-related transfer function (HRTF) measurements and accurately computing the spherical harmonic transform~(SHT). The scheme requires an optimal number of samples, given by the degrees of freedom in the spectral domain, for the accurate representation of the HRTF that is band-limited in the spherical harmonic domain. The proposed scheme allows for the samples to be easily taken over the sphere due to its iso-latitude structure and non-dense sampling near the poles. In addition, the scheme can be used when samples are not taken from the south polar cap region of the sphere as the HRTF measurements are not reliable in south polar cap region due to reflections from the ground. Furthermore, the scheme has a hierarchical structure, which enables the HRTF to be analysed at different audible frequencies using the same sampling configuration. In comparison to the proposed scheme, none of the other sampling schemes on the sphere simultaneously possess all these properties. We conduct several numerical experiments to determine the accuracy of the SHT associated with the proposed sampling scheme. We show that the SHT attains accuracy on the order of numerical precision $(10^-14)$ when samples are taken over the whole sphere, both in the optimal sample placement and hierarchical configurations, and achieves an acceptable level of accuracy $(10^-5)$ when samples are not taken over the south polar cap region of the sphere for the band-limits of interest. Simulations are used to show the accurate reconstruction of the HRTF over the whole sphere, including unmeasured locations.

Abstract: This paper proposes the use of discrete stochastic approximation (DSA) algorithm for a cross- layer adaptive modulation problem in wireless communications. In this system, the throughput in the physical (PHY) layer and quality of service (QoS) incurred by the queueing effects in the data link layer are required to be optimized simultaneously and in the long run. By assuming Markov decision process (MDP) modeling, we prove that the optimal transmission policy is characterized by a queue threshold vector and can be determined by a multivariate discrete convex optimization problem if the dynamic programming (DP) is submodular. We then propose to use DSA, a subgradient-based stochastic approximation (SA) algorithm with proven convergence rate, for approximating the optimal value of the queue threshold vector. By an application in a cross-layer transmission control problem in a network-coded two way relay channel (NC-TWRC), we compare the performance of DSA with that of simultaneous perturbation stochastic approximation (SPSA), the commonly used SA algorithm for threshold policy optimization problems. The results show that DSA converges faster than SPSA resulting in lower and controllable computational cost.

Abstract: For the fast and exact computation of spherical harmonic transform (SHT) of a band-limited signal defined on the sphere from its samples, the Gauss-Legendre (GL) and equiangular sampling schemes on the sphere require asymptotically least number of samples. In comparison to the equiangular scheme, the GL scheme has larger spatial dimensionality, defined as the number of the samples required for the exact computation of SHT. In this work, we propose an efficient GL sampling scheme with spatial dimensionality equal to that of equiangular scheme. We also propose op- timisation of samples along longitude to further reduce the spatial dimensionality of equiangular, GL and efficient GL sampling schemes. We also demonstrate that the accuracy of the SHT is not affected due to the proposed reduction in the spatial dimensionality.

Abstract: In this paper we study the applicability of classical blind deconvolution methods such as constant modulus algorithm (CMA) for blind adaptive image restoration. The requirements such as the source to be white, uniformly distributed and zero mean, which yield satisfactory convergence in the data communication application context, are revisited in the image restoration context, where a linear deblur kernel needs to be blindly adapted to compensate for an unknown image blur kernel with the objective to recover a source ground truth image. Through analysis and performance studies, we show that the performance of CMA is adversely affected by the intrinsic spatial correlation of natural images and by any deviation of their distribution from being platykurtic. We also show that decorrelation techniques designed to overcome spatial correlation cannot be effectively applied to rectify CMA performance for blind adaptive image restoration.

Abstract: In a mobile ad hoc network (MANET), effective prediction of time-varying interferences can enable adaptive transmission designs and therefore improve the communication performance. This paper investigates interference prediction in MANETs with a finite number of nodes by proposing and using a general-order linear model for node mobility. The proposed mobility model can well approximate node dynamics of practical MANETs. In contrast to previous studies on interference statistics, we are able through this model to give a best estimate of the time-varying interference at any time rather than long-term average effects. Specifically, we propose a compound Gaussian point process functional as a general framework to obtain analytical results on the mean value and moment-generating function of the interference prediction. With a series form of this functional, we give the necessary and sufficient condition for when the prediction is essentially equivalent to that from a Binomial Point Process (BPP) network in the limit as time goes to infinity. These conditions permit one to rigorously determine when the commonly used BPP approximations are valid. Finally, our simulation results corroborate the effectiveness and accuracy of the analytical results on interference prediction and also show the advantages of our method in dealing with complex mobilities

Abstract: We derive a closed-form expression for the spatial fading correlation (SFC) between two arbitrary points in 3D- space for the uniform limited azimuth-elevation angle of arrival probability density function (pdf). This expression simplifies the computation of the SFC, can be used in any 3D antenna array ge- ometry, and avoids the need to generate separate expressions for specific antenna array geometries. We corroborate the accuracy of the closed-form expression through application to 2D and 3D antenna array geometries. We expect the results presented in this letter to be of significant importance for performance evaluation and sensitivity analysis in multi-input multi-output (MIMO) systems.

Abstract: This paper presents a novel sampling scheme on the sphere for obtaining head-related transfer function (HRTF) measurements and accurately computing the spherical harmonic transform~(SHT). The scheme requires an optimal number of samples, given by the degrees of freedom in the spectral domain, for the accurate representation of the HRTF that is band-limited in the spherical harmonic domain. The proposed scheme allows for the samples to be easily taken over the sphere due to its iso-latitude structure and non-dense sampling near the poles. In addition, the scheme can be used when samples are not taken from the south polar cap region of the sphere as the HRTF measurements are not reliable in south polar cap region due to reflections from the ground. Furthermore, the scheme has a hierarchical structure, which enables the HRTF to be analysed at different audible frequencies using the same sampling configuration. In comparison to the proposed scheme, none of the other sampling schemes on the sphere simultaneously possess all these properties. We conduct several numerical experiments to determine the accuracy of the SHT associated with the proposed sampling scheme. We show that the SHT attains accuracy on the order of numerical precision $(10^-14)$ when samples are taken over the whole sphere, both in the optimal sample placement and hierarchical configurations, and achieves an acceptable level of accuracy $(10^-5)$ when samples are not taken over the south polar cap region of the sphere for the band-limits of interest. Simulations are used to show the accurate reconstruction of the HRTF over the whole sphere, including unmeasured locations.

Abstract: We consider the fairness in cooperative data exchange (CDE) problem among a set of wireless clients. In this system, each client initially obtains a subset of the packets. They exchange packets in order to reconstruct the entire packet set. We study the problem of how to find a transmission strategy that distributes the communication load most evenly in all strategies that have the same sum-rate (the total number of transmissions) and achieve universal recovery (the situation when all clients recover the packet set). We formulate this problem by a discrete minimization problem and prove its M-convexity. We show that our results can also be proved by the submodularity of the feasible region shown in previous works and are closely related to the resource allocation problems under submodular constraints. To solve this problem, we propose to use a steepest descent algorithm (SDA) based on M-convexity. By varying the number of clients and packets, we compare SDA with a deterministic algorithm (DA) based on submodularity in terms of convergence performance and complexity. The results show that for the problem of finding the fairest and minimum sum-rate strategy for the CDE problem SDA is more efficient than DA when the number of clients is up to five.

Abstract: This paper considers a heterogeneous multicell network where the base station (BS) in each cell communicates with its cell-edge user with the assistance of an amplify-and-forward relay node. Equipped with a power splitter and a wireless energy harvester, the relay scavenges RF energy from the received signals to process and forward the information. In the face of strong intercell interference and limited radio resources, we develop a resource allocation scheme that jointly optimizes (i) BS transmit powers, (ii) power splitting factors for energy harvesting and information processing at the relays, and (iii) relay transmit powers. To solve the highly non-convex problem formulation of sum-rate maximization, we propose to apply the successive convex approximation (SCA) approach and devise an iterative algorithm based on geometric programming. The proposed algorithm transforms the nonconvex problem into a sequence of convex problems, each of which is solved very efficiently by the interior-point method. We prove that our developed algorithm converges to an optimal solution that satisfies the Karush-Kuhn-Tucker conditions of the original nonconvex problem. Numerical results confirm that our joint optimization solution substantially improves the network performance, compared to the existing solution wherein only the received power splitting factors at the relays are optimized.

Abstract: We consider wireless-powered amplify-and-forward relaying in cooperative communications and propose block-wise time-switching based energy harvesting protocol to implement wireless energy harvesting (EH) and information transmission (IT) at the energy constrained relay node. The time-switching EH protocol switches the relay operation between EH and IT such that during EH, relay harvests energy through the received radio-frequency signal from the source and during IT, the relay receives information signal from the source and uses the harvested energy to amplify and forward source signal to the destination. In our proposed block-wise time-switching EH protocol, the whole transmission block time is used for either EH or IT. The attractive feature of our proposed protocol is that the relay transmits at preset fixed transmit power and no channel state information is required either by the source or relay node. We derive exact expression of the analytical throughput for the proposed protocol and verify it through simulation. In addition, we show that our proposed protocol outperforms the existing time-switching EH protocol because it allows efficient use of resources by intelligently switching between EH and IT in an online fashion.

Abstract: We consider wireless-powered amplify-and-forward and decode-and-forward relaying in cooperative communications, where an energy constrained relay node first harvests energy through the received radio-frequency signal from the source and then uses the harvested energy to forward the source information to the destination node. We propose time-switching based energy harvesting (EH) and information transmission (IT) protocols with two modes of EH at the relay. For continuous time EH, the EH time can be any percentage of the total transmission block time. For discrete time EH, the whole transmission block is either used for EH or IT. The proposed protocols are attractive because they do not require channel state information at the transmitter side and enable relay transmission with preset fixed transmission power. We derive analytical expressions of the achievable throughput for the proposed protocols. The derived expressions are verified by comparison with simulations and allow the system performance to be determined as a function of the system parameters. Finally, we show that the proposed protocols outperform the existing fixed time duration EH protocols in the literature, since they intelligently track the level of the harvested energy to switch between EH and IT in an online fashion, allowing efficient use of resources.

Abstract: In this work, we design complete orthonormal basis functions, which are referred to as optimal basis functions, that span the vector sum of subspaces formed by band-limited spatially concentrated and space-limited spectrally concentrated functions. The optimal basis are shown to be a linear combination of band-limited functions with maximized energy concentration in some spatial region of interest and space-limited functions which maximize the energy concentration in some spectral region. The linear combination is designed with an optimality condition of maximizing the product of measures of energy concentration in the spatial and spectral domain. We also show that each optimal basis is an eigenfunction of a linear operator which maximizes the product of energy concentration measures in spatial and spectral domain. Finally, we discuss the properties of the proposed optimal basis functions and highlight their usefulness for the signal representation and data analysis due to the simultaneous concentration of the proposed basis functions in spatial and spectral domains.

Abstract: We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.

Abstract: We consider the fairness in cooperative data exchange (CDE) problem among a set of wireless clients. In this system, each client initially obtains a subset of the packets. They exchange packets in order to reconstruct the entire packet set. We study the problem of how to find a transmission strategy that distributes the communication load most evenly in all strategies that have the same sum-rate (the total number of transmissions) and achieve universal recovery (the situation when all clients recover the packet set). We formulate this problem by a discrete minimization problem and prove its M-convexity. We show that our results can also be proved by the submodularity of the feasible region shown in previous works and are closely related to the resource allocation problems under submodular constraints. To solve this problem, we propose to use a steepest descent algorithm (SDA) based on M-convexity. By varying the number of clients and packets, we compare SDA with a deterministic algorithm (DA) based on submodularity in terms of convergence performance and complexity. The results show that for the problem of finding the fairest and minimum sum-rate strategy for the CDE problem SDA is more efficient than DA when the number of clients is up to five.

Abstract: This paper considers a functional modeling of a head-related transfer function (HRTF) where the spatial-portion is constrained to be expanded using spherical harmonics and the frequency-portion is expanded in terms of standard closed-form orthonormal functions, which may be user selected. We derive an objective evaluation metric to compare the relative energy efficiencies of candidate functional models using empirical HRTF database measurements and robust estimation techniques. Among four sets of closed-form orthonormal functions the complex exponentials are identified as the most efficient to represent the frequency-portion in the spherical harmonics-based HRTF functional model. The proposed model is evaluated across three HRTF data sets: 1) CIPIC database, 2) the MIT KEMAR (Knowles Electronics Mannequin for Acoustics Research) database, and 3) the ANU KEMAR database.

Abstract: This paper considers the 3D spatial fading correlation (SFC) resulting from an angle-of-arrival (AoA) distribution that can be modeled by a mixture of Fisher-Bingham distributions on the sphere. By deriving a closed-form expression for the spherical harmonic transform for the component Fisher-Bingham distributions, with arbitrary parameter values, we obtain a closed-form expression of the 3D-SFC for the mixture case. The 3D-SFC expression is general and can be used in arbitrary multiantenna array geometries and is demonstrated for the cases of a 2D uniform circular array and a 3D regular dodecahedral array. In computational aspects, we use recursions to compute the spherical harmonic coefficients and give pragmatic guidelines on the truncation size in the series representations to yield machine precision accuracy results. The results are further corroborated through numerical experiments to demonstrate that the closedform expressions yield the same results as significantly more computationally expensive numerical integration methods.

Abstract: We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation). The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions. Equivalence between the spatial and spectral problems is shown. The spherical Shannon number on the ball is derived, which acts as the analog of the space-bandwidth product in the Euclidean setting, giving an estimate of the number of concentrated eigenfunctions and thus the dimension of the space of functions that can be concentrated in both the spatial and spectral domains simultaneously. Various symmetries of the spatial region are considered that reduce considerably the computational burden of recovering eigenfunctions, either by decoupling the problem into smaller subproblems or by affording analytic calculations. The family of concentrated eigenfunctions forms a Slepian basis that can be used be represent concentrated signals efficiently. We illustrate our results with numerical examples and show that the Slepian basis indeeds permits a sparse representation of concentrated signals.

Abstract: This paper considers a transmission control problem in network-coded two-way relay channels (NC-TWRC), where the relay buffers randomly arrived packets from two users, and the channels are assumed to be fading. The problem is modeled by a discounted infinite horizon Markov decision process (MDP). The objective is to find an adaptive transmission control policy that minimizes the packet delay, buffer overflow, transmission power consumption and downlink error rate simultaneously and in the long run. By using the concepts of submodularity, multimodularity and L-convexity, we study the structure of the optimal policy searched by dynamic programming (DP) algorithm. We show that the optimal transmission policy is nondecreasing in queue occupancies and/or channel states under certain conditions such as the chosen values of parameters in the MDP model, channel modeling method, and the preservation of stochastic dominance in the transitions of system states. Based one these results, we propose to use two low-complexity algorithms for searching the optimal monotonic policy: monotonic policy iteration (MPI) and discrete simultaneous perturbation stochastic approximation (DSPSA). We show that MPI reduces the time complexity of DP, and DSPSA is able to adaptively track the optimal policy when the statistics of the packet arrival processes change with time.

Abstract: We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L2 samples. We obtain the optimal number of samples given by the degrees of freedom of the signal in harmonic space. The number of samples required in our scheme is a factor of two or four fewer than existing techniques, which require either 2L^2 or 4L^2 samples. We note, however, that we do not recover a sampling theorem on the sphere, where spherical harmonic transforms are theoretically exact. Nevertheless, we achieve high accuracy even for very large band-limits. For our optimal-dimensionality sampling scheme, we develop a fast and accurate algorithm to compute the spherical harmonic transform (and inverse), with computational complexity comparable with existing schemes in practice. We conduct numerical experiments to study in detail the stability, accuracy and computational complexity of the proposed transforms. We also highlight the advantages of the proposed sampling scheme and associated transforms in the context of potential applications.

Abstract: Oscillator phase noise (PHN) and carrier frequency offset (CFO) can adversely impact the performance of orthogonal frequency division multiplexing (OFDM) systems, since they can result in inter carrier interference and rotation of the signal constellation. In this paper, we propose an expectation conditional maximization (ECM) based algorithm for joint estimation of channel, PHN, and CFO in OFDM systems. We present the signal model for the estimation problem and derive the hybrid Cramer- Rao lower bound (HCRB) for the joint estimation problem. Next, we propose an iterative receiver based on an extended Kalman filter for joint data detection and PHN tracking. Numerical results show that, compared to existing algorithms, the performance of the proposed ECM-based estimator is closer to the derived HCRB and outperforms the existing estimation algorithms at moderate-to-high signal-to-noise ratio (SNR). In addition, the combined estimation algorithm and iterative receiver are more computationally efficient than existing algorithms and result in improved average uncoded and coded bit error rate (BER) performance.

Abstract: The problem of joint oscillator phase noise (PHN) estimation and data detection for multi-input multi-output (MIMO) systems using bit-interleaved-coded modulation is analysed. A new MIMO receiver that iterates between the estimator and the detector, based on the expectation-maximisation (EM) framework, is proposed. It is shown that at high signal-to-noise ratios, a maximum a posteriori (MAP) estimator can be used to carry out the maximisation step of the EM algorithm. Moreover, to reduce the computational complexity of the proposed EM algorithm, a soft decision-directed extended Kalman filter-smoother (EKFS) is applied instead of the MAP estimator to track the PHN parameters. The numerical results show that by combining the proposed EKFS-based approach with an iterative detector that employs low-density parity check codes, PHN can be accurately tracked. The simulations also demonstrate that compared to the existing algorithms, the proposed iterative receiver can significantly enhance the performance of MIMO systems in the presence of PHN.

Abstract: We analyse the characteristics of spherical harmonics to derive a tighter bound on the minimum number of required measurements to accurately recover a sparse signal in spherical harmonic domain. We numerically show the coherence of spherical harmonic matrix can be reduced from a polynomial order of $N^1/4$ or $N^1/6$ (both achieved by preconditioning) to a logarithmic order, i.e., $\log^2(L)$. Hence, one can, with high probability, recover $s$-sparse spherical harmonic expansions from $M\ge s\log^3N$ measurements randomly sampled from the uniform $\sin\theta\,d\theta \,d\varphi$ measure on sphere.

Abstract: We analyse the characteristics of spherical harmonics to derive a tighter bound on the minimum number of required measurements to accurately recover a sparse signal in spherical harmonic domain. We numerically show the coherence of spherical harmonic matrix can be reduced from a polynomial order of $N^1/4$ or $N^1/6$ (both achieved by preconditioning) to a logarithmic order, i.e., $\log^2(L)$. Hence, one can, with high probability, recover $s$-sparse spherical harmonic expansions from $M\ge s\log^3N$ measurements randomly sampled from the uniform $\sin\theta\,d\theta \,d\varphi$ measure on sphere.

Abstract: This paper introduces an adaptive, multi-resolution windowing technique that can be used in conjunction with the spatially localized spherical harmonic transform (SLSHT) to process signals on the 2-sphere in the spatio-spectral domain. In contrast with the standard formulation, which uses a fixed window, the new windowing technique is able to respond locally to the signal under analysis, that is, be adaptive, and also is formulated to depend on the spectral degree to give it a multi-resolution character. We further enhance its simultaneous spatial and spectral localization by basing the window on a parametric band-limited Slepian maximum spatial concentration eigenfunction. The criterion for window design is to maximize the energy concentration in each spectral component in the spatio-spectral domain. A computationally efficient method is also developed to implement the adaptive window design. An example is also provided to demonstrate the superiority of the new adaptive, multiresolution window technique.

Abstract: In this paper we consider the zero-forcing (ZF) and minimum mean square error (MMSE) criteria for signal recovery using linear operators as equalizers for signals observed on the 2-sphere that are subject to linear distortions and noise. The distortions considered are bounded operators and can include convolutions, rotations, spatial and spectral truncations, projections or combinations of these. Likewise the signal and noise are very general being modeled as anisotropic stochastic processes on the 2-sphere. In both the distortion model and signal model the findings in this paper are significantly more general than results that can be found in the literature. The MMSE equalizer is shown to reduce to the ZF equalizer when the distortion operator has an inverse and there is an absence of noise. The ability of the MMSE to recover a Mars topography map signal from a projection operator, which fails to have a ZF solution, is given as an illustration.

Abstract: Cooperative communication systems employ coopera- tion among nodes in a wireless network to increase data throughput and robustness to signal fading. However, such advantages are only possible if there exist perfect synchronization among all nodes. Impairments like channel multipath, time varying phase noise (PHN) and carrier frequency offset (CFO) result in the loss of synchro- nization and diversity performance of cooperative communication systems. Joint estimation of these multiple impairments is necessary in order to correctly decode the received signal in cooperative systems. In this paper, we propose an iterative pilot-aided algorithm based on expectation conditional maximization (ECM) for joint estimation of multipath channels, Wiener PHNs, and CFOs in amplify-and-forward (AF) based cooperative orthogonal frequency division multiplexing (OFDM) system. Numerical results show that the proposed estimator achieves mean square error performance close to the derived hybrid Cramer-Rao lower bound (HCRB) for different PHN variances.

Abstract: Two-way relaying networks (TWRNs) allow for more bandwidth efficient use of the available spectrum since they allow for simultaneous information exchange between two users with the assistance of an intermediate relay node. However, due to superposition of signals at the relay node, the received signal at the user terminals is affected by multiple impairments, i.e., channel gains, timing offsets, and carrier frequency offsets, that need to be jointly estimated and compensated. This paper presents a training-based system model for amplify-and-forward (AF) TWRNs in the presence of multiple impairments and proposes maximum likelihood and differential evolution based algorithms for joint estimation of these impairments. The Cramer-Rao lower bounds (CRLBs) for the joint estimation of multiple impairments are derived. A minimum mean-square error based receiver is then proposed to compensate the effect of multiple impairments and decode each user's signal. Simulation results show that the performance of the proposed estimators is very close to the derived CRLBs at moderate-to-high signal-to-noise-ratios. It is also shown that the bit-error rate performance of the overall AF TWRN is close to a TWRN that is based on assumption of perfect knowledge of the synchronization parameters.

Abstract: In this paper, we consider a decode-and-forward (DF) relaying network based on wireless energy harvesting. The energy constrained relay node first harvests energy through radio-frequency (RF) signals from the source node. Next, the relay node uses the harvested energy to forward the decoded source information to the destination node. The source node transfers energy and information to the relay node through two mechanisms, i) time switching-based relaying (TSR) and ii) power splitting-based relaying (PSR). Considering wireless energy harvesting constraint at the relay node, we derive the exact analytical expressions of the achievable throughput and ergodic capacity of a DF relaying network for both TSR and PSR schemes. Through numerical analysis, we study the throughput performance of the overall system for different system parameters, such as energy harvesting time, power splitting ratio, and signal-to-noise-ratio (SNR). In particular, the throughput performance of the PSR scheme outperforms the throughput performance of the TSR scheme for a wide range of SNRs.

Abstract: This paper investigates spectral filtering using isotropic spectral windows, which is a computationally efficient method of spatial smoothing on the sphere. We propose a Slepian eigenfunction window, which is obtained as a solution of the concentration problem on the sphere, as a good choice of the window function. We also unify a comprehensive set of quantitative tools, both spatial and spectral, to assess and compare the performance of different smoothing windows (i.e., smoothers). We analyze and compare the performance of the proposed window against the two best available candidates in the literature: von-Hann window and von Mises-Fisher distribution window. We establish that the latter window includes the popular Gauss window as a subcase. We show that the Slepian eigenfunction window has the smallest spatial variance (better spatial localization) and the smallest side-lobe level.

Abstract: We investigate the problem of extrapolation of band-limited signals on the 2-sphere in the presence of noise. Specifically, given incomplete or spatially limited measurements subject to noise, find the unique extrapolation to the complete 2-sphere. We present an analytic solution to the extrapolation problem based on the expansion of a signal in Slepian basis corresponding to an orthogonal set of eigenfunctions of an associated energy concentration problem. An alternative equivalent iterative algorithm is also developed for practical implementation and guidelines are proposed to choose the parameters of the iterative algorithm. The capability of the proposed extrapolation is compared and demonstrated with the help of an illustration example.

Abstract: In this paper we show that the spatially localized spherical harmonic transform (SLSHT), which represents a signal on the 2-sphere in the spatio-spectral domain, can be efficiently computed using new kernel-based formulations. In addition to the standard spatio-spectral domain, we show there are three other related transforms that provide alternative representations in the spatio-spatial, spectro-spatial and spectro-spectral domains. We provide inversion results that extend available results for the SLSHT. We show that for signals on the 2-sphere band-limited to degree $L$, the computational complexity using our class of kernel-based SLSHT transforms is $O(L^4)$ and outperforms the previous best known fast methods, which have complexity $O(L^5)$.

Abstract: Smallcell is emerging as a cost-effective solution for satisfying the huge demands of mobile data. It can be deployed at any place where mobile traffic is required without the need for cell planning. However, coexistence of many uncontrolled smallcells using the same licensed frequency band can result in serious interference problems. In order to utilize smallcell efficiently, it is highly desirable that the smallcell can self-organize the network and mitigate interference automatically. In this paper, we propose a dynamic fractional frequency reuse (FFR) method for reducing the intercell interference automatically and improving the spectral efficiency. Key features of the proposed method are sub-band optimization with a central manner and sub-band size adjustment with a distributed manner. The proposed method has a low complexity and can be implemented as a feature of a self-organizing network (SON) in smallcell. Simulation results verify the effectiveness of the proposed method.

Abstract: An emerging solution for prolonging the lifetime of energy constrained relay nodes in wireless networks is to avail the ambient radio-frequency (RF) signal and to simultaneously harvest energy and process information. In this paper, an amplify-and-forward relaying network is considered, where an energy constrained relay node harvests energy from the received RF signal and uses that harvested energy to forward the source information to the destination. Based on the time switching and power splitting receiver architectures, two relaying protocols, namely, i) time switching-based relaying (TSR) protocol and ii) power splitting-based relaying (PSR) protocol are proposed to enable energy harvesting and information processing at the relay. In order to determine the throughput, analytical expressions for outage probability and ergodic capacity are derived for delay-limited and delay-tolerant transmission modes, respectively. The numerical analysis provides practical insights into the effect of various system parameters, such as energy harvesting time, power splitting ratio, source transmission rate, source to relay distance, noise power, and energy harvesting efficiency, on the performance of wireless energy harvesting and information processing using AF relay nodes. In particular, the TSR protocol outperforms the PSR protocol in terms of throughput at relatively low signal-to-noise-ratios and high transmission rate.

Abstract: For distributed multi-user and multi-relay cooperative networks, the received signal may be affected by multiple timing offsets (MTOs) and multiple channels that need to be jointly estimated for successful decoding at the receiver. This paper addresses the design of optimal training sequences for efficient estimation of MTOs and multiple channel parameters. A new hybrid Cramer-Rao lower bound (HCRB) for joint estimation of MTOs and channels is derived. Subsequently, by minimizing the derived HCRB as a function of training sequences, three training sequence design guidelines are derived and according to these guidelines, two training sequences are proposed. In order to show that the proposed design guidelines also improve estimation accuracy, the conditional Cramer-Rao lower bound (ECRB), which is a tighter lower bound on the estimation accuracy compared to the HCRB, is also derived. Numerical results show that the proposed training sequence design guidelines not only lower the HCRB, but they also lower the ECRB and the mean-square error of the proposed maximum a posteriori estimator. Moreover, extensive simulations demonstrate that application of the proposed training sequences significantly lowers the bit-error rate performance of multi-relay cooperative networks when compared to training sequences that violate these design guidelines.

Abstract: In multi-relay cooperative systems, the signal at the destination is affected by impairments such as multiple channel gains, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs). In this paper we account for all these impairments and propose a new transceiver structure at the relays and a novel receiver design at the destination in distributed space-time block code (DSTBC) based amplifyand- forward (AF) cooperative networks. The Cramer-Rao lower bounds and a least squares (LS) estimator for the multi-parameter estimation problem are derived. In order to significantly reduce the receiver complexity at the destination, a differential evolution (DE) based estimation algorithm is applied and the initialization and constraints for the convergence of the proposed DE algorithm are investigated. In order to detect the signal from multiple relays in the presence of unknown channels, MTOs, and MCFOs, novel optimal and sub-optimal minimum mean-square error receiver designs at the destination node are proposed. Simulation results show that the proposed estimation and compensation methods achieve full diversity gain in the presence of channel and synchronization impairments in multi-relay AF cooperative networks.

Abstract: We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional spatially localized spherical harmonic transform (directional SLSHT) which extends the SLSHT from the literature whose usefulness is limited to symmetric windows. We present an inversion relation to synthesize the original signal from its directional- SLSHT distribution for an arbitrary window function. As an example of an asymmetric window, the most concentrated band-limited eigenfunction in an elliptical region on the sphere is proposed for directional spatio-spectral analysis and its effectiveness is illustrated on the synthetic and Mars topographic data-sets. Finally, since such typical data-sets on the sphere are of considerable size and the directional SLSHT is intrinsically computationally demanding depending on the band-limits of the signal and window, a fast algorithm for the efficient computation of the transform is developed. The floating point precision numerical accuracy of the fast algorithm is demonstrated and a full numerical complexity analysis is presented.

Abstract: The problem of automatic administration of vasoactive drugs to a patient can be treated as a regulation problem of a system which is characterised by large parametric uncertainty, non-gaussian disturbances and unmodelled dynamics, yet carries strict requirements in terms of robustness and performance. A number of approaches have been proposed in the past to tackle this problem, particularly for the postoperative management of blood pressure in cardiac surgery patients. We describe the design of a Robust Multiple-Model Adaptive Control (RMMAC) architecture and investigate whether this can overcome some issues observed with earlier methods. Key features of RMMAC are robust optimal controller design using an iterative mu-synthesis algorithm and improved system estimation. Simulation results indicate that RMMAC is capable of avoiding transient instability and delivering performance in the face of significant parameter changes over time and large disturbances including non-zero-mean signals. The findings support further research into RMMAC as a potentially viable approach to the design of safer automatic closed-loop drug administration technologies capable of operating under challenging clinical conditions such as may arise in an intraoperative setting.

Abstract: This paper presents a general framework for spatially-varying spectral filtering of signals defined on the unit sphere, as an analogy to joint time-frequency filtering. For this purpose, we first map spherical signals from spatial domain into joint spatio-spectral domain, where a spatio-spectral signal transformation or modification is introduced. For mapping spatial signals into joint spatio-spectral domain, we use the spatially localized spherical harmonic transform (SLSHT) from the literature. We then propose a suitable scheme to transform the modified signal from the spatio-spectral domain back to an admissible signal in the spatial domain using the least squares approach. We also show that the overall action of the SLSHT and spatio-spectral signal modification can be described through a single transformation matrix, which is useful in practice. Finally, we discuss two specific and useful instances of spatially-varying spectral filtering, defined through multiplicative and convolutive modification of the SLSHT distribution, and show through numerical examples their effectiveness in selective spectral filtering of different spatial regions of the signal.

Abstract: This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.

Abstract: We analyse the characteristics of spherical harmonics to derive a tighter bound on the minimum number of required measurements to accurately recover a sparse signal in spherical harmonic domain. We numerically show the coherence of spherical harmonic matrix can be reduced from a polynomial order of $N^1/4$ or $N^1/6$ (both achieved by preconditioning) to a logarithmic order, i.e., $\log^2(L)$. Hence, one can, with high probability, recover $s$-sparse spherical harmonic expansions from $M\ge s\log^3N$ measurements randomly sampled from the uniform $\sin\theta\,d\theta \,d\varphi$ measure on sphere.

Abstract: The modeling performance of three models for the 3D Head Related Transfer Function (HRTF) are compared. One of these models appeared recently in the literature whilst the other two models are novel. All models belong to the class of functional models whereby the 3D-HRTF is expressed as an expansion in terms of basis functions, which are functions of azimuth, elevation, radial distance and frequency. The expansion coefficients capture the 3D-HRTF individualization. The models differ in the choice of basis functions and the degree of orthogonality that is possibly given the constraint that for each frequency the HRTF needs to satisfy the Helmholtz wave equation. One model introduced in this paper is designed to provide a functional representation that is orthonormal on a sphere at some nominal radius and approximately so around that nominal radius. This model is shown to be superior to the other two in being able to reconstruct most efficiently the 3D-HRTF derived from a spherical head 3D-HRTF model. For all cases we show that there is a unified technique to estimate expansion coefficients from measurements taken on a sphere of arbitrary radius.

Abstract: In this paper we give a general expression for the 3D spatial correlation experienced between two sensors in 3D-space for the class of normalized power distributions (representing farfield multipath sources) having a rotational symmetry about their mean direction axis. A general expansion for the 3D spatial correlation is presented and interpreted in terms of an associated eigenfunction equation. This enables us to develop closed-form coefficient expressions for the spatial correlation for a number of distributions such as the Gauss-Weierstrass kernel based distribution and the previous known results for the von Mises-Fisher power distribution. Analytical results generated fully account for the effect of varying in the relative orientation between the sensors in 3D and the power distribution mean direction which can be arbitrarily oriented. The results provide information on placement of sensors to reduce correlation effects.

Abstract: This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alter- native to the conventional Hilbert space using the inner product that yields the L2(S2) function space of finite energy signals. In comparison with wavelet representations which have multi-resolution properties on L2(S2), the representations that arise from the RKHS approach which uses different inner products have an overall smoothness constraint which may offer advantages and simplifications in certain contexts. The key contribution of this paper is to construct classes of closed-form kernels, such as one based on the von-Mises Fisher distribution, which permits efficient inner product computation using kernel evaluations. Three classes of RKHS are defined: isotropic kernels and non-isotropic kernels both with spherical harmonic eigenfunctions, and general anisotropic kernels.

Abstract: In this paper, we present the optimal filter for the enhancement or estimation of signals on the 2-sphere corrupted by the noise, when both the signal and noise are realizations of anisotropic process on the 2-sphere. The estimation of such a signal in the spatial or spectral domain is not adequate. Therefore, we develop the optimal filter in the spatio-spectral domain by using the framework presented in the literature for filtering of signals in the spatio- spectral domain. The filtering of the signal in the spatio-spectral domain enables the proposed framework to take into account the anisotropic properties of the process. The spatio-spectral filtering is made optimal under the mean-square error criterion. The capability of the proposed filtering framework is demonstrated with the help of an example to enhance the signal corrupted by anisotropic noise process.

Abstract: In this paper, we investigate the performance of compressive sampling (CS) for ECG compression in telecardiology, when the signal acquisition is noisy and unavoidable body movements lead to varying heartbeat rate and sparsity of the signal. We show analytically that CS recovery noise does not scale linearly with the input noise. Hence, it is not easy to reduce the adverse impact of noise in CS. Additionally, any variation in the heartbeat rate changes the sparsity and can adversely affect compression. We compare the performance of CS with thresholding discrete wavelet transform (TH-DWT), which is the best technique for real-time ECG compression. We show that CS is quite sensitive to sparsity and compression ratio, while the reconstruction quality of TH-DWT is quite stable. Our results suggest that while CS is an attractive option for telecardiology due to its encoder simplicity, caution should be exercised in applying it for ECG signal compression.

Abstract: We develop a new type of convolution between two signals on the 2-sphere. This is the first type of convolution on the 2-sphere which is commutative. Two other advantages, in comparison with existing definitions in the literature, are that 1) the new convolution admits anisotropic filters and signals and 2) the domain of the output remains on the sphere. Therefore, the new convolution well emulates the conventional Euclidean convolution. In addition to providing the new definition of convolution and discussing its properties, we provide the spectral analysis of the convolution output. This convolutional framework can be useful in filtering applications for signals defined on the 2-sphere.

Abstract: This paper proposes a framework for joint blind timing and carrier offset estimation and data detection using a Sequential Importance Sampling (SIS) particle filter in Additive White Gaussian Noise (AWGN) channels. We assume baud rate sampling and model the intractable posterior probability distribution functions for sampling timing and carrier offset particles using beta distributions. To enable the SIS approach to estimate static synchronization parameters, we propose new resampling guidelines for dealing with the degeneracy problem and fine tuning the estimated values. We derive the Weighted Bayesian Cramer Rao Bound (WBCRB) for joint timing and carrier offset estimation, which takes into account the prior distribution of the estimation parameters and is an accurate lower bound for all considered Signal to Noise Ratio (SNR) values. Simulation results are presented to corroborate that the Mean Square Error (MSE) performance of the proposed algorithm is close to optimal at higher SNR values (above 20 dB). In addition, the bit error rate performance approaches that of the perfectly synchronized case for small unknown carrier offsets and any unknown timing offset. The advantage of our particle filter algorithm, compared to existing techniques, is that it can work for the full range acquisition of carrier offsets.

Abstract: This correspondence studies a spatially localized spectral transform for signals on the unit sphere, which we call spatially localized spherical harmonics transform (SLSHT). For a systematic treatment, we explicitly express the transform in terms of rotated versions of an azimuthally symmetric window function and introduce the spatio-spectral SLSHT distribution with a succinct matrix representation. We present guidelines for the choice of the window function in the SLSHT, based on the inherent tradeoff between the spatial and spectral resolution of different window functions from the perspective of the uncertainty principle. We demonstrate the use of an eigenfunction window, obtained from the Slepian concentration problem on the sphere, as a good choice for window function. As an illustration, we apply the transform to the topographic map of Mars, which can reveal spatially localized spectral contributions that were not obtainable from traditional spherical harmonics analysis.

Abstract: Multiple distributed nodes in cooperative networks generally are subject to multiple carrier frequency offsets (MCFOs) and multiple timing offsets (MTOs), which result in time varying channels and erroneous decoding. This paper seeks to develop estimation and detection algorithms that enable cooperative communications for both decode and forward (DF) and amplify-and-forward (AF) relaying networks in the presence of MCFOs, MTOs, and unknown channel gains. A novel transceiver structure at the relays for achieving synchronization in AF-relaying networks is proposed. New exact closed-form expressions for the Cramer-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. Next, two iterative algorithms based on the expectation conditional maximization (ECM) and space-alternating generalized expectation-maximization (SAGE) algorithms are proposed for jointly estimating MCFOs, MTOs, and channel gains at the destination. Though the global convergence of the proposed ECM and SAGE estimators cannot be shown analytically, numerical simulations indicate that through appropriate initialization the proposed algorithms can estimate channel and synchronization impairments in a few iterations. Finally, a maximum likelihood (ML) decoder is devised for decoding the received signal at the destination in the presence of MCFOs and MTOs. Simulation results show that through the application of the proposed estimation and decoding methods, cooperative systems result in significant performance gains even in presence of impairments.

Abstract: This paper deals with two significant questions associated with HRTF measurement: (i) what is the required angular resolution, and (ii) what is the most suitable sampling scheme. The paper shows that a well-defined finite number of spherical harmonics can capture the HRTF spatial variations in sufficient detail, which is defined as the HRTF spatial dimensionality. For the 20 kHz audible frequency range, the value of the dimensionality means a high directional resolution HRTF measurement is required. Considering such a high resolution measurement, a number of sampling criteria have been identified from both mechanical setup and data processing aspects. Different sampling candidates are then compared to demonstrate that the best method which satisfies all requirements is the class termed as IGLOO. A fast spherical harmonic transform algorithm based on the IGLOO scheme is developed to accelerate the high resolution data analysis. The proposed method is validated through simulation and experimental data acquired from a KEMAR mannequin.

Abstract: Recently, the commutative anisotropic convo- lution has been defined for signals defined on the 2-sphere. Here, we present exact and efficient methods for compu- tation of commutative convolution of two signals defined on the sphere. For the fast computation of commutative convolution, we first review the use of existing efficient techniques developed to evaluate SO(3) convolution. By employing the factoring of a rotation into two rotations, followed by the separation of variables, we propose the fast algorithm for the efficient computation of commutative convolution. In terms of computational complexity, our proposed algorithm provides the saving of O(N) over the existing algorithms, where the convolution output is evaluated on O(N2) samples on the 2-sphere. Through numerical experiments, we also verify the improvement in the computational complexity.

Abstract: We propose a method for constructing a spherical harmonic sensing matrix that can be used to effectively recover a sparse signal on the sphere from limited measurements. For such a sensing matrix, in a compressed sensing setting, it is desirable that the restricted isometry property (RIP) holds. Our sensing matrix is obtained by drawing random samples from a grid derived from minimal discrete energy spiral distribution of sample points (spiral scheme). This sampling scheme and construction of sampling matrix is shown to be superior to the use of preconditioned equiangular samples from the literature (regular scheme). Our numerical results show that the success rate in near exact recovery of a sparse coefficient vector with our spiral scheme is superior to that of the regular scheme over a range of SNRs.

Abstract: We propose a method for constructing a spherical harmonic sensing matrix that can be used to effectively recover a sparse signal on the sphere from limited measurements. For such a sensing matrix, in a compressed sensing setting, it is desirable that the restricted isometry property (RIP) holds. Our sensing matrix is obtained by drawing random samples from a grid derived from minimal discrete energy spiral distribution of sample points (spiral scheme). This sampling scheme and construction of sampling matrix is shown to be superior to the use of preconditioned equiangular samples from the literature (regular scheme). Our numerical results show that the success rate in near exact recovery of a sparse coefficient vector with our spiral scheme is superior to that of the regular scheme over a range of SNRs.

Abstract: We propose a method to reduce the spectrum noise when compressed sensing (CS) is applied to spectrum sensing. Since CS is susceptible to noise, the quality of the recovered spectrum using CS can be significantly degraded if the measurements are contaminated with noise. This will be particularly problematic in case of detecting weak signals. In this paper, a method which exploits the diversity of CS measurements is introduced to reduce the noise of CS recovered spectrum. Diversity gain is extracted from measurements using only a single physical sensor, but with virtual parallel branches. The results show that the noise is reduced sufficiently to detect weak signals using our method.

Abstract: Automatic administration of medicinal drugs has the potential of delivering benefits over manual practices in terms of reduced costs and improved patient outcomes. Safe and successful substitution of a human operator with a computer algorithm relies, however, on the robustness of the control methodology, the design of which depends, in turn, on available knowledge about the underlying dose-response model. Real-time estimation of a patient's actual response would ensure that the most suitable control algorithm is adopted, but the potentially time-varying nature of model parameters and the limited number of observation signals may cause the estimation problem to be ill-posed, posing a challenge to adaptive control methods. We propose the use of Bayesian inference through a particle filtering approach as a way to overcome these limitations and improve the robustness of automatic drug administration methods. We report on the results of a simulation study modeling the infusion of vasodepressor drug sodium nitroprusside for the control of mean arterial pressure in acute hypertensive patients. The proposed control architecture was able to meet the required performance objectives under challenging operating conditions.

Abstract: In cooperative networks, multiple carrier frequency offsets (MCFOs) and multiple timing offsets (MTOs) originate due to multiple distributed nodes. In this paper, algorithms for joint estimation of these parameters and channels in amplify-and-forward (AF) relaying networks are proposed. A new training model and transceiver structure at the relays for achieving synchronization throughout the network is devised. New exact closed-form expressions for the Cramer-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. An estimation method is proposed for jointly estimating MCFOs, MTOs, and channel gains at the destination based on space-alternating generalized expectation maximization (SAGE) and compared to a computationally-intensive least squares (LS) approach. The proposed estimator's performance is shown to be close to the CRLB at mid-to-high signal-to-noise ratio (SNR) resulting in significant cooperative performance gains in the presence of practical impairments.

Abstract: Cooperative jamming as a physical layer security enhancement has recently drawn considerable attention. While most existing works focus on communication systems with a small number of nodes, we investigate the use of cooperative jamming for providing secrecy in large-scale decentralized networks consisting of randomly distributed legitimate users and eavesdroppers. A modified slotted ALOHA protocol, named CJ-ALOHA, is considered where each legitimate transmitter either sends its message signal or acts as a helping jammer according to a message transmission probability p. We derive the secrecy transmission capacity to characterize the network throughput and show how the throughput is affected by the CJ-ALOHA protocol. Both analytical and numerical insights are provided on the design of the CJ-ALOHA protocol for optimal throughput performance.

Abstract: The uncertainty principle is an important and powerful tool, with many applications in signal processing. This paper presents two concentration uncertainty principles for signals on the sphere which relate the localization of the concentration of a signal in spa- tial and spectral domains, as an analogue of the general Donoho and Stark uncertainty principles in time-frequency analysis. Using the spherical and spectral truncation operators, we derive the L1- norm and L2-norm uncertainty principles which respectively relate the signal concentration in spatial and spectral domains as absolute value and the energy of a signal. We also analyze the sharpness of the bound imposed by the derived L2-norm uncertainty principle. The proposed uncertainty measures can be applied to signal process- ing problems on the sphere.

Abstract: The ambiguity function and the Wigner distribution are fundamental tools in the time-frequency analysis. In this paper, we present an analog of the ambiguity function and the Wigner distribution for signals on the sphere. First, we formulate the ambiguity function for signals on the sphere which represents the signals in joint spatio- spectral domain and derive an inversion operation to obtain the signal from its ambiguity function. Next, we formulate the Wigner distribution for azimuthally symmetric signals on the sphere as a two dimensional spherical harmonics transform of the ambiguity function. We provide the matrix formulation of the Wigner distribu- tion and discuss some of its useful properties. Finally, we illustrate the use of Wigner distribution for spatial and/or spectral localization of a signal in joint spatio-spectral domain. The obtained results provide the first step in designing more sophisticated transforms on the sphere.

Abstract: In this paper, we consider the problem of signal extrapolation for discrete (i.e., sampled) signals on the sphere. We propose conjugate gradient based algorithm for estimating a signal on the sphere from limited or incomplete measurements in a spatial domain. We prove that the proposed algorithm is guaranteed to converge and show that it has faster convergence compared to the Papoulis algorithm. The results also show that the incomplete measurements distributed in different non-connected spatial regions yield better extrapolation results, compared to the connected region case.

Abstract: The problem of automatic administration of vasoactive drugs to regulate mean arterial pressure in surgical and postsurgical patients can be considered as a setpoint tracking problem involving a system which is characterised by significant modelling uncertainty in the form of uncertain parameters, unmodelled dynamics and disturbances. Yet, specific levels of performance are required and patient safety must be guaranteed. As part of the development process of a novel Multiple-Model Adaptive Control (MMAC) architecture for this application, we have adopted a mixed-mu synthesis approach to controller design. Simulation results show that the new controllers are capable of improved disturbance rejection and robustness even in the face of large system delays and parametric uncertainty.

Abstract: Automatic closed-loop administration of sodium nitroprusside for the regulation of blood pressure in patients experiencing acute hypertension has been the subject of intense research over the last three decades. Yet, to date, manual administration of vasoactive drugs by a human operator remains the standard of care in the clinical setting. This manuscript describes a novel control approach for this application based on Robust Multiple-Model Adaptive Control (RMMAC). The RMMAC architecture features robust controllers designed with mu-synthesis and Kalman filtering for system estimation. The new system was coupled with a mathematical model of a patient's response to drug infusion and tested in computational simulations. The results indicate that the RMMAC approach has the potential to deliver robust performance even in challenging operating conditions, with mean arterial pressure remaining within the specified target range over 99% of the time.

Abstract: This paper introduces a quadratic variational framework for solving a broad class of signal design problems on the 2-sphere. The functional, to be extremized, combines energy concentration measures using a weighting function in the spatial domain, multiplicative weights in the spectral domain, and a total energy constraint. This leads to two formulations of the signal design problem on the 2- sphere, one a Fredholm integral equation in the spatial domain and the other an infinite matrix equation in the spectral domain. The framework is illustrated by deriving the key equations for the two classical spatio-spectral concentration problems on the 2-sphere, and for an isotropic filter design that maximizes the filtered energy. In addition, using the proposed framework, we formulate a joint 3- D beamforming application which achieves optimal directivity and spatial resolution simultaneously.

Abstract: We consider the problem of azimuthally symmetric convolution of signals defined on the 2-Sphere. Applications of such convolution include but are not limited to: geodesy, astronomical data (such as the famous Wilkinson Microwave Anisotropy Probe data), and 3D beamforming/sensing. We review various definitions of convolution from the literature and show a nontrivial equivalence between different definitions. Some convolution formulations based on SO(3) are shown not to be well formed for applications and we demonstrate a simpler framework to understand, use and generalize azimuthally symmetric convolution.

Abstract: This study addresses the problem of joint blind timing and carrier synchronisation in a (distributed-M)xN antenna system where the objective is to estimate the M carrier offsets, the M timing offsets and to recover the transmitted symbols for each of the M users given only the measured signal at the N antennas of the receiver. The authors propose a modular receiver structure that exploits blind source separation to reduce the problem into more tractable sub-problems of estimating individual timing and carrier offsets for multiple users. This leads to a robust solution of low complexity. The authors investigate the performance of the estimators analytically using modified Cramer-Rao bounds and computer simulations. The results show that the proposed receiver exhibits robust performance over a wide range of parameter values, even with worst-case Doppler of 200-300-Hz and frame size as small as 400 symbols. This work is relevant to future wireless networks and is a complete solution to the problem of estimating multiple timing and carrier offsets in distributed multiple input multiple output (MIMO) communication systems.

Abstract: The problems of filtering, spectral analysis and spectral estimation have been investigated on the sphere using azimuthally symmetric functions as kernels which treat all the directions uniformly. In this work, we extend the concentration problem on the sphere for an azimuthally non-symmetric spatial region on the sphere. Our approach is different in a sense that we obtain the family of spatially concentrated bandlimited mutually orthogonal functions by maximizing the contribution of spherical harmonics components of all degrees and orders within the spectral bandwidth. We also provide analysis of the eigenfunctions for different bandwidths and non-symmetric regions and illustrate the concentration of eigenfunctions with the help of examples. Also we formulate the definition of filtering using azimuthally non-symmetric functions. The proposed eigenfunctions can be used to revisit the problems of estimation, localized spectral analysis, smoothing and filter design on the sphere.

Abstract: Spherical harmonics serve as basis functions on the unit sphere and spherical harmonic transform is required in analysis and processing of signals in the spectral domain. We investigate the possibility of parallel computation of spherical harmonic transform using Compute Unified Device Architecture (CUDA) with no communication between parallel kernels. We identify the parallel components in the widely used spherical harmonic transform method proposed by Driscoll and Healy. We provide the implementation details and compare the computational complexity with the sequential algorithm. For a given bandlimited signal with maximum spherical harmonics degree L, using the O(L) number of parallel processing kernels, we present that the spherical harmonic coefficients can be calculated in O(L log^2 L) time as compared to O(L^2 log^2 L). For corroboration, we provide the simulation results using CUDA which indicate the reduction in computational complexity.

Abstract: In cooperative communications, estimation and compensation of multiple carrier frequency offsets is an important implementation issue that needs to be addressed in practice. This paper proposes an efficient maximum likelihood estimator (MLE) using alternating projection technique, for the joint estimation of Rayleigh fading channels and multiple carrier frequency offsets (MCFO) in cooperative communication systems. Our proposed equalizer incorporates these channel and MCFO estimates and uses matrix inverse technique to decode the transmitted symbols. Unlike existing schemes for equalizer design, the proposed design does not assume any perfect MCFO and/or channel estimate knowledge at the receiver or code redundancy or delay diversity and works for the full range ($\pm$0.5 cycles/sec) of the normalized frequency offsets. We present simulation results to illustrate that the Mean Square Error (MSE) of MCFO achieves the Cramér Rao Bound (CRB) above 7 dB signal-to-noise ratio (SNR) while the MSE of channel estimation achieves the CRB for all SNR values. In addition, the Bit Error Rate (BER) performance shows that our proposed equalizer can achieve the full spatial diversity gain of space-time block codes.

Abstract: This paper derives closed form expressions for second order statistics of mobile-to-mobile wireless channels in non isotropic environments. Specifically, we consider Rice, Rayleigh and Nakagami fading channels in four different non isotropic scattering environments with Angle of Departure (AOD) and Angle of Arrival (AoA) distributions given by (i) separable Truncated Gaussian, (ii) separable von-Mises, (iii) Truncated Gaussian bivariate and (iv) Truncated Laplacian bivariate distributions. We have shown that the second order statistics, namely, the Level Crossing Rate (LCR) and the Average Fade Duration (AFD) in different fading channels can be expressed in terms of known scattering coefficients of the above angle of departure and arrival distributions. We have illustrated the usefulness of the results by plotting LCR and AFD against the channel correlation for various scattering scenarios.

Abstract: Automatic administration of drugs to control cardiovascular function during and after surgery has received considerable attention. Although the potential benefits associated with such a technology remain unquestioned, the several adaptive control strategies proposed thus far have had very limited success in practice. In developing robust adaptive control methodologies for drug dosing in cardiovascular applications, we have analysed a well-known multiple-model adaptive control strategy for blood pressure control. The results reveal that no guarantee of protection against actually inserting a destabilising controller into the closed-loop is given and one cannot even put a global upper bound on the time during which the destabilising controller is attached. We advocate caution towards issues which in the past may have been either disregarded or not subjected to a systematic analysis as instability could be fatal in the context of a clinical application.

Abstract: In this paper, we address the problem of sparse signal reconstruction using compressive sampling (CS) in the presence of unknown multiplicative perturbations. Such pertur- bations cause mismatch between the true signal basis and that in the measurements. We propose an algorithm which iteratively determines active bases, estimates the mismatch in the identi- fied active bases, and adjusts the CS reconstruction equation according to compensated bases. We apply our technique to sparse signal acquisition and CS reconstruction in wireless fading channels with high Doppler frequencies, which are the source of multiplicative perturbations, and verify the effectiveness of our algorithm in suppressing reconstruction noise and accurate signal recovery.

Abstract: Synchronization in Decode and Forward (DF) cooperative communication systems is a complex and challenging task requiring estimation of many independent timing and carrier offsets at each relay in the broadcasting phase and multiple timing and carrier offsets at the destination in the relaying phase. This paper presents a scheme for blind channel, timing and carrier offset estimation in a DF cooperative system with one source, M relays and one destination equipped with N antennas. In particular, we exploit blind source separation at the destination to convert the difficult problem of jointly estimating multiple synchronization parameters in the relaying phase into more tractable sub-problems of estimating many individual timing and carrier offsets for the independent relays. We also modify and propose a criteria for best relay selection at the destination. Simulation results demonstrate the excellent end-to-end Bit Error Rate (BER) performance of the proposed blind scheme with relay selection, which is shown to achieve the maximum diversity order with M = 4 relays using N = 5 antennas at the destination. The presented work is a complete solution to blind synchronization and channel estimation in DF cooperative communication systems.

Abstract: This paper considers the problem of construction of low-pass filters on the unit sphere, which has wide ranging applications in the processing of signals on the unit sphere. We propose a design criterion for the construction of strictly bandlimited low-pass filters in the spectral domain with optimal concentration in the specified polar cap region in the spatial domain. Our approach uses the weighted sum of the first optimally concentrated eigenfunctions from appropriately formulated Slepian concentration problems on the sphere. Furthermore, in order to reduce the computational complexity of the proposed algorithm, we develop a closed-form expression to accurately model these eigenfunctions. We illustrate the construction of low-pass filters using the proposed approach and demonstrate the advantage of our method approach compared to a diffusion based approach in the literature in terms of control over both bandwidth in the spectral domain and concentration in the spatial domain.

Abstract: This paper proposes a new blind algorithm, based on Mixture Kalman Filtering (MKF), for joint carrier recovery and channel estimation in time-selective Rayleigh fading channels. MKF is a powerful tool for estimating unknown parameters in non-linear, non-Gaussian, real-time applications. We use a combination of Kalman filtering and Sequential Monte Carlo Sampling to estimate the channel fading coefficients and joint posterior probability density of the unknown carrier offset and transmitted data respectively. We study the effect of Signal to Noise Ratio (SNR) and doppler shift on Mean Square Error (MSE) and Bit Error Rate (BER) performance of the proposed algorithm through computer simulations. The results show that BER of the proposed algorithm achieves the theoretical performance slope for the full acquisition range of normalized carrier frequency offsets.

Abstract: This paper consider the problem of how to evaluate the efficiency of a 3D continuous functional HRTF model. The proposed method is based on Karhunen-Loeve theorem. After investigating the optimization problem of representing the process with an finite linear combination of orthogonal functions in L2 space by means of the least squared method, the variance of random variables involved in the model is found the key metric in efficiency evaluation of functional model. Then, the coefficients of the 3D continuous HRTF model are analyzed. The results show that the efficiency of the model in spatial component expansion is around 70\% and the best choice in frequency component expansion is the spherical Bessel function.

Abstract: We design a zero-forcing filter and a minimum mean square error (MMSE) filter on the 2-sphere by a spherical harmonic multiplication operator. Compared with the traditional optimal filters, our filters, determined by the signal and noise statistics, have such advantages: 1) can be asymmetric, and 2) simple calculation of our filters is involved.

Abstract: We propose a novel algorithm for temporal tracking of the fibrillatory frequency for Atrial Fibrillation (AF) ECG. Both Atrial activity extraction and fibrillatory frequency tracking are combined into a single algorithm and analytical expressions are derived for final time-frequency distributions, thus the proposed method is computationally efficient. It can also serve the general purpose of time-frequency analysis of a non-stationary signal with missing or corrupted data segments. The method uses short-time expansion of an orthogonal basis set, and regularized least squares solution used to compute a stable coefficients for the basis. A simplified and computationally efficient time-frequency distribution is derived based only on the coefficient vector. The algorithm is successfully applied to simulated as well as real ECG with AF, and its advantages over conventional average beat subtraction method are discussed.

Abstract: This paper identifies the main anthropometric parameters which strongly influence the head-related transfer functions (HRTFs) in a direct physical way using statistical analysis on HRTF measured data. Principle component analysis is separately performed on the head-related impulse responses of all subjects at each direction for each ear to extract the individual information. Then the individual information, along with all anthropometric parameters, is introduced in the multiple linear regression analysis, where F statistic and t statistic are used to characterize the key parameters having strong direct physical effect on the HRTFs. Ultimately, combining with the results of the analysis of the inter-parameter correlations, only eight anthropometric parameters out of 27 are identified as the crucial elements in the role of spatial localization, which provides a guide for efficient HRTF individualization using key anthropometric parameters.

Abstract: This paper studies signal concentration in the time and frequency domains using the general constrained variational method of Franks. The minimum k th (k = 0, 2, 4,...) moment time-duration measure for band-limited signals is formulated. A complete, orthonormal set of band-limited functions in L2([-W,W]) with the minimum fourth-moment time-duration measure is obtained. Numerical investigations of our optimal 4th moment functions show: 1) less energy concentration in the main lobe than the prolate spheroidal wave functions (PSWF); 2) higher energy concentration in the main lobe than Gabor's function; and 3) a larger main lobe than both PSWF and Gabor. Applications for our basis functions include: 1) radar systems and high resolution communication systems, and 2) representation and approximation to any band-limited signal in a given time interval.

Abstract: In this letter, a closed form expression for the conditional bit error probability (BEP) with static timing errors of binary phase shift keying (BPSK) modulation over a Rayleigh fading channel is presented. The expressions for average BEP are then given for dynamic timing errors assuming the normalized timing error has either a Gaussian probability density function (pdf) or a Tikhonov pdf. Numerical results to corroborate the derived analytic expressions are presented for average BEP obtained by averaging the conditional error probability over the pdf of normalized timing errors.

Abstract: Due to processing constraints, automatic image-based registration of medical images has been largely used as a pre-operative tool. We propose a novel method named sort and count for efficient parallelization of mutual information (MI) computation designed for massively multi-processing architectures. Combined with a parallel transformation implementation and an improved optimization algorithm, our method achieves real-time (less than 1 s) rigid registration of 3D medical images using a commodity graphics processing unit (GPU). This represents a more than 50-fold improvement over a standard implementation on a CPU. Real-time registration opens new possibilities for development of improved and interactive intraoperative tools that can be used for enhanced visualization and navigation during an intervention.

Abstract: A framework based on the $n$ -dimensional Fourier transform of a radially symmetric function is introduced to design kernels for Cohen time-frequency distributions. Under this framework, we derive a kernel formula which generalizes and unifies Margenau-Hill, Born-Jordan, and Bessel distributions, using a realization based on a $n$-dimensional radial delta function. The higher order radial kernels suppress more cross-term energy compared with existing lower order kernels, which is illustrated by the time-frequency analysis of atrial fibrillation from surface electro cardiogram data.

Abstract: The head-related transfer function (HRTF) varies with range as well as with azimuth and elevation of the sound source and forms the basis of human sound localization. In this study, we are discussing the sampling and synthesis of the HRTF in three-dimensional auditory scene. Given a typical size of human head/torso, there is an information theoretical limit of the HRTF, that is the dimensionality of the HRTF for a given frequency. The insights into dimensionality tell the necessary angular sampling to reconstruct the HRTF up to some frequency. We then propose a new continuous representation of the three-dimensional HRTF which can capture both the HRTF spatial and spectral variations in separate bases. The derived spatial basis modes can achieve HRTF near-field and far-field representations in one formulation. The remaining HRTF spectral components are compactly represented using the Fourier Spherical Bessel (FSB) series, where the aim is to generate the HRTF with much higher spectral resolution in few parameters from finite measurements which usually have limited spectral resolution constrained by the sampling rate and number of samples. A low computation method is developed to obtain the model coefficients with good reconstruction results. The HRTF sampling theory and synthesis using the proposed model are validated by three sets of data, (i) synthetic HRTFs from the spherical head model, (ii) MIT KEMAR data and (iii) 45-sub ject CIPIC measurements.

Abstract: FAST TCP is a new promising TCP protocol developed for high-speed long-latency networks, whose performance has only been studied in single direction connections. We propose a mathematical model for bi-directional connections using the FAST TCP protocol which captures the asymmetric bandwidth dynamics in duplex dumbbell networks, prevalent in ADSL, satellite and other high-speed technologies. Using this model, we establish the stability conditions under which the bidirectional FAST TCP flows achieve stability, and on this basis the throughputs of the forward and backward flows at steady-state are deduced. We find that, in the case of bandwidth asymmetry, the throughput of the bi-directional FAST TCP flows can only achieve the minimum capacity of the duplex links, and the link with larger capacity is not fully occupied. These theoretical findings are corroborated by NS2 simulations.

Abstract: In this article, we look at early, recent, and state-of-the-art methods for registration of medical images using a range of high-performance computing (HPC) architectures including symmetric multiprocessing (SMP), massively multiprocessing (MMP), and architectures with distributed memory (DM), and nonuniform memory access (NUMA). The article is designed to be self-sufficient. We will take the time to define and describe concepts of interest, albeit briefly, in the context of image registration and HPC. We provide an overview of the registration problem and its main components in the section "Registration." Our main focus will be HPC-related aspects, and we will highlight relevant issues as we explore the problem domain. This approach presents a fresh angle on the subject than previously investigated by the more general and classic reviews in the literature [1]-[3]. The sections "Multi-CPU Implementations" and "Accelerator Implementations" are organized from the perspective of high-performance and parallel-computing with the registration problem embodied. This is meant to equip the reader with the knowledge to map a registration problem to a given computing architecture.

Abstract: Error control techniques in wireless links such as Automatic Repeat Request (ARQ) and Forward Error Correction (FEC) are still quite effective approaches in the improving system throughput in particular in time-varying channel environments. In this paper, a dual-branch selection diversity receiver of combining Selective Repeat-ARQ scheme and BCH channel coding (hybrid ARQ) in mobile cellular networks like UMTS is proposed. The aim is to provide maximal achievable throughput when a predefined channel code is employed under various Rayleigh fading channel conditions. Both spatially uncorrelated and correlated antenna branches are investigated for identical and non-identical channels. The numerical results show that significant redundancy coding has a reasonable effect on the overall throughput performance. In contrary, the channel coding influences significantly on the lower range of operating channel SNR in the selection combining receiver when identical and non-identical correlated antenna branches are considered.

Abstract: A novel 2D Mobile-to-Mobile physical model is developed in this paper by considering the underlying physics of free space propagation. When compared to existing statistical channel models, the development and application of our new model is better in terms of complexity as it requires less parameters. In addition, the proposed new model is flexible in applying to any scattering environment whereas the design of the existing models could not easily be extended for any scattering environment.

Abstract: This paper proposes a new blind algorithm for joint carrier offset estimation and data detection, which is based on particle filtering and recursively estimates the joint posterior probability density function of the unknown transmitted data and the unknown carrier offset. We develop new guidelines for resampling of the particles to take into account carrier offset estimation ambiguity at the edges of the range, and for fine tuning estimates to achieve fast, accurate convergence. The Mean Square Error (MSE) and Bit Error Rate (BER) performance of the proposed algorithm is studied through computer simulations. The results show that the proposed algorithm achieves fast convergence for the full acquisition range for normalized carrier frequency offsets.

Abstract: Principal component analysis (PCA) is known to be a powerful linear technique for data set dimensionality reduction. This paper focuses on revealing the essence of PCA to interpret the data, which is to identify the internal structure of the random process from a large experimental data set. We give an explanation of the PCA procedure performed on a generated data set to demonstrate the exact meaning of the dimensionality reduction. Especially, a method is proposed to precisely determine the number of significant principal components for a random process. Then, the internal structure of the random process can be modeled by analyzing the relation between the PCA results and the original data set. This is vital in the efficient random process modeling, which is finally applied to an application in HRTF Modeling.

Abstract: In this paper, we analyze the applicability of Constant Modulus Algorithm (CMA), one of the most widely used and tested blind equalization technique to blind image deconvolution. With a detailed mathematical analysis, we show that the strong correlation between the neighboring spatial locations found in natural images becomes a major constraint on the convergence of CMA. In order to overcome this constraint, we introduce a novel image pixel correlation model in relation with natural image statistics. Based on this model, a segmented blind image deconvolution through CMA is proposed. The robustness of the proposed algorithm with natural images is discussed in terms of efficiency and effectiveness.

Abstract: We investigate the robustness of Compressive Sensing (CS) as a direct signal acquisition and reconstruction method at the wireless receiver in fading channels. The wireless channel introduces additive as well as multiplicative random perturbations to the received signal. The original CS theory considers only additive and bounded perturbation for signal reconstruction with an a priori known basis. However, the impact of multiplicative perturbations, which manifests itself as basis mismatch, on the CS reconstruction performance is largely unknown. In this paper we first formulate such multiplicative perturbations of wireless fading channel in the CS acquisition and reconstruction problem. We then show that these perturbations can result in significant errors in signal reconstruction if the basis is not properly adjusted. Furthermore, we will propose a method for adjusting the elements of basis to the fading channel coefficients and discuss possible improvements in the signal reconstruction.

Abstract: This paper formulates a spatially-limited signal energy concentration problem on the 2-sphere using a generalized moment criterion in the spectral domain. The set of optimal signals with maximum concentration for general positive spherical harmonic coefficient frequency weightings is obtained. Numerically solving the resulting integral equation optimization show that this set of functions not only decays slower but also has higher sidelobes than the set of spherical Slepian functions. This result on the 2-sphere contrasts with the findings from the time-frequency analogy which compares the classical Slepian eigenfunctions with the minimum bandwidth basis functions for the fourth-moment bandwidth measure.

Abstract: The development of low-complexity blind techniques for equalization and timing synchronization is of enormous importance in the design of wireless communication systems. In this paper, we propose a practical solution for blind equalization and timing recovery in fast-fading time and frequency selective wireless communication channels. We develop a general framework for Constant Modulus Algorithm (CMA) based joint Fractionally Spaced Equalization (FSE) and timing recovery. We use differential modulation to deal with any arbitrary carrier offset. We propose a data reuse strategy to achieve improved short burst wireless communication in CMA based equalization systems. Our results show that FSE outperforms T-Spaced Equalization (TSE) with approximately 2 times faster Mean Square Error (MSE) convergence and approximately 2 dB gain in Bit Error Rate (BER) performance in wireless fading channels. In addition, we demonstrate that the BER performance of the proposed FSE receiver meets the theoretical bounds with only a few dB loss in Stanford University Interim (SUI) channels, which are relevant to IEEE 802.16.3c standard for Wireless Metropolitan Area Networks.

Abstract: The theory of compressive sampling (or compressed sensing) is very attractive in that it is possible to reconstruct some signals with a sub-Nyquist sampling rate provided that they are sparse in some basis domain. But if there exists a mismatch between the signal basis and the pre-defined reconstruction basis, the reconstruction performance is significantly degraded even if the signal is sparse enough. In this paper, the degradation due to this basis mismatch is investigated and a way to minimize the effects of basis mismatch in compressive sampling of continuous sinusoidal signals is discussed.

Abstract: The performance of OFDM receivers is very sensitive to timing synchronization errors. This paper makes an analysis of different proposed timing synchronization algorithms, their training symbol patterns and their effect on the performance of OFDM systems under severe frequency selective Rayleigh fading. We show BER and MSE performance of six popular preamble based algorithms using joint synchronization and channel estimation to make an insightful and thorough comparison. We analyze the performance with both coarse and fine timing recovery and show that BER performance with fine timing is better for every algorithm. We propose a new technique for timing synchronization that uses Constant Amplitude Zero Auto Correlation (CAZAC) sequences to acquire unit Peak to Average Power Ratio (PAPR) for the preambles. We show that the proposed technique is robust under high delay spread environments with BER and MSE performance comparable to the best case.

Abstract: Signals defined on the unit sphere cannot be simultaneously concentrated in a spatial region and in the spherical harmonic spectrum. In this paper we develop a unique spatial concentration measure, a kth moment azimuthal measure, for real-valued spectral-limited signals defined on the unit sphere. The optimal functions with the 2nd and 4th minimum azimuthally moment weighting are obtained and simulation results show: 1) the waveforms tend to be even as k increases, 2) have good energy concentration in the spatial region, and 3) have better decaying tails than spherical Slepian functions, which form the benchmark set of basis functions for spherical filter design.

Abstract: This paper formulates a novel class of signals which are concentrated simultaneously in time and frequency. Two concentration measures studied are second-moment and fourth-moment bandwidth measures in frequency subject to 1 - gamma proportion of the energy inside the time interval [-T/2, T/2] for some nominal small gamma. We employ the general constrained variational method of Franks to determine the integral equations for the optimal signals. Simulation results show that the optimal functions with minimum fourth-moment weighting have more energy in the main lobe and quicker decaying tails than Gabor half sinusoids.

Abstract: A three-dimensional single-input single-output Mobile-to-Mobile wireless channel model is developed in this paper by considering the underlying physics of free space wave propagation. Based on this channel model, the temporal correlation function for a general three dimensional scattering environment is derived. The temporal correlation function is characterized by the joint angular power distribution at the transmitter and receiver antennas and the speed of transmitter and receiver antennas. Using a von Mises-Fisher distribution as the angular power distribution, the usefulness of the derived temporal correlation function is discussed.

Abstract: The development of low-complexity blind techniques for equalization, timing and carrier offset recovery is of enormous importance in the design of high data rate wireless systems. In this paper, we propose a practical solution for blind equalization, timing recovery and small carrier offset correction in slowly-fading frequency selective wireless communication channels. We extend the Modi ed Constant Modulus Algorithm (MCMA) to handle the timing offset parameter. We propose a single objective function to achieve equalization, timing and carrier recovery without the need of any training sequences. Our algorithm achieves 5-10 times faster convergence, compared to previous research, for the Mean Square Error (MSE) at the equalizer output due to the nely tuned step sizes and updating the equalizer taps and timing offset jointly to minimize the mean dispersion and inter symbol interference. Our results show that the proposed technique can successfully handle synchronization and combat the frequency selectivity of the wireless channel.

Abstract: This paper introduces a continuous functional model for head-related transfer functions (HRTFs) in the horizontal auditory scene. The approach uses a separable representation consisting of a Fourier-Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial components. Being independent of the data, these two sets of basis functions remain unchanged for all subjects and measurement setups. Hence, the model can transform an individualized HRTF to a subject specific set of coefficients. A continuous functional model is also developed in the time domain. We show the efficient model performance in approximating experimental measurements by using the HRTF measurements from a KEMAR manikin and the synthetic data from the spherical head model. The statistical results are determined from a 50-subject HRTF data set. We also corroborate the predictive capability of the proposed model. The model has near optimal performance, which can be ascertained by comparison with the standard principle component analysis (PCA) and discrete Karhunen-Loeve expansion (KLE) methods at the measurement points and for a given number of parameters.

Abstract: We consider the optimum design of pilot-symbol-assisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized feedback-less PSAM, our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in medium-rate fading channels. In faster fading channels, suboptimal feedbackless equal power allocation to data and pilot is close to optimal at high SNR regime or when there is a delay in the feedback link.

Abstract: A novel sinhc kernel, which generates a Kaiser window based time-frequency distribution for non-stationary signal analysis is introduced. The Kaiser distribution belongs to the Cohen class of time-frequency distributions, and satisfies desirable distribution properties. By controlling the shape of the Kaiser window, auto-term resolutions and cross-term magnitudes can be successfully traded.

Abstract: In this article, we present a simple cross-layer model that leads to the optimal throughput of multiple users for multicasting MPEG-4 video over a heterogeneous network. For heterogeneous wired-to-wireless network, at the last wireless hop there are bit errors associated with the link-layer packets that are arising in the wireless channel, in addition of overflow packet dropping over wired links. We employ a heuristic TCP function to optimize the cross-layer model of data link and physical (radio-link) layer. An adaptive Forward-Error-Correction (FEC) scheme is applied at the byte-level as well as at the packet-level. The corresponding optimal video quality can be evaluated at each client end. The results show that a server can significantly adapt to the bandwidth and FEC codes to maximize the video quality of service (QoS) in terms of temporal scaling when a maximum network throughput for each client is reached.

Abstract: This paper presents a generalized expression for space-time cross correlation between signals at receiver antennas on a moving mobile in 3D space. This expression, which is a function of scattering environment coefficients, antenna locations and velocity of the mobile unit, will be useful for designers of communication systems in understanding space time correlation under various channel environments. A series of simulations are carried out in order to analyze the novel expression derived in the paper.

Abstract: Presenting sounds to humans in virtual environments requires convolving the free field signals with a head related transfer function (HRTF), which is a frequency response describing the filtering effects of the pinna, head and torso of a human. Sets of HRTFs are usually measured on the dummy head or human subjects at different directions in an anechoic room. This paper describes the details of an experimental HRTF measurement procedure with emphasis on the design of the test signal and the post-processing to extract HRTFs. We construct a pre-emphasized logarithmic sweep as the excitation signal which separates the nonlinear and time variant distortions from the main desired response. For the received raw data, a series of signal processing techniques are applied to determine the timing offset when the head response begins, to mitigate room reverberation, and to equalize the HRTF measurements. One of the goals of this paper is to provide details of the experimental setup. Also, we intend to publish our processed measurements in the form of a HRTF data base as a resource for the acoustic community.

Abstract: Automatic repeat request (ARQ) schemes are quite effective for improving the throughput of system diversity in time-varying channel environments. In this paper, a dual-branch selection diversity receiver based selective repeat-ARQ scheme is investigated to evaluate the optimal throughput performance in terms of the average bit error rate in Rayleigh fading channels. Both uncorrelated and correlated antenna branches are considered. The numerical results shows the effect of optimal switching threshold on the throughput performance in case of switched diversity as well as the mobility effect of the selection combining diversity receiver when correlated antenna branches are present. A significant improvement in the system throughput of selection diversity outperforms that of switched diversity.

Abstract: Conventional transmission schemes perform poorly in wireless channels. In this paper, an analytical adaptive model for wireless links via heuristic TCP/FEC functions is proposed with chosen modulation format for transporting mobile MPEG-4 video. A wireless channel introduces that the bit errors at the link-layer packets are due to time-invariant features over UMTS network and consequently the optimal perceived video quality at the client can be improved when adaptive TCP throughput after error-corrections is achieved for the certain predefined system threshold of the residual packet error rate. The simulation results show that a video quality can dynamically adapt to the optimal FEC codes at an appropriate selection for modulation scaling in the radio-link layer.

Abstract: This paper studies signal concentration in time-frequency using the general constrained variational method of Franks. We apply this method to formulate the minimum fourth-moment time-duration measure in the time interval $[-T/2,T/2]$ for band-limited signals. An orthonormal basis of band-limited functions with the minimum fourth-moment time-duration measure is obtained. Comparing our optimal band-limited signals with Gabor's function with the minimum second-moment time-duration measure, simulation results show that our function has better properties: 1) faster decaying rate; 2) larger main lobe; and 3) higher energy concentration measure.

Abstract: In this paper we develop a new fast non-blind image restoration algorithm with the goals of simplicity, high performance and computational efficiency. The speed advantage over previous algorithms, which is up to two orders of magnitude over existing schemes, is achieved by a novel choice of ground truth prior which enables the use of frequency domain methods for constrained deconvolution. In addition, we study recent likelihood models used in image restoration to guide the most effective likelihood model for image restoration. We show that the use of image derivatives in the likelihood function formulation proposed by some researchers does not lead to significant performance improvements over the standard likelihood function.

Abstract: We propose a novel algorithm for extracting atrial activity from single lead electrocardiogram (ECG) signal sustained with atrial fibrillation (AF), based on a short-time expansion of an orthogonal basis function set. The method preserves the time variation of spectral content of the underlying AF signal, thus time-frequency analysis of the AF signal can be successfully performed. The new method is compared to the standard average beat subtraction (ABS) method using synthetic AF sustained ECG data. The orthogonal basis expansion method has a higher correlation with the original AF signal compared to the ABS method for a range of signal to noise ratio (SNR) levels, and correlation is improved by 16% at an SNR of 0dB. Time-frequency analysis of the reconstructed AF signal based on Bessel distribution also shows the superiority of the orthogonal basis expansion method over ABS.

Abstract: This paper proposes a continuous HRTF representation in both 3D spatial and frequency domains. The method is based on the acoustic reciprocity principle and a modal expansion of the wave equation solution to represent the HRTF variations with different variables in separate basis functions. The derived spatial basis modes can achieve HRTF near-field and far-field representation in one formulation. The HRTF frequency components are expanded using Fourier Spherical Bessel series for compact representation. The proposed model can be used to reconstruct HRTFs at any arbitrary position in space and at any frequency point from a finite number of measurements. Analytical simulated and measured HRTFs from a KEMAR are used to validate the model.

Abstract: A communication system model for mutual information performance analysis of multiple-symbol differential M-phase shift keying over time-correlated, time-varying flat-fading communication channels is developed. This model is a finite-state Markov (FSM) equivalent channel representing the cascade of the differential encoder, FSM channel model and differential decoder. A state-space approach is used to model channel phase time correlations. The equivalent model falls in a class that facilitates the use of the forward-backward algorithm, enabling the important information theoretic results to be evaluated. Using such a model, one is able to calculate mutual information for differential detection over time-varying fading channels with an essentially finite time set of correlations, including the Clarke fading channel. Using the equivalent channel, it is proved and corroborated by simulations that multiple-symbol differential detection preserves the channel information capacity when the observation interval approaches infinity.

Abstract: Wireless communication systems that operate through fading channels have become more diverse and complex. In the last ten years, there has been a growing interest for research and development of advanced wireless communications systems that employ multicarrier (MC) techniques. So far, applications of FSMC models for fading channels has been mainly limited to single carrier (SC) communications with very few exceptions [24], [47]. FSMC models are particulary suitable to represent and estimate the relatively fast flat-fading channel gain in each subcarrier. An unexplored avenue for research is to find appropriate FSMC models to represent MC fading channels. However, the number of TV-FFC gains to be modeled in the MC system is often much higher than in a SC system and a major challenge would be to keep the number of FSMC states to computationally manageable levels.

Abstract: A method for selecting the order in which the users are detected in communication systems employing adaptive successive decision feedback multiuser detection is proposed. Systems employing channel coding without the assumption of perfect decision feedback are analyzed. The method is based on the Mean Squared Error (MSE) measurements during a training period for each user. The analysis shows that the method delivers BER performance improvement relative to other previously proposed ordering methods.

Abstract: We investigate reduced-rank shift-invariant technique and its application for synchronization and channel identification in UWB systems. Shift-invariant techniques, such as ESPRIT and the matrix pencil method, have high resolution ability, but the associated high complexity makes them less attractive in real-time implementations. Aiming at reducing the complexity, we developed novel reduced-rank identification of principal components (RIPC) algorithms. These RIPC algorithms can automatically track the principal components and reduce the computational complexity significantly by transforming the generalized eigen-problem in an original high-dimensional space to a lower-dimensional space depending on the number of desired principal signals. We then investigate the application of the proposed RIPC algorithms for joint synchronization and channel estimation in UWB systems, where general correlator-based algorithms confront many limitations. Technical details, including sampling and the capture of synchronization delay, are provided. Experimental results show that the performance of the RIPC algorithms is only slightly inferior to the general full-rank algorithms.

Abstract: A critical assumption in applying Godard CMA algorithm for blind deconvolution and equalization is the assumption of an independently distributed source. Almost all the applications in the literature have based their implementations on this assumption. To our knowledge, no research has been done on the effect of source correlation on adaptive blind deblurring of images through CMA, and this paper addresses that gap, coming up with a novel model of addressing the source correlation problem in the image deblurring through CMA.

Abstract: We consider the fundamental ability of multisensor receiver of finite spatial extent to localize a wireless transmitter in space. Spatial localization is identified with a multisensor receiver's ability to distinguish source transmitters from different regions in space based on imperfect measurements within the finite spatial extent spanned by the receiver's sensors. Two transmitters positioned within a determined spatial region cannot be distinguished or resolved according to a given measurement threshold. The space outside that occupied by the receiver is shown to be tiled by a finite number of such regions. Further, the regions depend on whether intensity information only is used or whether there is both magnitude and phase information available. Numerical examples are given based on a novel tiling algorithm.

Abstract: The classical problem of extrapolation of a bandlimited signal from limited time domain data is revisited for signals defined on the sphere. That is, given limited or incomplete measurements of an isotropic low pass signal on the unit sphere, find the unique extrapolation to the complete unit sphere. Signals defined on the unit sphere arise in a number of applications, such as beampatterns in azimuth and elevation and head related transfer functions. Our investigations explore the role of integral equation operators in characterizing the extrapolation problem which leads to an iterative algorithm analogous to that obtained in the time-frequency case.

Abstract: In this paper, we further illustrate the versatility and effectiveness of our novel tests for ensuring safe adaptive control in practice. The tests utilize a limited amount of experimental and possibly noisy data obtained from a closed-loop --- consisting of an existing known stabilizing controller connected to an unknown plant --- to infer if the introduction of a prospective controller will stabilize the unknown plant. The need and importance of this arise in iterative identification and control algorithms, multiple-model adaptive control (MMAC), and multi-controller adaptive switching.

Abstract: This paper develops a novel, efficient, 2D, blind deconvolution algorithm for restoring images corrupted by an unknown 2D blurring kernel satisfying a separable property. The algorithm builds on know results for 2D deconvolution using the Constant Modulus Algorithm (CMA) which is an archtype blind algorithm used in 1D blind deconvolution of communication systems. By exploiting the separable property of kernels there is a substantial speedup relative to an unstructured 2D blurring kernel. That is, for a 2N+1 x 2N+1 kernel the complexity is improved by a factor of O(N), the reduction in parameters greatly improves speed of convergence, robustness and accuracy of the deconvolution. The algorithm and a class of generalizations are derived, and the performance improvement claims are corroborated through a set of simulations.

Abstract: We propose a Bessel kernel based time frequency distribution technique for identification and tracking of spectrum of Atrial Fibrillation (AF) in ECG. The algorithm shows a good frequency resolution and a low RMS error even when the noise dominates the signal which is critical for detecting the low amplitude AF activity within the ECG. In comparison with other time frequency distributions, the Bessel kernel reduces cross terms between frequencies in the multi-component ECG signal. Superiority of the Bessel kernel method over the short time Fourier transform (STFT) is demonstrated using a frequency modulated sinusoidal model and using real AF data. At low signal to noise levels the Bessel distribution outperforms the STFT and at an SNR of -5dB the RMS error is reduced from 1.8Hz to 0.8Hz. Also it achieves a frequency resolution of 0.5Hz at an SNR of 0dB which is four times better than that of the STFT.

Abstract: In this paper, we first propose an alternative decision feedback equalizer (DFE) scheme to the DFE scheme of Labat, Macchi and Laot. Both schemes are broken into two distinct operation modes which feature a linear equalizer during acquisition and a DFE after the initial convergence has been achieved. While avoiding some potential problems with the latter DFE, our scheme achieves similar overall performance in terms of convergence speed and steady state error. A second contribution is the development of a strategy that simultaneously adapts the linear equalizer and the DFE in a parallel fashion such that the switch-over between modes is no longer necessary. Consequently, smoother and usually faster convergence is achieved as switching disruptions are reduced. This scheme is especially advantageous under noisy and severe conditions as supported by our simulations.

Abstract: Given limited or incomplete measurement data on a sphere, a new iterative algorithm is proposed on how to extrapolate signal over the whole sphere. The algorithm is based on a priori assumption that the Fourier decomposition of the signal on the sphere has finite degree of spherical harmonic coefficients, that is, the signal is modelimited. The algorithm is a simple iteration involving only the spherical harmonic decomposition. It is proven that the algorithm converges to the original signal over observation region and the convergence rate is lower bounded by the largest eigenvalue of an associated Fredholm integral equation.

Abstract: An iterative algorithm is proposed to estimate a signal on the sphere from limited or incomplete measurements. The algorithm is based on a priori assumption that the Fourier decomposition of the signal on the sphere has finite degree of spherical harmonic coefficients, that is, the signal is mode-limited or low-pass in character. The iteration algorithm is to reduce the mean square error between the spherical harmonic coefficients of the estimated and that of the original signal. Convergence and its numerical properties are determined using spherical harmonic analysis. A practical example of antenna radiation pattern reconstruction is given with detailed analysis.

Abstract: In realistic channel environments the performance of space-time coded multiple-input multiple output (MIMO) systems is significantly reduced due to non-ideal antenna placement and non-isotropic scattering. In this paper, by exploiting the spatial dimension of a MIMO channel we introduce the novel idea of linear spatial precoding (or power-loading) based on fixed and known parameters of MIMO channels to ameliorate the effects of non-ideal antenna placement on the performance of coherent (channel is known at the receiver) and non-coherent (channel is un-known at the receiver) space-time codes. Antenna spacing and antenna placement (geometry) are considered as fixed parameters of MIMO channels, which are readily known at the transmitter. With this design, the precoder is fixed for fixed antenna placement and the transmitter does not require any feedback of channel state information (partial or full) from the receiver. We also derive precoding schemes to exploit non-isotropic scattering distribution parameters of the scattering channel to improve the performance of space-time codes applied on MIMO systems. However, these schemes require the receiver to estimate the non-isotropic parameters and feed them back to the transmitter. Closed form solutions for precoding schemes are presented for systems with up to three receive antennas. A generalized method is proposed for more than three receive antennas.

Abstract: This paper provides mutual information performance analysis of the differential MPSK ($M$-phase shift keying) over time-varying correlated flat-fading communication channels. It is shown that if time-varying channel phase is modeled as an autoregressive (AR) Markov process, then the differential detection is determined only by the channel phase process innovation, which is essentially memoryless. It enables the adoption of familiar ML coding tools for memoryless channels for capacity achieving mutual information performance. It is proven that differential detection scheme theoretically preserves the channel information capacity when observation interval approaches infinity. The simulation analysis corroborates theoretical results, showing that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals.

Abstract: We study the dimensions or degrees of freedom of farfield multipath that is observed in a limited, source-free region of space. The multipath fields are studied as solutions to the wave equation in an infinite-dimensional vector space. We prove two universal upper bounds on the truncation error of fixed and random multipath fields. A direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension. This finite dimension is linearly proportional to the radius of the two-dimensional spatial region where the field is coupled to. We use the Karhunen-Loeve (KL) expansion of random multipath fields to quantify the notion of multipath richness. The multipath richness is defined as the number of significant eigenvalues in the KL expansion that achieves 99\% of the total multipath energy. We prove a lower bound on the largest multipath eigenvalue and use this bound to show that reducing the angular range of multipath power spectrum reduces multipath richness. We also provide a systematic numerical algorithm to find multipath eigenvalues, which unlike the Fredholm equation, does not require selecting quadrature points.

Abstract: In this paper we analyze the impact of mutual coupling on MIMO channel capacity, considering its effect on both signal and thermal noise. We calculate noise correlation matrix in the multi-antenna system with closely spaced antenna by applying Nyquist's thermal noise theorem. Then, we employ the noise correlation matrix in the channel capacity formula, which enables the identification of thermal noise correlation contribution on the MIMO channel capacity. In addition, we examine the variations in the mean branch signal-to-noise ratios (SNR) due to the noise correlation. Our simulation results corroborate the theoretical analysis that mean and outage MIMO channel capacity is underestimated if noise correlation due to mutual coupling effect is not accounted for.

Abstract: We propose a new broadband beamformer design technique which produces an optimal receiver beam pattern for any set of field measurements in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can be applied to both sparse and dense arrays, nonuniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beam pattern type, including frequency-invariant and spot pattern designs. A simple extension to the technique is presented for oversampled arrays, which allows high-resolution beamforming whilst carefully controlling input energy and error sensitivity.

Abstract: We present two efficient histogram algorithms designed for NVIDIA's compute unified device architecture (CUDA) compatible graphics processor units (GPUs). Our algorithm can be used for parallel computation of histograms on large data-sets and for thousands of bins. Traditionally histogram computation has been difficult and inefficient on the GPU. This often means that GPU-based implementation of the algorithms that require histogram calculation as part of their computation, require to transfer data between the GPU and the host memory, which can be a significant bottleneck. Our algorithms remove the need for such costly data transfers by allowing efficient histogram calculation on the GPU. We show that the speed of histogram calculations can be improved by up to 30 times.

Abstract: We consider the optimal design of pilot-symbol-ulation (PSAM) in time-varying flat-fading channels (FFC). The FFC is modeled as an autoregressive Gauss-Markov random process, whose realization is unknown at the transmitter or at the receiver. Our measure of optimality for channel estimation is the rate of information transfer through the channel. The parameters that are available for this optimization are the power ratio and the fraction of time that are allocated to pilot transmission. Our approach is different from (and builds upon) a recent study of PSAM for the Gauss-Markov FFC, where the aim was to minimize the maximum steady-state minimum mean square error (MMSE) of channel estimation for equal power allocated to pilot and data symbols and for a fixed pilot insertion ratio. To this end, we examine a lower bound on the capacity and find the optimal pilot transmission parameters that maximize this bound. Our analysis shows that this capacity lower bound is more sensitive to the pilot power allocation ratio in relatively slow fading channels (with the normalized fading rate fD Ts 0.01). We observe that for such slow fading rates, optimal power allocation and optimal pilot spacing are more sensitive to the operating SNR. Another finding is that equal power allocation strategy is suboptimal by at most 1 dB for the slow fading rate of fD Ts = 0.01.

Abstract: We present an efficient and accurate method for similarity (rigid+scale) registration of 3D images by decoupled estimation of transformation parameters. The estimated parameters are used to initialize the search for a more accurate alignment by optimizing a mutual information-based cost function. We use computationally inexpensive methods based on image gradients to obtain the original estimates. Our method improves the efficiency of the overall registration task by allowing the more expensive optimization step to converge quickly. It also makes the registration more robust and less sensitive to the shape of the cost function by reducing the chance of the optimization algorithm being caught by a local minimum. Our experiments demonstrate up to 10-fold increase in computational efficiency and significant reduction in misalignment.

Abstract: In this paper we propose a practical radio location scheme for fixed wireless networks, relying on only one base station. We exploit the already available channel impulse response (CIR) of fixed wireless terminals as a location fingerprint in wireless localisation. We show and interpret why the localisation accuracy achieved by the support vector machine (SVM) has no significant improvement compared to general instance-based learning algorithms.

Abstract: We present a fast and accurate framework for registration of multi-modal volumetric images based on decoupled estimation of registration parameters utilizing spatial information in the form of `gradient intensity'. We introduce gradient intensity as a measure of spatial strength of an image in a given direction and show that it can be used to determine the rotational misalignment independent of translation between the images. The rotation parameters are obtained by maximizing the mutual information of 2D gradient intensity matrices obtained from 3D images, hence reducing the dimensionality of the problem and improving efficiency. The rotation parameters along with estimations of translation are then used to initialize an optimization step over a conventional pixel intensity-based method to achieve sub-voxel accuracy. Our optimization algorithm converges quickly and is less subject to the common problem of mis-registration due to local extrema. Experiments show that our method significantly improves the robustness, performance and efficiency of registration compared to conventional pixel intensity-based methods.

Abstract: Conventional mutual information (MI)-based registration using pixel intensities is time-consuming and ignores spatial information, which can lead to misalignment. We propose a method to overcome these limitation by acquiring initial estimates of transformation parameters. We introduce the concept of `gradient intensity' as a measure of spatial strength of an image in a given direction. We determine the rotation parameter by maximizing the MI between gradient intensity histograms. Calculation of the gradient intensity MI function is extremely efficient. Our method is designed to be invariant to scale and translation between the images. We then obtain estimates of scale and translations parameters using methods based on the centroids of gradient images. The estimated parameters are used to initialize an optimization algorithm which is designed to converge more quickly than the standard Powell algorithm in close proximity of the minimum. Experiments show that our method significantly improves the performance of the registration task and reduces the overall computational complexity by an order of magnitude.

Abstract: This paper proposes a method to reproduce the Head Related Transfer Function (HRTF) in the horizontal auditory scene. The method is based on a separable representation which consists of a Fourier Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial dependence. The proposed representation can be used to predict HRTFs at any azimuth position and at any frequency sampling point from a finite number of measurements. Implementation details are demonstrated in the paper. Measured HRTFs from a KEMAR manikin and analytically simulated HRTFs were used to validate the fidelity and predictive capabilities of the method. The average mean square error for model reconstruction is less than two percent.

Abstract: In this paper we consider the spatial degrees of freedom in the context of a multi-antenna wireless communication system. We investigate how the degrees of freedom depend on important system parameters such as the spatial extent of a region containing the antennas and, more importantly, the angular correlation of multipath. These results naturally augment known results which show how the degrees of freedom are affected by multipath from a restricted range of angles. We clarify the distinction between the spatial degrees of freedom with respect to an orthonormal basis and the concept of richness of multipath which is related to the Karhenen Loeve expansions for a random multipath field.

Abstract: A magnitude only equalizer equalizes a magnitude of a received wireless signal without regard to phase distortions introduced, and transmits the magnitude equalized signal to a timing recovery loop for improved correlation peak detection in a sync based timing recovery scheme. A channel equalizer receiving the output signal from the timing recovery loop equalizes the signal and corrects any phase distortions introduced by the magnitude only equalizer. The magnitude only equalizer includes at least one filter utilizing only real coefficients and constrained such that the direct term of the overall filter structure within the magnitude only equalizer is unity.

Abstract: In this paper, we investigate the thermal noise behavior of the multi-antenna communication systems, when antenna elements are closely spaced. We analyze the mutual coupling effect on thermal noise. We apply the Nyquist's thermal noise theorem to determine thermal noise power in the multi-antenna system and to confirm the partial correlation of thermal noise for antenna spacing lower then one wavelength. Simulation results confirm the decrease of thermal noise power level when antenna spacings drop below a half of wavelength.

Abstract: In this paper, we derive an analytical expression for the exact pairwise error probability (PEP) of a space-time coded system operating over a spatially correlated slow fading channel using a moment-generating function-based approach. This analytical PEP expression is more realistic than previously published exact-PEP expressions as it fully accounts for antenna spacing, antenna geometries (Uniform Linear Array, Uniform Grid Array, Uniform Circular Array, etc.) and scattering models (Uniform, Gaussian, Laplacian, Von-mises, etc). Inclusion of spatial information provides valuable insights into the physical factors determining the performance of a space-time code. We demonstrate the strength of our new analytical PEP expression by evaluating the performance of two space-time trellis codes proposed in the literature for different spatial scenarios.

Abstract: This paper derives a general upper bound on the degrees of freedom of multipath field based only on angular power spectrum limited measurements. The numerical results demonstrate that the low-order modal concentration of a wave field based on statistical measurement is proportional to richness of multipath of the wave field. This indicates that we can have a more compact dimensionality of a receiver region when the information is limited to the angular power spectrum with richer multipath.

Abstract: This paper shows the existence of the optimal training, in terms of achievable mutual information rate, for an output feedback implicit estimator for finite-state Markov communication channels. A proper quantification of source redundancy information, implicitly used for channel estimation, is performed. This enables an optimal training rate to be determined as a tradeoff between input signal entropy rate reduction (source redundancy) and channel process entropy rate reduction (channel estimation). The maximal mutual information rate, assuming the optimal implicit training and the presence of channel noise, is shown to be strictly below the ergodic channel information capacity. It is also shown that this capacity penalty, caused by noisy time-varying channel process estimation, vanishes only if the channel process is known or memoryless (channel estimation cannot improve system performance).

Abstract: In this paper, we study the effect of channel memory order on the information rate bounds in time-varying flat-fading (FF) channels. We model time variations of the FF channel with autoregressive (AR) processes with varying degrees of model order. We observe that in high SNR conditions (SNR 20 dB), the information rate penalty of not knowing the AR channel is a non-increasing function of the AR model order. This is expected, since the AR channel predictability cannot decrease with increasing its order. However, in low SNR conditions, the information rate penalty in low-order AR channels can be lower than those in high-order AR channels. Likewise, the intuitive and universal monotonic increase of the information rate bounds with the AR model order is only observed in almost noiseless conditions. In the low SNR regime, however, the achievable information rate bounds in low-order AR channels can be higher than those in high-order AR channels.

Abstract: In this paper, we introduce the novel idea of linear spatial precoding based on fixed and known parameters of MIMO channels to improve the performance of differential space-time coding schemes. Antenna spacing and antenna placements (geometry) are considered as fixed parameters of MIMO channels, which are known at the transmitter. This new linear spatial precoding scheme exploits the antenna placement information at both ends of the MIMO channel to ameliorate the effect of non-ideal antenna placement on the performance of differential space-time coded systems. With this design, the precoder is fixed for fixed antenna placement and the transmitter does not require any feedback of channel state information (partial or full) from the receiver. A second precoding scheme is proposed by exploiting the non-isotropic scattering distribution parameters of the scattering channel. Unlike in the first scheme, the second scheme requires the receiver to estimate the non-isotropic distribution parameters and feed them back to the transmitter. Simulation results show that first scheme provides significant performance improvements at low SNRs and the second scheme provides significant performance improvements both at low and high SNRs.

Abstract: In this paper, we study the effect of directional random scattering on the capacity of multiple-input multiple-output (MIMO) systems. First, we use the spatial decomposition of the MIMO channel matrix to analyze the randomness (entropy) of directional scattering. The analysis shows that directional scatterers (with at least a null in the angular power spectrum) will no longer be random when the receiver observation radius is sufficiently large. Therefore, directional scattering limits the expected linear increase of MIMO capacity with increasing the number of antennas. Second, we consider the effect of receiver antenna arrangement (positions) on the capacity of MIMO systems. For any random scatterer with a given angular power spectrum, we show that it is possible to choose the receiver antenna arrangement with the optimum whitening of the MIMO channel matrix that, in turn, maximizes MIMO channel capacity.

Abstract: We study the dimensions or degrees of freedom of random multipath fields in wireless communications. Random multipath fields are presented as solutions to the wave equation in an infinite-dimensional vector space. We prove a universal bound for the dimension of random multipath field in the mean square error sense. The derived maximum dimension is directly proportional to the radius of the two-dimensional spatial region where the field is coupled to. Using the Karhunen-Loeve expansion of multipath fields, we prove that, among all random multipath fields, isotropic random multipath achieves the maximum dimension bound. These results mathematically quantify the imprecise notion of rich scattering that is often used in multiple-antenna communication theory and show that even the richest scatterer (isotropic) has a finite intrinsic dimension.

Abstract: We propose a new broadband beamformer design technique which produces an optimal beampattern for any set of samples in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern, in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can produce optimal beamformers for both sparse and dense arrays, non-uniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beampattern type, including frequency-invariant and spot pattern design.

Abstract: This paper presents a method which allows to obtain expressions for the space-time cross correlation (STCC) and the space-frequency cross spectrum (SFCS) between signals at two receiver antennas on a mobile unit (MU) for an arbitrary scattering distribution surrounding the MU.

Abstract: This paper shows through theory and simulation the superiority of model-based adaptive algorithms relative to observation-based adaptive algorithms, such as the LMS and RLS, when applied to tracking time-varying channels. The model- based formulation reveals RLS is a degenerate algorithm which does not explicitly recognize the time-varying nature of the channel and consequently is ill-suited to tracking in non-stationary environments. Simulation results for MSE performance of the various adaptive algorithms applied to adaptive MMSE multiuser receiver corroborate the theoretical analysis.

Abstract: This paper shows the existence of the optimal training, in terms of achievable mutual information rate, for an output feedback implicit estimator for finite-state Markov communication channels. Implicit (blind) estimation is based on a measure of how modified is the input distribution when filtered by the channel transfer function and it is shown that there is no modification of an input distribution with maximum entropy rate. Input signal entropy rate reduction enables implicit (blind) channel process estimation, but decreases information transmission rate. The optimal input entropy rate (optimal implicit training rate) which achieves the maximum mutual information rate, is found.

Abstract: This paper presents an analytical model for the fading channel correlation in general scattering environments. In contrast to the existing correlation models, our new approach treats the scattering environment as non-separable and it is modeled using a bi-angular power distribution. The bi-angular power distribution is parameterized by the mean departure and arrival angles, angular spreads of the univariate angular power distributions at the transmitter and receiver apertures, and a third parameter, the covariance between transmit and receive angles which captures the statistical interdependency between angular power distributions at the transmitter and receiver apertures. When this third parameter is zero, this new model reduces to the well known Kronecker model. Using the proposed model, we show that Kronecker model is a good approximation to the actual channel when the scattering channel consists of a single scattering cluster. In the presence of multiple remote scattering clusters we show that Kronecker model over estimates the performance by artificially increasing the number of multipaths in the channel.

Abstract: In this paper we propose a new Turbo Equalization algorithm with Decision Aided Equalizer (DAE). The algorithm takes into account that the soft feedback decisions from the previous iteration contain errors that cannot be neglected. The proposed algorithm finds the error variance and recalculates DAE coefficients at each turbo iteration. The algorithm shows Bit Error Rate (BER) performance improvement relatively to the conventional Turbo DAE for severe frequency-selective channels. The achieved improvement is 0.8 dB at BER of 10^5.

Abstract: A vestigial sideband (VSB) modulation minimum output energy (MOE) pre-equalizer operating on a received ATSC 8-VSB DTV signal includes one or more of an adaptive feed-forward filter and an adaptive feedback filter each utilizing only real adaptive coefficients, with the direct term for the overall filter constrained to unity to remove one degree of filter parameterization freedom. Adaptation of the filter(s) is based on minimizing a blind energy cost function, and is independent of adaptation of a conventional adaptive channel equalizer. The pre-equalized signal is passed to the conventional adaptive equalizer for channel equalization utilizing DFE, IIR-CMA, etc., resulting in performance improvements including faster convergence and greater robustness with relatively small implementation costs.

Abstract: In this letter, we propose a new turbo decision feedback equalizer (DFE) algorithm that takes into account decision feedback error propagation. We derive the exact mathematical expression for the probability density function (pdf) of soft decision feedback symbols, assuming that soft outputs from channel decoder are independent identically distributed Gaussian random variables with known mean and variance. We find a new set of "imperfect" turbo minimum mean-square error DFE coefficients based on the derived pdf. The proposed turbo detector outperforms other turbo equalization algorithms of similar computational complexity in terms of bit-error rate. The achieved improvement is up to 3.8 dB for severe frequency-selective channels.

Abstract: In this paper, we derive analytical expressions for the exact pairwise error probability (PEP) of a space-time coded system operating over spatially correlated fast (constant over the duration of a symbol) and slow (constant over the length of a code word) fading channels using a moment-generating function-based approach. We discuss two analytical techniques that can be used to evaluate the exact-PEPs (and therefore, approximate the average bit error probability (BEP)) in closed form. These analytical expressions are more realistic than previously published PEP expressions as they fully account for antenna spacing, antenna geometries (uniform linear array, uniform grid array, uniform circular array, etc.) and scattering models (uniform, Gaussian, Laplacian, Von-mises, etc.). Inclusion of spatial information in these expressions provides valuable insights into the physical factors determining the performance of a space-time code. Using these new PEP expressions, we investigate the effect of antenna spacing, antenna geometries and azimuth power distribution parameters (angle of arrival/departure and angular spread) on the performance of a four-state QPSK space-time trellis code proposed by Tarokh et al. for two transmit antennas.

Abstract: We present Cram\'er-Rao lower bounds (CRLBs) for the synchronization of UWB signals which should be tight lower bounds for the theoretical performance limits of UWB synchronizers. The CRLBs are investigated for both single-pulse systems and time-hopping systems in AWGN and multipath channels. Insights are given into the relationship between CRLBs for different Gaussian monocycles. An approximation method of the CRLBs is discussed when nuisance parameters exist. CRLBs in multipath channels are studied and formulated for three scenarios depending on the way multipath interference is treated. We find that a larger number of multipaths implies higher CRLBs and inferior performance of the synchronizers, and multipath interference on CRLBs cannot be eliminated completely except in very special cases. As every estimate of time delay could not be perfect, the least influence of the synchronization error on the performance of receivers is quantified.

Abstract: In this chapter we present a realistic new model for wireless multiple-input multiple-output (MIMO) channels which is more general than previous models. A novel spatial decomposition of the channel is developed to provide insights into the spatial aspects of multiple antenna communication systems. By exploiting the underlying physics of free-space wave propagation we characterize the fundamental communication modes of a physical aperture and develop an intrinsic capacity which is independent of antenna array geometries and array signal processing. We show there exists a maximum achievable capacity for communication between spatial regions of space, which depends on the size of the regions and the statistics of the scattering environment.

Abstract: In this paper we estimate the MIMO channel capacity in the presence of correlated noise. We employ the normalized noise correlation matrix in channel capacity formula, in order to identify the noise correlation contribution on the MIMO subchannels decorrelation. Then, we analyze the thermal noise correlation due to mutual coupling effect. We calculate thermal noise correlation matrix in the multi-antenna system with closely spaced antennae by applying the Nyquist's thermal noise theorem. Simulation results shows that mean and outage MIMO channel capacity is underestimated if the noise correlation due to mutual coupling effect is not accounted. We present results for both cases when the transmitter does and does not know the channel realization.

Abstract: It has been shown that the effects of multipath propagation in a mobile wireless communications system can be mitigated if the receiver can make predictions about the multipath fading. In this paper, we introduce a novel scheme for extrapolating multipath fields outwards in space, given field observations within a limited region. Whereas previous work has concentrated on simple multipath propagation with a finite number of plane wave scatterers, we use a less restrictive continuous model of scattering. The extrapolation scheme is based on a information-weighted modal expansion of the field, where modes containing too little information are penalized to minimize the extrapolation error. The performance of this scheme is shown to be far better than pessimistic error bounds derived in previous work.

Abstract: In this paper, we introduced the novel idea of linear spatial precoding based on fixed and known parameters of a MIMO channel where antenna spacing and antenna placement at the transmitter and receiver arrays are considered as fixed parameters. This precoder reduces the effects of antenna spacing and antenna placement and improves the performance of spacetime coded MIMO systems. Unlike the previous precoder designs found in the literature, this precoder does not require frequent feedback of channel state information (partial or full) from the receiver. Closed form solutions for the precoder is presented for systems with up to three receiver antennas. A generalized method is proposed for more than three receiver antennas. Simulation results show that at low SNRs, this precoder provides significant performance improvement over a non-precoded system for small antenna aperture sizes.

Abstract: This paper presents a new receiver structure that addresses the difficult problem of achieving symbol synchronization given a frequency-selective channel. The new joint timing recovery and equalizer structure is partitioned into a number of component parts. The most critical of these component parts, a magnitude equalizing portion which is insensitive to timing errors, is positioned prior to timing recovery, effectively creating an all-pass channel between the transmitter and timing recovery portion of the receiver. Such a structure gives rise to gains in both receiver performance and robustness, and allows the use of less complex symbol synchronization schemes. It is also shown that the magnitude equalizing portion of the equalizer can be retro-fitted to existing receiver designs for corresponding gains.

Abstract: In this paper we analyze the impact of mutual coupling on MIMO channel capacity, considering its effect on both, signal and thermal noise. We calculate noise correlation matrix in the multi-antenna system with closely spaced antennae by applying the Nyquist's thermal noise theorem. Then, we employ noise correlation matrix in channel capacity formula, that enables the identification of thermal noise correlation contribution on the MIMO channel capacity. In addition, we examine thermal noise correlation due to mutual coupling effect. Our simulation results confirm theoretical analysis that mean and outage MIMO channel capacity is underestimated if noise correlation due to mutual coupling effect is not accounted for.

Abstract: UWB pulses are the unique labels of UWB systems. This paper investigates the role of pulse systematically and highlights the central position of the pulse in UWB systems. Four system properties related closely to the pulse are discussed: propagation properties, capacity, interference to existing systems and performance of correlation receivers. The properties of pulses which function directly on every aspect are highlighted. Novel viewpoint is provided for the evaluation of capacity and interference. Suggestions are given on the pulse design, with emphasis on the whole system performance.

Abstract: In this paper we analyze the causes and effects of mutual coupling on MIMO channel capacity. Mutual coupling not only affects the signal through correlation but also the thermal noise-a critical factor omitted from previous work. We study a two-antenna array by applying the Nyquist's thermal noise theorem. Simulation results shows that mean MIMO channel capacity is underestimated if the noise correlation due to mutual coupling effect is not accounted for. We present results for both cases when the transmitter does and does not know the channel realizations.

Abstract: In this paper, we investigate the performance of the multi-antenna communication systems, when antenna elements are closely spaced. We analyze the combined mutual coupling effect on both, signal and thermal noise. We apply the Nyquist's thermal noise theorem to determine the thermal noise in the multi-antenna system and to confirm the partial correlation of thermal noise for antenna spacing lower then one wavelength. Then, we evaluate the thermal noise power behavior for the coupled multi-element antenna system. Simulation results show that the signal-to-noise ratio level is underestimated if the effect of mutual coupling for thermal noise is not accounted for.

Abstract: In this paper, we investigate the signal-to-noise ratio (SNR) in the palm-sized multi-antenna communication systems. The presented analysis includes the mutual coupling on both, signal and thermal noise. We apply the Nyquist's thermal noise theorem to determine the thermal noise behavior in the multi-antenna system and to confirm the partial correlation of thermal noise for antenna spacing lower then one wavelength. Then, we develop a method for thermal noise power calculation for the multi-antenna system with coupled antennae. Simulation results shows that SNR is underestimated if the effect of mutual coupling for thermal noise is not accounted for.

Abstract: This paper provides the analysis of the Least Mean Square (LMS) and the Recursive Least Square (RLS) adaptive algorithms performance for adaptive CDMA receivers in slowly time varying communication channels in the presence of multipath. We confirm that neither the LMS algorithm nor the RLS algorithm has a complete monopoly over good performance in a non-stationary environment. Rather, one or the other of these two algorithms is preferred, depending on the environmental conditions that are prevalent. We show that the LMS algorithm provides a good tracking if speed of channel change is slow, but LMS stability criteria depend on signal statistics (and so, on channel conditions). The RLS convergence and stability criteria do not depend of signal statistics, but the RLS involves memory and does not explicitly recognize time varying nature of the channel. Presented simulation results confirm the theoretical analysis.

Abstract: In this paper, we derive an upper bound on the channel capacity of MIMO systems in the presence of correlated noise. We isolate the noise correlation factor in the channel capacity formula, enabling the identification of the noise correlation contribution on the MIMO channel capacity. We analyze the thermal noise correlation due to the mutual coupling effect. Then, we calculate the thermal noise correlation matrix in the multi-antenna system with closely-spaced antennae by applying the Nyquist's thermal noise theorem. Simulation results shows that ergodic and outage MIMO channel capacity are underestimated if the noise correlation due to the mutual coupling effects is not accounted for. Additionally, it is demonstrated that the upper bound can be used for a first estimation of MIMO channel capacity in the presence of correlated noise, reducing the calculation complexity.

Abstract: In this paper, performance and parameter optimization of RAKE reception for time-hopping Ultra Wideband (TH-UWB) systems is investigated when interchip interference (ICI) is taken into consideration. For a TH-UWB system, ICI is closely related to the relationship between the number of chips in a frame (Nc), and the period of the TH code (Nf). In a fixed data-rate case, larger Nf implies higher transmitted symbol signal-to-noise ratio (SNR) and larger ICI in RAKE fingers. So there is a tradeoff between Nc and Nf to optimize the RAKE performance. In this paper, two models are suggested to describe the ICI, and this tradeoff is investigated in the single user case based on the traditional Gaussian approximation method and other flexible methods. Given the lack of explicit knowledge of the relationship among Nf, Nc and the interference, a rule of thumb is proposed to configure Nf and Nc.

Abstract: In this paper, we demonstrate that the performance of a direction of arrival (DOA) estimator is fundamentally limited by the size of the region over which we measure a wavefield. That is, even assuming continuous field measurements across the region, we still cannot achieve perfect performance. We use an approach based on modal decomposition of a spatially truncated field, and completely independent of sensor geometry, to derive the Cramer-Rao Bound (CRB) for spatially limited DOA estimators. The model is validated by comparison with results from a uniform circular array (UCA) as the number of sensors goes to infinity. Simulations of the spatial CRB show how DOA performance improves as the measurement region expands. Simulations of the bound also indicate that P sources can only be effectively resolved once a certain threshold region size is reached.

Abstract: In this paper, we derive an upper-bound for the pair-wise error probability of space-time codes which captures the effects of the transmitter and the receiver antenna configurations (antenna separation and antenna geometry) and the surrounding scattering distributions at the transmitter and the receiver antenna arrays. This new upper-bound allows investigation of the individual effects of antenna configuration and scattering environment parameters on the performance of space-time codes. Using this upper-bound, we quantify the degree of the effect of antenna configuration on the diversity advantage given by a space-time code. Simulation results show that as the number of antennas increase within a fixed aperture, the diversity advantage of a space-time code is upperlimited by the size of the antenna aperture.

Abstract: This paper presents a framework for the thermal noise analysis of mutually-coupled antennae in the multi-antenna system. The electromagnetic coupling for thermal noise is included in the analysis of the multi-antenna system with small antenna element spacings. The method for thermal noise power calculation for the multi-antenna system with coupled antennae is presented. The thermal noise behavior in the multi-antenna system is determined by applying the Nyquist's thermal noise theorem. The partial correlation of thermal noise for antenna spacing lower then a wavelength is confirmed. The signal-to-noise ratio (SNR) for the closely spaced antennae in the multi-antenna system is then estimated, using presented method for thermal noise analysis. Simulation results confirm that as the antenna spacing decreases to zero, the multi-antenna system starts to act like a single antenna system.

Abstract: This paper analyzes the theoretical limits of the Least Mean Square (LMS) and Recursive Least Square (RLS) adaptive algorithms performance for the adaptive CDMA receivers in slowly time varying communication channels in the presence of multi-path. We show that since the RLS involves memory and does not explicitly recognize time varying nature of the channel (time varying true weights), it has worse tracking performance then the LMS adaptive algorithm. Thus, the implementation of the RLS algorithm for adaptive CDMA receivers operating in time varying channels is very limited. The LMS algorithm provides better tracking, but still speed of channel change must be slow. In addition, we present simulation results which confirm the theoretical analysis.

Abstract: In this paper we analyze the decision feedback error propagation in the adaptive turbo equalization with a decision feedback loop. We derive the exact mathematical expression for the feedback error probability density function (pdf) with the assumption that the soft outputs of channel decoder are identical independent distributed (i.i.d) Gaussian random variables with known mean value and variance. We also find a new set of turbo equalizer coefficients based on the feedback error pdf and MMSE criterion. New turbo equalizer is shown to outperform the conventional one (assuming no feedback error propagation) in terms of Bit Error Rate (BER). The achieved improvement is up to 4 dB for severe frequency-selective channels. The analysis is applicable to other turbo detection methods employing the feedback loop.