We propose a method for the accurate and robust reconstruction of the non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based method for the accurate recovery of parameters of the Dirac functions using a finite number of observations of the bandlimited signal. In comparison to existing techniques, the proposed method enables more accurate reconstruction primarily due to the better conditioning of systems involved in the recovery of parameters. In order to reconstruct K Diracs on the sphere, the proposed method requires samples of the signal bandlimited in the spherical harmonic (SH) domain at SH degree equal or greater than K + √K + 1/4 - 1/2. In comparison to the existing state-of-the-art technique, the required bandlimit, and consequently the number of samples, of the proposed method is (approximately) the same. We also conduct numerical experiments to demonstrate that the proposed technique is more accurate than the existing methods by a factor of 107or more for 2 ≤ K ≤ 20.

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, the transmitter (TX) sends a common information symbol to multiple receivers (RXs) and a fusion center (FC) chooses the TX symbol that is more likely, given the likelihood of its observations from all RXs. The transmission of a sequence of binary symbols and the resultant intersymbol interference are considered in the cooperative MC system. Three ML detection variants are proposed according to different RX behaviors and different knowledge at the FC. The system error probabilities for two ML detector variants are derived, one of which is in closed form. The optimal molecule allocation among RXs to minimize the system error probability of one variant is determined by solving a joint optimization problem. Also for this variant, the equal distribution of molecules among two symmetric RXs is analytically shown to achieve the local minimal error probability. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of simpler, non-ML cooperative variants and demonstrate that these simpler cooperative variants have error performance comparable to ML detectors.

We propose an iso-latitude sampling scheme for the representation of band-limited signals on the sphere. The proposed scheme is designed as a variant of the widely used Hierarchical Equal Area iso-Latitude Pixelization (HEALPix) scheme on the sphere. We use HEALPix grid of resolution Nsideto represent a signal of bandlimit (spherical harmonic degree) L. To reduce the number of samples, the proposed algorithm takes only L iso-latitude rings out of 4Nside-1 rings of the HEALPix. This selection is carried out by ensuring that the spherical harmonic transform (SHT) of the signal is computed accurately from the samples. The number of samples required by the proposed sampling scheme is smaller than that required by HEALPix by at least a factor of 3/2. For the proposed sampling scheme, we also formulate the spherical harmonic transform and conduct numerical experiments to evaluate the number of samples required by the proposed sampling scheme and the accuracy of the associated SHT.

We develop an algorithm for the extrapolation of band-limited signals on the sphere. The proposed algorithm improves the accuracy of the extrapolation of band-limited signal by using the information contained in the out-of-band harmonic coefficients of the signal to update the extrapolated signal at each iteration. The estimation of signals on the sphere from incomplete measurements finds applications in acoustics, cosmology and geophysics. The proposed algorithm does not only exploit the band-limited property of the signal, that is, force the harmonic coefficients outside the band-limit to zero, at each iteration as carried out in the existing algorithms but also uses the harmonic coefficients outside the harmonic domain to improve the accuracy of signal extrapolation. To demonstrate the improvement in the accuracy enabled by the proposed algorithm, we conduct numerical experiments and compare the results of the proposed algorithm with the existing iterative conjugate gradient method.

To support the applications where the measurements can only be taken over spatially limited region on the sphere due to practical limitations, we design a spatially-limited sampling scheme on the sphere for the computation of spherical harmonic transform (SHT) of band-limited signals. By enclosing the inaccessible region with the (anisotropic) ellipsoidal region followed by the rotation of the region to the pole or the equator, we propose an iso-latitude sampling scheme on the sphere. We also present a method to place the samples over the spatially-limited region such that the SHT can be computed accurately. Moreover, we formulate the SHT associated with the proposed sampling scheme and analyse its accuracy through numerical experiments. We also provide an illustration where we reconstruct the head-related transfer function (HRTF) from spatially-limited measurements and demonstrate that the proposed sampling design enables more accurate computation than the existing sampling schemes.

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, a fusion center (FC) chooses the transmitter's symbol that is more likely, given the likelihood of the observations from multiple receivers (RXs). We propose three different ML detection variants according to different constraints on the information available to the FC, which enables us to demonstrate trade- offs in their performance versus the information available. The system error probability for one variant is derived in closed form. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of the simpler cooperative variants and demonstrate that majority rule detection has performance comparable to ML detection when the reporting is noisy.

For the representation of spin-s band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require ~2L2samples for the representation of spin-s functions band-limited at L, the proposed scheme requires No= L2- s2samples for the accurate computation of the spin-s spherical harmonic transform (s-SHT). For the proposed sampling scheme, we also develop a method to compute the s-SHT. We place the samples in our design scheme such that the matrices involved in the computation of s-SHT are well-conditioned. We also present a multipass s-SHT to improve the accuracy of the transform. We also show the proposed sampling design exhibits superior geometrical properties compared to existing equiangular and Gauss-Legendre sampling schemes, and enables accurate computation of the s-SHT corroborated through numerical experiments.

This paper considers the communication for omniscience problem: a set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise-free broadcast communications. We study the problem of how to determine an optimal rate vector that attains omniscience with the minimum sum rate, the total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We propose a modified decomposition algorithm (MDA) and a sum-rate increment algorithm (SIA) for the asymptotic and non-asymptotic models, respectively, both of which determine the value of the minimum sum rate and a corresponding optimal rate vector in polynomial time. For the coordinate saturation capacity algorithm, a nesting algorithm in MDA and SIA, we propose to implement it by a fusion method and show by experimental results that this fusion method contributes to a reduction in computation complexity. Finally, we show that the separable convex minimization problem over the optimal rate vector set in the asymptotic model can be decomposed by the fundamental partition, the optimal partition of the user set that determines the minimum sum rate, so that the problem can be solved more efficiently.

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 optimisation of samples along longitude to further reduce the spatial dimensionality of equiangular, GL and efficient GL sampling schemes. Furthermore, we demonstrate that the accuracy of the SHT is not affected with the proposed reduction in the spatial dimensionality.

We develop a robust method for the accurate reconstruction of non-bandlimited finite rate of innovation signals composed of finite number of Diracs. For the recovery of parameters of K Diracs defining the signal, the proposed method requires more than (K + √K)2samples of the signal band-limited in harmonic domain such that the spherical harmonic transform can be computed using the samples. In comparison with the existing methods, the proposed method is robust in a sense that it does not require all Diracs to have distinct colatitude parameter. We first estimate the N number of Diracs which do not have distinct colatitude parameter. Once N is determined, the proposed method requires, at most, N2+N/2 + 1 unique and intelligently chosen rotations of the signal to recover all parameters accurately. We also provide illustrations to demonstrate the accurate reconstruction using the proposed method.

The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO.

This paper studies a wireless network consisting of multiple transmitter-receiver pairs where interference is treated as noise. Previously, the throughput region of such networks was characterized for either one time slot or an infinite time horizon. We aim to fill the gap by investigating the throughput region for transmissions over a finite time horizon. Unlike the infinite-horizon throughput region, which is simply the convex hull of the throughput region of one time slot, the finite-horizon throughput region is generally non-convex. Instead of directly characterizing all achievable rate-tuples in the finite-horizon throughput region, we propose a metric termed the rate margin, which not only determines whether any given rate-tuple is within the throughput region (i.e., achievable or unachievable), but also tells the amount of scaling that can be done to the given achievable (unachievable) rate-tuple such that the resulting rate-tuple is still within (brought back into) the throughput region. Furthermore, we derive an efficient algorithm to find the rate-achieving policy for any given rate-tuple in the finite-horizon throughput region.

We propose a novel algorithm to design user load- achieving pilot sequences that mitigate pilot contamination in multi-cell massive multiple-input multiple-output (MIMO) networks. To this end, we first derive expressions for the user load and the load region of the network considering both small- scale and large-scale propagation effects. We then develop the pilot sequence algorithm for multi- cell massive MIMO networks as per the rules of generalized Welch bound equality design. Notably, we find that our algorithm and the corresponding downlink power allocation ensure that the user load is achieved when the signal-to-interference- plus-noise ratio (SINR) requirements for the users lie within the load region. Furthermore, we demonstrate the performance advantage of our proposed design relative to the existing designs, in terms of a larger load region and a higher maximum permitted SINR. Finally, we show that our proposed design can satisfy the pre-defined SINR requirements for users with a finite number of antennas at the base station (BS), while the existing designs cannot satisfy the same requirements even with an infinite number of antennas at the BS.

This paper studies a wireless network consisting of multiple transmitter-receiver pairs sharing the same spectrum where interference is regarded as noise. Previously, the throughput region of such a network was characterized for either one time slot or an infinite time horizon. This work aims to close the gap by investigating the throughput region for transmissions over a finite time horizon. We derive an efficient algorithm to examine the achievability of any given rate in the finite-horizon throughput region and provide the rate-achieving policy. The computational efficiency of our algorithm comes from the use of A* search with a carefully chosen heuristic function and a tree pruning strategy. We also show that the celebrated max-weight algorithm which finds all achievable rates in the infinite-horizon throughput region fails to work for the finite-horizon throughput region.

In this paper, a cooperative diffusion-based molecular communication system is considered where distributed receivers collaboratively determine a transmitter's signal. In this system, the receivers first make local hard decisions about the current transmitted bit and then report these decisions to a fusion center (FC). The FC combines the local hard decisions to make a global decision using an N-out-of-K fusion rule. Asymmetric and symmetric topologies are considered and for each topology, two reporting scenarios, namely, perfect reporting and noisy reporting, are addressed. Closed-form analytical expressions for the expected global error probability are derived for all considered topologies and scenarios. Numerical and simulation results show that system reliability can be greatly improved by combining the detection information of distributed receivers.

We consider the problem of how to fairly distribute the minimum sum-rate among the users in communication for omniscience (CO). We formulate a problem of minimizing a weighted quadratic function over a submodular base polyhedron which contains all achievable rate vectors, or transmission strategies, for CO that have the same sum-rate. By solving it, we can determine the rate vector that optimizes the Jain's fairness measure, a more commonly used fairness index than the Shapley value in communications engineering. We show that the optimizer is a lexicographically optimal (lex-optimal) base and can be determined by a decomposition algorithm (DA) that is based on submodular function minimization (SFM) algorithm and completes in strongly polynomial time. We prove that the lex-optimal minimum sum-rate strategy for CO can be determined by finding the lex-optimal base in each user subset in the fundamental partition and the complexity can be reduced accordingly.

We design a sampling scheme on the sphere and a corresponding spherical harmonic transform (SHT) for the measurement and reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry property of the diffusion signal in the spectral (spherical harmonic) domain, we design a sampling scheme that attains the optimal number of samples, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral domain. Compared with other sampling schemes that can be used with the optimal number of samples, we demonstrate, through numerical experiments, that the proposed scheme enables more accurate computation of the SHT, and this accuracy is practically rotationally invariant. In addition, it results in more efficient computation of the SHT and storage of the diffusion signal.

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.

We propose a novel pilot sequence design to mitigate pilot contamination in multi-cell multiuser massive multiple-input multiple-output networks. Our proposed design generates pilot sequences in the multi-cell network and devises power allocation at base stations (BSs) for downlink transmission. The pilot sequences together with the power allocation ensure that the user capacity of the network is achieved and the pre-defined signal-to-interference-plus-noise ratio (SINR) requirements of all users are met. To realize our design, we first derive new closed-form expressions for the user capacity and the user capacity region. Built upon these expressions, we then develop a new algorithm to obtain the required pilot sequences and power allocation. We further determine the minimum number of antennas required at the BSs to achieve certain SINR requirements of all users. The numerical results are presented to corroborate our analysis and to examine the impact of key parameters, such as the pilot sequence length and the total number of users, on the network performance. A pivotal conclusion is reached that our design achieves a larger user capacity region than the existing designs and needs less antennas at the BS to fulfill the pre-defined SINR requirements of all users in the network than the existing designs.

This paper considers a cross-layer adaptive modulation system that is modeled as a Markov decision process. We study how to utilize the monotonicity of the optimal transmission policy to relieve the computational complexity of dynamic programming (DP). In this system, a scheduler controls the bit rate of the m-quadrature amplitude modulation in order to minimize the long-term losses incurred by the queue overflow in the data link layer and the transmission power consumption in the physical layer. The work is done in two steps. First, we observe the L#-convexity and submodularity of DP to prove that the optimal policy is always nondecreasing in queue occupancy/state and derive the sufficient condition for it to be nondecreasing in both queue and channel states. We also show that, due to the L#-convexity of DP, the variation of the optimal policy in queue state is restricted by a bounded marginal effect. The increment of the optimal policy between adjacent queue states is no greater than one. Second, we use the monotonicity results to present two low complexity algorithms: monotonic policy iteration (MPI) based on L#-convexity and discrete simultaneous perturbation stochastic approximation (DSPSA). We run experiments to show that the time complexity of MPI based on L#-convexity is much lower than that of DP and the conventional MPI that is based on submodularity and DSPSA is able to adaptively track the optimal policy when the system parameters change.

This paper considers the discrete convexity of a cross-layer on-off transmission control problem in wireless communications. In this system, a scheduler decides whether or not to transmit in order to optimize the long-term quality of service (QoS) incurred by the queueing effects in the data link layer and the transmission power consumption in the physical (PHY) layer simultaneously. Using a Markov decision process (MDP) formulation, we show that the optimal policy can be determined by solving a minimization problem over a set of queue thresholds if the dynamic programming (DP) is submodular. We prove that this minimization problem is discrete convex. In order to search the minimizer, we consider two discrete stochastic approximation (DSA) algorithms: 1) discrete simultaneous perturbation stochastic approximation (DSPSA) and 2) L#-convex stochastic approximation (L#-convex SA). Through numerical studies, we show that the two DSA algorithms converge significantly faster than the existing continuous simultaneous perturbation stochastic approximation (CSPSA) algorithm in multiuser systems. Finally, we compare the convergence results and complexity of two DSA and CSPSA algorithms where we show that DSPSA achieves the best tradeoff between complexity and accuracy in multiuser systems.

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.

We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality regular sampling grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a regular grid composed of L iso-latitude rings of samples with only L samples in each ring along longitude. Since a signal band-limited at L is represented by L2 degrees of freedom in the spectral (spherical harmonic) domain, the proposed method requires the minimal number of samples for the computation of SHT. In comparison to the other schemes that require 2L - 1 samples along each iso-latitude ring, we show that the SHT can be computed, by exploiting the structure of spectral domain, from only L samples in each iso-latitude ring. We also analyse the numerical accuracy and the computational complexity of our proposed SHT for a regular grid with equiangular sampling. We demonstrate, through numerical experiments, that the proposed SHT is sufficiently accurate for band-limits of interest in diffusion magnetic resonance imaging.

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.

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.

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.

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.

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 analyzed 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.

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.

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.

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.

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.

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(L4) and outperforms the previous best known fast methods, which have complexity O(L5).

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.

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.

Cooperative communication systems employ cooperation 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 synchronization 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.

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.

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.

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 Cramér-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.

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.

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.

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 (AF) 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 the outage probability and the 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 rates.

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 distribution 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.

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 spatial 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 processing problems on the sphere.

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.

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 Cramér-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.

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.

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.

This paper deals with two important questions associated with HRTF measurement: 1) “what is the required angular resolution?,” and 2) “what is the most suitable sampling scheme?.” The paper shows that a well-defined finite number of spherical harmonics can capture the head-related transfer function (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.

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.

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.

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 ad vantages over conventional average beat subtraction method are discussed.

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 offset.

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.

This paper consider the problem of how to evaluate the efficiency of a 3D continuous functional HRTF model in rep resenting measured data. 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 L 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 a given 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.

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.

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.

This study addresses the problem of joint blind timing and carrier synchronisation in a (distributed-M)×N 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.

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.

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 - γ proportion of the energy inside the time interval [-T/2, T/2] for some nominal small γ. 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.

FAST TCP is a promising new transfer control protocol developed for high-speed long-latency networks, whose performance has previously only been studied for data traffic sent in one direction. In this study, the authors 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, the authors obtain a powerful result that the queue delays observed by opposite FAST TCP flows only have a time difference in a dumbbell network. Furthermore, the authors establish the conditions under which the bi-directional FAST TCP flows achieve stability, and on this basis the throughput rates of the forward and backward flows at steady-state are deduced. The authors find that, in the case of bandwidth asymmetry and one flow in each direction, in equilibrium the throughput of the bi-directional FAST TCP flows can only achieve the smaller link capacity of the duplex links, and the link with larger capacity is not fully occupied. These theoretical findings are corroborated by NS2 simulations.

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.

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.

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 open-loop PSAM (i.e., the case where no feedback is provided from the receiver), 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. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.

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 mode limited. 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.

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.

This paper provides mutual information performance analysis of multiple-symbol differential MPSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown 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.

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.

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.

Conventional mutual information (Ml)-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 translation 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.

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.

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 misregistration 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.

This paper looks at capacity achieving detection strategies for information transfer over time-varying channels. The time-varying binary symmetric channel (TV-BSC) is identified as the basic binary state-space model. Separation of entropies principles and the TV-BSC model-based state-space approach are used to determine the performance bounds for coherent and non-coherent detection over time-varying communication channels. The mutual information rate over the TV-BSC, assuming channel estimation in the presence of channel noise, is shown to be below the channel information capacity because of lack of perfect channel knowledge. Furthermore, it is shown that TV-BSC model-based differential detection has a fundamental advantage over the channel estimation based detection since it theoretically preserves the TV-BSC information capacity when the observation interval approaches infinity. Simulation analysis corroborates the theoretical results, showing that multiple-symbol differential detection practically achieves the TV-BSC capacity in just a few symbol observation times.

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

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

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

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.

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)

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.

This paper shows through theory and simulation the superiority of model-based adaptive algorithms relative to observation-only-based adaptive algorithms, such as LMS and RLS, when applied to tracking time-varying channels. The model-based formulation reveals RLS as 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

In this paper we determine the MIMO channel capacity in the presence of correlated noise. We employ a normalized noise correlation matrix in the channel capacity formula, in order to identify the noise correlation contribution to the MIMO subchannel decorrelation. Then, we analyze the thermal noise correlation due to mutual coupling. We calculate thermal noise correlation matrix in the multi-antenna system with closely spaced antenna 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 is not accounted for. We present results for cases when the transmitter does and does not know the channel realization

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 (N/sub c/), and the period of the TH code (N/sub f/). In a fixed data-rate case, larger N/sub f/ implies higher transmitted symbol signal-to-noise ratio (SNR) and larger ICI in RAKE fingers. So there is a tradeoff between N/sub c/ and N/sub f/ 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 N/sub f/, N/sub c/ and the interference, a rule of thumb is proposed to configure N/sub f/ and N/sub c/.

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

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.

This work analyses the time varying nature of the mobile communications channel which affects the channel information capacity. The channel uncertainty is a fundamental issue for the information theory of the time varying mobile communication channels and here we use an information theoretic approach to channel uncertainty modeling. Although we analyse the final state Markov channel (FSMC) models, our approach still enables considerable conceptual insight to be gained. In the first step of our analysis, we define four axioms which qualitatively describe the non-trivial influence of the channel uncertainty on the time-varying channel information capacity. Then, we focus on the FSMC models which capture these axioms. We present the concept of time varying binary symmetric channel (TV-BSC) to further support our analysis. The TV-BSC is the simplest FSMC model that shows a non-trivial influence on capacity due to the channel uncertainty. We provide the information theoretic analysis of the TV-BSC model including the information capacity calculation and the TV-BSC estimation analysis.

We propose a new technique that facilitates the soft transition between a startup algorithm and a decision directed (DD) algorithm in blind adaptive equalizers. The algorithm-pair is combined using a reliability measure that is proportional to an estimate of the probability of the equalizer detecting a correct symbol. This measure takes into account both the equalized signal and its statistical distribution. The main feature of the technique is in the smooth and automatic switching from the startup algorithm to the DD algorithm and vice versa depending on the value of the reliability measure. This technique has been compared with the popular Benveniste-Goursat and stop-and-go algorithms and is shown to exhibit a faster rate of convergence and lower steady state error.

In this paper, we present the Cramer-Rao lower bounds (CKLBs) for the time delay estimation of UWB signals which could 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. It is found that larger number of multipath signals implies higher CRLBs and inferior performance of synchronizers, and multipath interference on CRLBs can not 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.

Using a spatial region as an information bearing resource is considered and an analogy drawn with the work on essentially time- and band-limited signals by Slepian, Landau and Pollack. This paper considers the fundamental limits to the use of free-space as an information bearing resource, a concept for wireless communication which exploits space to achieve information transfer.

In this paper we present a new upper bound on the mutual information of MIMO systems. By characterizing the fundamental communication modes between two physical regions, we develop an intrinsic capacity which is independent of antenna array geometries and array signal processing, and depends only on the size of the regions and the statistics of the scattering environment.

We present information theoretic capacity results for information transfer in space, under the general assumption that the receiver applies a spatial filter to receive signals. Our work presents novel applications of linear, bounded, invariant operators to communication channels. We outline the procedure for calculating the information theoretic capacity for this restricted class of operator channels and apply this result to wireless information transfer.

A bound is derived for the extent to which narrowband knowledge of a multipath field inside a spatially limited region can be extrapolated beyond that region. The bound is independent of any model which may be applied to the multipath field, relying on the field being a solution to the homogeneous Helmholtz wave equation. The bound has implications for the extent and reliability of long-range channel prediction, particularly when the multipath is diffuse.

We develop a general mathematical model for nearfield multipath scattering as a basis for studying the spatial limits imposed on multi-antenna wireless communication systems. This model generalizes the Herglotz wave function, which is an important tool in the study of inverse scattering problems, to a form where the scatterers can be nearfield. This permits the development of the most general form of spatial correlation which is known to constrain the capacity of wireless systems.

We investigate the behaviour of MIMO capacity when the size of the antenna array is constrained. By increasing the number of antennas within a small region in space the antenna array becomes dense and spatial correlation inhibits capacity growth. A theoretically derived antenna saturation point is shown to exist for dense array MIMO systems, at which there is no capacity growth with increasing antenna numbers. We show this saturation point increases linearly with the radius of the region containing the antenna array and is independent of the number of antennas.

A theoretically derived antenna saturation point is shown to exist for MIMO systems, at which the system suffers a capacity growth decrease from linear to logarithmic with increasing antenna numbers. We show this saturation point increases linearly with the radius of the region containing the receiver antennas and is independent of the number of antennas. Using an alternative formulation of capacity for MIMO systems we derive a closed form capacity expression, which uses the physics of signal propagation combined with statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and show that the saturation effect is due to spatial correlation between receiver antennas.

This paper investigates the performance of ultra-wideband (UWB) correlator receivers for Gaussian monocycles under the condition of equal mean power and provides constructive reference to the selection of pulses. Several channel situations are examined including ideal single user AWGN channel, non-ideal synchronous, multipath fading and multiple access interference. Both numerical and analytical techniques show that the shapes of pulses have notable impact on the performance of correlator receivers, especially on the interference resistance ability and signal-to-noise ratio (SNR) of the output. he results are also extended to the field of fractional bandwidth to better understand the possible relationship between fractional bandwidth and correlator receivers.

In this paper, some new results on the capacity of a typical M-ary pulse position modulation (M-PPM) time hopping (TH) ultra-wideband (UWB) systems are presented. Previous results using a "pure PPM model" are proven to exaggerate the real capacity of a UWB system. Based on an extended model containing correlator and soft decision decoding, the capacity is evaluated in the single-user case and in the case of a system with asynchronous multiple user interference (MUI) when the inputs are equiprobable. It is found that only when bit- signal-to-noise ratio (bit-SNR) is high enough, larger M leads to higher capacity; and for a specific M, the optimal values of PPM time offset parameter T/sub d/, which maximizes the capacity, are independent of bit-SNR. The influence of MUI on capacity is detrimental, especially in the case of high bit-SNR.

We derive an infinite series expression of the average signal-to-noise ratio (SNR) gain for a dual selection combining system under Nakagami-m fading using a series representation of the bivariate cumulative probability distribution function. The average SNR gain expression is shown to relate to the Nakagami shape factor m, the power correlation and the power allocation ratio.

We establish that an arbitrary narrowband multi path field in any circular region in two dimensional space has an intrinsic functional dimensionality of (πe) R/λ ≈ 8.54 R/λ. that scales only linearly with radius R/λ. in wavelengths. This result implies there is no such thing as an arbitrarily complicated multi path field. That is, a field generated by any number of nearfield and farfield, specular and diffuse multipath reflections is no more complicated than a field generated by a limited number plane waves. As such, there are limits on how rich multipath can be. This result has significant implications including means: i) to determine a parsimonious parameterization for arbitrary multipath fields, ii) of synthesizing arbitrary multi path fields with arbitrarily located nearfield or farfield, spatially discrete or continuous sources. We give examples of multipath field analysis and synthesis.

The well known results of the spatial correlation function for 2-dimensional and 3-dimensional diffuse fields of narrowband signals are generalised to the case of general distributions of scatterers. A method is presented which allows closed form expressions for the correlation function to be obtained for arbitrary scattering distribution functions. These closed form expressions are derived for a variety of commonly used scattering distribution functions.

The well-known results of the spatial correlation function for two-dimensional and three-dimensional diffuse fields of narrowband signals are generalized to the case of general distributions of scatterers. A method is presented that allows closed-form expressions for the correlation function to be obtained for arbitrary scattering distribution functions. These closed-form expressions are derived for a variety of commonly used scattering distribution functions.

We define and apply a new algorithm called the iterative Viterbi decoding algorithm (IVA) to decode a high-rate parity-concatenated TCM system in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. With trellis shaping, the IVA can achieve a performance 1.25 dB away from the Shannon limit at a BER of 3/spl times/10/sup -5/ with low complexity. By augmenting the system with a binary BCH code, the error floor can be reduced to 10/sup -9/ with very little additional cost.

In multiuser wireless systems using multiple antennas in a multipath environment it has been asserted that whenever users are at least a distance of /spl lambda//2 apart, it is possible to recover their respective signals with appropriate signal-processing (Winters 1984). This paper significantly strengthens this remarkable assertion by: 1) showing explicitly that separability of the users' signals is possible using the simplest class of linear detectors; 2) showing that the /spl lambda//2 rule of thumb can be quite conservative with meaningful signal separability achievable at separations around /spl lambda//10; and 3) identifying critical geometrical properties, such as position of users and multipath geometry that permit the best separability.

It has long been known that the performance of a channel with intersymbol interference (ISI) not only depends on the signal to noise ratio, but on the actual impulse response coefficients as well. In this paper, a technique for approximating the performance of a communications channel in the presence of ISI is presented. It is assumed that the finite length impulse response of the channel is known, and that a maximum likelihood sequence estimation (MLSE) technique is used for equalisation. The technique consists of identifying for the modulation and impulse response duration, those few error events which are most likely to occur. This selection process is computationally intensive, but once it has been performed for a given modulation, the results can be used to enable very efficient approximation. Results are presented for some common modulation schemes.

This paper investigates the perceptual significance of residual phase distortion due to an approximate equalization of the nonminimum-phase room response from a sound source to a microphone in a reverberant room. It is shown that disrupted phase relationships introduced by a minimum-phase equalization filter may have a detrimental effect on perceived sound quality. The subjective assessment of phase distortion on speech signals is related to an objective error criterion, newly introduced in this paper. An alternative approach to the minimum-phase/all-pass decomposition based on iterative flattening of the room transfer function (RTF) magnitude is also presented, which overcomes potential numerical problems and provides more insight into subjective aspects of magnitude and phase equalization in the reduction of acoustic reverberation. Factors contributing to the results and practical implications for equalization are discussed.

This paper investigates the robustness of sound equalization using a room response inverse filter with respect to changing or uncertain source or microphone positions. It is shown that due to the variations of the transfer function from point to point in a room, even small changes in the source or microphone position of just a few tenths of the acoustic wavelength can cause large degradations in the equalized room response. The robustness problem is especially acute at high frequencies, which are known to carry some important attributes of the speech signal. The spatial extent of equalization, derived from the statistical-average properties of sound transmission in rooms, is illustrated by computer simulations which corroborate the theoretical results presented.

The performance of equalizers depends on the discrete time model of the input signal and noise. The use of a higher sampling rate results in colored noise when the bandwidth of the noise-limiting prefilter is not sufficiently large. It is shown that the mean square error (MSE) performance of linear equalizers becomes sensitive to the decision delay when the input noise is colored, and by using the appropriate delay, a significant improvement in the MSE can be achieved. This is in contrast to the behaviour observed in the white noise case well known in the literature. This behaviour is explained in time domain by showing the contributions to the MSE from the columns of the channel convolution matrix and the noise eigenvectors. In the frequency domain, it is shown that the equalizer exploits the noise correlation to improve the MSE.

This paper examines the sensitivity of sound equalization to source or microphone position changes in a reverberant room. It is demonstrated that even small displacements from the reference (equalization) point, of the order of a tenth of the acoustic wavelength, can cause large degradations in the equalized room response. The general theory developed in this paper, which implies that the sound equalization in practical environments may be an ill-posed problem, is verified by the simulation results averaged over different source and microphone positions.

An exact series representation for a nearfield spherically isotropic noise model is introduced. The proposed noise model can be utilized effectively to apply well-established farfield array processing algorithms for nearfield applications of sensor arrays. A simple array gain optimization is used to demonstrate the use of the new noise model.

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm.

This paper presents a new method of designing a beamformer having a desired broadband beampattern with focusing capability to operate at any radial distance from the array origin. An important consequence of our result is that the beamformer processing can be factored in to three levels of filtering: (i) beampattern independent elementary beamformers; (ii) beampattern shape dependent filters; and (iii) radial zooming filters where a single parameter can be adjusted to zoom-focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequency range of 1:10.

This paper studies the effect of arrival of new users to the synchronous blind multiuser receivers namely one based on the minimum output energy (MOE) criterion and one based on the constant modulus algorithm (CMA). The perturbation caused by this sudden birth of interferers is examined from the viewpoint of the change of the cost function under the noiseless assumption. The CMA and MOE detectors are compared with the training-based minimum mean-squared-error (MMSE) detector. It is shown that in the vicinity of lock convergence, the CMA minimum stays in the neighborhood of the MMSE minimum if the perturbation is small enough. The changes in the MMSE and MOE costs are the same if all users are independent. It is observed that the transient behavior of the CMA detector deteriorates the fastest as the existing number of users approaches the processing gain.

The performance and complexity of blind algorithms in a digital receiver is dependent on the prefilter prior to discretization of the received continuous time signal and the sampling rate. This paper shows that symbol spaced blind equalization algorithms are in general sub-optimal, since a matched filter cannot be used. We show that, for fractionally spaced equalizers, the prefilter can be a general low-pass filter and does not need to be matched to the unknown channel. This flexibility on choosing the prefilter can result in different discrete time models with different complexities for the signal processing algorithms to follow. As for example, a simpler whitening filter design which is needed for the success of several important blind equalization algorithms can be realized using this flexibility.

We establish the asymptotic equivalence, up to complex conjugation, of two problems: (i) determining the nearfield performance of a farfield beampattern specification, and (ii) determining the equivalent farfield beampattern corresponding to a nearfield beampattern specification. Using this reciprocity relationship we develop a computationally simple procedure to design a beamforming array to achieve a desired nearfield beampattern response. The superiority of this approach to existing methods, both in ease of design implementation and performance obtained, is illustrated by a design example.

Frequency invariant beamforming is array processing in which the spatial response remains constant (with respect to frequency) within a wide frequency band of interest. We present a new algorithm for adaptive broadband beamforming which solves a minimum variance beamforming problem, with a structural frequency invariant beampattern constraint. This constraint allows us to reduce the dimension of the adaptation problem. The proposed algorithm is a block adaptive LMS algorithm which uses only a fraction of the parameters of a conventional fully adaptive array. Hence, the computational complexity is reduced and the convergence speed is increased. A simulation example is presented to demonstrate the new algorithm.

A modified reduced-state sequencer estimator (RSSE) with a reverse-time structure is proposed for postcursor dominated impulse response channels. This structure can provide significant performance improvements over a conventional RSSE of similar complexity for a well-defined and practically motivated class of channels.

In adaptive channel equalization, transmitted symbol estimates at the equalizer output may be in error because of excessive channel noise, convergence of the equalizer to a "closed-eye" local minimum, or error propagation if the equalizer has a decision feedback structure. This paper is concerned with the detection of equalization errors (i.e., errors in transmitted symbol estimates) in a blindfolded manner whereby no direct access to the channel input is required. The detection problem is cast into a binary hypothesis testing framework. Assuming a linear communication channel that is time-invariant during the test interval, a relationship between the presence of equalization errors and time variations in the underlying linear model taking the transmitted symbol estimates to the equalizer input is established. Based on this relationship, a uniformly most powerful test is constructed to detect the presence of equalization errors in finite-length observations. Finite sample size and asymptotic detection performance of the test is studied. A method for estimating the equalization delay without direct access to the channel input is developed. The effectiveness of the test is illustrated by way of computer simulations.

This paper presents a method for nearfield frequency invariant broadband array beamforming. This means that we can design an array with associated signal processing to achieve a desired frequency invariant beam pattern (as a function of direction) at any nominal finite distance over an arbitrarily wide range of frequencies. The challenge here is to compensate accurately for the nearfield distortions (both magnitude and phase) which are more acute at the lower frequencies of the operating bandwidth than the higher frequencies. The methodology uses spherical harmonics to transform the nearfield broadband frequency invariant beampattern specification to an equivalent farfield frequency varying beampattern specification. A simulation example is presented to demonstrate the effectiveness of this method in producing a nearfield beam pattern which is frequency invariant over an octave bandwidth.

This paper presents a new method of beam-space direction of arrival (DOA) estimation for multiple far-field broadband signals. A novel multi-rate beamforming structure having a frequency invariant property is applied to the array outputs. Using this multi-rate structure, only a single vector of parameters is required to implement a desired frequency invariant beam pattern regardless of the bandwidth or number of sensors in the array. This frequency-invariant beamformer performs focusing over a very wide bandwidth without resorting to the frequency bin design approach of other methods in which the solution of a multiparameter optimisation problem is required to design the beam-space focusing matrices.

Two methods of implementing FIR filters for a frequency invariant beamformer are presented. Each of these methods uses a single underlying set of filter coefficients obtained directly from the desired beamformer response. One method uses multirate processing, and the other is based on a single sampling rate.

We present an off-line algorithm to recover the binary input sequence to a nonminimum phase communication channel using only the second- and fourth-order moments at the channel output. The algorithm, originally motivated by the well-known constant modulus algorithm (CMA), estimates the equaliser parameters directly without assuming that the channel input is an independent sequence. Consistency of the estimates for the channel inverse impulse response is established by means of a uniqueness theorem. An effective method for determining whether the equaliser has too many taps is proposed and illustrated by simulation examples.>

A variety of blind equalization algorithms exist. These algorithms, which draw on some theoretical justification for the demonstration or analysis of their purportedly ideal convergence properties, almost invariably rely on the input data being independent and identically distributed (i.i.d.). In contrast, in this paper we show that input correlation can have a marked effect on the character of algorithm convergence. We demonstrate that under suitable input data correlation and channels: (i) undesirable local minima present in the i.i.d. case are absent for certain correlated sources implying ideal global convergence for some situations and, (ii) the most commonly employed practical algorithm can exhibit ill-convergence to closed-eye minima even under the popular single spike initialization when an eye-opening equalizer parameterization is possible.>

A globally convergent blind equalization algorithm for QAM systems based on the minimization of a linearly-constrained convex function of the equalizer output is presented. Geometric methods are employed to establish a framework in which a proof of global convergence readily follows. The analysis assumes an arbitary linear constraint on the equalizer parameters and an arbitrary QAM constellation with minor assumptions on its distributional properties. Minimization is shown to occur either uniquely in the generic case or non-uniquely on a compact set in the equalizer parameter space that contains at least one open-eye solution. The framework also provides insight into the case of non-unique minimization and serves as a basis for strategies to avoid such behaviour.>

The algorithms for adaptive quantization and adaptive prediction in existing adaptive differential pulse code modulation (ADPCM) are distinct and decoupled. The designs of the two algorithms are based on the assumption that they act independently whereas, due to the feedback configuration, they must interact in some way. The authors present a preliminary investigation of a new design approach where they perform joint adaptation based on a common cost function, considering the overall system. A “backward” adaptive algorithm is presented and applied to a simple example to demonstrate the feasibility of the general approach.

An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Y. Sato (1975). An important generalization of the Sato algorithm with extensive analysis appears in the work of A. Benveniste et al. (1980). These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.>

The emulation of a nonadaptive, binary, decision-feedback equalizer, operating on a noiseless, finite impulse response channel, by a feedforward multilayer processor is considered. This feedforward perceptron equalizer comprises a triangular array of bandlimiting processing elements. The functional similarity between the two systems is exploited to obtain a tight upper bound on the probability of error as a function of the number of layers, using the theory of finite-state Markov processes.>

Blind equalization up to a constant gain of linear time-invariant channels is studied. Dropping the requirement of gain identification allows equalizer anchoring. This results in the elimination of a degree of freedom that causes ill-convergence of conventional blind equalizers, and affords the possibility of using simple update rules based on the stochastic approximation of output energy. Unlike conventional blind equalizers, truncations of the nonrecursive infinite-dimensional realizations of those equalizers inherit the convergence properties of their infinitely parametrized counterparts. A globally convergent blind recursive equalizer for channels without all-pass sections is obtained based on the exact equalization of the minimum-phase part of the channel and the identification of its nonminimum-phase zeros.>

A set of memoryless blind adaptive equalization algorithms for nonminimum phase complex data systems is proposed and evaluated on the basis of admissibility. The algorithms are based on variations of a minimax cost on the equalizer output and actually take the form of gradient descent of linearly constrained convex cost functions. These investigations represent a systematic study based on nontrivial generalizations of admissible designs developed for real data systems. It is shown that for one such candidate generalization admissibility holds.>

A natural generalization of the conventional decision feedback equalizer (DFE) based on block processing and maximum a posteriori decisions is presented. This block DFE is indexed by two parameters depending on the block length p and the number of decisions q>

It is shown, through the analysis of nullspace for the channel convolution matrix, that the behavior of a finitely parameterized Godard equalizer in general can never achieve or approximate the desirable global convergence performance of an infinitely parameterized noncausal Godard equalizer. Nullspace theory is supported by a simple example showing ill-convergence of the Godard algorithm.>

The emulation of a tuned decision feedback equalizer operating on a noiseless finite impulse response channel by a feedforward multilayer neural network is considered. The similarity between the two structures is exploited to obtain tight bounds on the probability of error for the neural nets as a function of the number of layers, using the theory of finite state Markov processes. A class of channels for which exact representation by a neural net of finite complexity is possible is established.>

Blind equalization of systems which contain a nonminimum phase component is a difficult task. Minimizing the energy (l/sub 2/ minimization) of the equalizer output (under a fixed tap constraint) cannot be guaranteed to open the eye (to reliably unscramble the message) because it tends to converge to an equalizer setting that contains a reflection of the unstable zeros inside the unit circle. It is shown that, in at least one simple setup involving a mixture of minimum and nonminimum phase elements, an l/sub infinity / minimization of the equalizer output is the appropriate criterion which should be minimized in order to successfully open the eye. Utilizing a finite impulse response equalizer constrained to have a unity coefficient on the center tap, it is shown that for a large enough dimension (depending on the closeness of the zeros of the channel to the unit circle) the eye will be opened. There is no simple (gradient) scheme to exactly implement the l/sub infinity / minimization. The use of a gradient l/sub p/ scheme for large p is proposed.>

The existence of stable undesirable equilibria for the Godard algorithm is demonstrated through a simple autoregressive (AR) channel model. These undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function, and thus permit the ill-convergence of the Godard algorithms which are stochastic gradient descent in nature. Simulation results confirm predicted misbehavior. For channel input of constant modulus, it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization. A criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached.>

Clarification is presented of the property that adaptive blind equalization algorithms may not always result in desired convergence. Those algorithms that can always converge (perhaps with the aid of a special initialization strategy) to desired equilibria offering an open eye pattern are classified as admissible. Various classes of existing blind equalization algorithms are described and the possibility of ill-convergence for these algorithms is illustrated. The general inadmissibility and the reason for earlier misconception regarding their admissibility development of new, admissible algorithms and certain initialization guidelines that can prevent weakly admissible algorithms from converging to undesirable equilibria is established.>

The authors define the DFE (decision feedback equalizer) system of interest and their finite-error-recovery-time problem. They present their basic result, which establishes that whenever the channel satisfies a simple frequency-domain constraint, the error recovery time of an ideal DFE is always finite. They also include four applications of this theorem, including analysis of a real channel. Convergence rates and explicit bounds, given an exponential overbound on the channel impulse response, are presented. Results of greater practical interest, where the authors relax most of the major idealized assumptions, are also given. The authors present the result for M-ary data and relate the error recovery time bound back to the binary case. A formula for the error probability, given a high signal-to-noise-ratio channel, is provided.>

Adaptive decision-directed equalizers can become locked for long periods onto incorrect equilibria. A test involving data available at the equalizer output is proposed for determining whether an equilibrium is correct or not, up to a fixed overall delay. If an independent sequence of random variables taking values +or-1 is the input to a finite impulse response filter, and the output of the filter is passed through a slicer, then the slicer output is uncorrelated if and only if it is a delayed version of the filter input. An analogous result for M-ary rather than binary data is outlined.>

In this correspondence we determine an upper bound on the error recovery time of a decision feedback equalizer (DFE) operating on a high signal to noise ratio channel of exponential impulse response to be used for binary transmission. This bound is related to the channel time constant and we show that exponential impulse response channels form a favourable class of channels with regard to DFE error recovery properties.

The performance of decision feedback equalizers (DFE's) working on a noiseless channel with correct tap weights is studied. We show that the space of channel parameters can accordingly be partitioned into a finite number of sets. The error recovery performance of a DFE is the same for all DFE's within one such set, and is determinable. We also discuss some tight bounds for recovery time statistics, which are particularly important when the number of equalizer taps is not small. We argue that minimum phase or near minimum phase character for the channel does not necessarily guarantee short recovery time.

A decision feedback equalizer (DFE) with correct tap weights operating on a noisy channel is considered. We show how the results concerning a noiseless channel can be extended to yield tight bounds on the stationary error probability performance for the noisy case. The effect of noise on DFE performance is classified according to the noise distribution and the channel parameters.