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IEEE Transactions on Signal ProcessingTable of contentsPresents the table of contents for this issue of the periodical.
Categories: Scientifical publications
Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and AlgorithmsThis paper considers the regularized Tyler's scatter estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler's estimators have been proposed in the literature and proved work effectively in the “large $p$ small $n$” scenario. Nevertheless, the existence and uniqueness properties of the estimators are not thoroughly studied, and in certain cases the algorithms may fail to converge. In this work, we provide a general result that analyzes the sufficient condition for the existence of a family of shrinkage Tyler's estimators, which quantitatively shows that regularization indeed reduces the number of required samples for estimation and the convergence of the algorithms for the estimators. For two specific shrinkage Tyler's estimators, we also proved that the condition is necessary and the estimator is unique. Finally, we show that the two estimators are actually equivalent. Numerical algorithms are also derived based on the majorizationminimization framework, under which the convergence is analyzed systematically.
Categories: Scientifical publications
Enabling D2D Communications Through Neighbor Discovery in LTE Cellular NetworksThis work studies the problem of neighbor discovery for devicetodevice (D2D) communications of LTE user equipments (UEs) in a modern cellular network. By listening to cellular uplink transmissions, UEs can detect potential D2D partners through a neighbor discovery process compatible with the standard LTE network protocol. We focus on neighbor discovery utilizing sounding reference signal (SRS) channel, which can be accessed by peer UEs that are LTEcompliant. Under the constraint of unknown channel statistics during uplink hearing, we propose joint neighbor detection and D2D channel estimation for listening UEs using the framework of sparse channel recovery. Composite hypothesis testing methods are further developed to refine neighbor detection accuracy. We evaluate the performance of our neighbor discovery methods under various network parameters to facilitate practical design and implementation of D2D in 4G cellular networks.
Categories: Scientifical publications
A SteeredResponse Power Algorithm Employing Hierarchical Search for Acoustic Source Localization Using Microphone ArraysThe localization of a speaker inside a closed environment is often approached by realtime processing of multiple audio signals captured by a set of microphones. One of the leading related methods for sound source localization, the steeredresponse power (SRP), searches for the point of maximum power over a spatial grid. Highaccuracy localization calls for a dense grid and/or many microphones, which tends to impractically increase computational requirements. This paper proposes a new method for sound source localization (called HSRP), which applies the SRP approach to space regions instead of grid points. This arrangement makes room for the use of a hierarchical search inspired by the branchandbound paradigm, which is guaranteed to find the global maximum in anechoic environments and shown experimentally to also work under reverberant conditions. Besides benefiting from the improved robustness of volumewise search over pointwise search as to reverberation effects, the HSRP attains high performance with manageable complexity. In particular, an experiment using a 16microphone array in a typical presentation room yielded localization errors of the order of 7 cm, and for a given fixed complexity, competing methods' errors are two to three times larger.
Categories: Scientifical publications
On the Epsilon Most Stringent Test Between Two Vector Lines in Gaussian NoiseThis paper addresses the problem of distinguishing between two vector lines observed through noisy measurements. This is a hypothesis testing problem where the two hypotheses are composite since the signal amplitudes are deterministic and not known. An ideal criterion of optimality, namely the most stringent test, consists in minimizing the maximum shortcoming of the test subject to a constrained false alarm probability. The maximum shortcoming corresponds to the maximum gap between the power function of the test and the envelope power function which is defined as the supremum of the power over all tests satisfying the prescribed false alarm probability. The most stringent test is unfortunately intractable. Hence, a suboptimal test, called the epsilon most stringent test, is proposed. This test has a very simple form and its statistical properties are expressed in closedform. It is numerically shown that the proposed test has a small loss of optimality and that it outperforms the generalized likelihood ratio test.
Categories: Scientifical publications
Distributed Compressed Sensing for Static and TimeVarying NetworksWe consider the problem of innetwork compressed sensing from distributed measurements. Every agent has a set of measurements of a signal $x$ , and the objective is for the agents to recover $x$ from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute innetwork computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with timevarying topologies. The network dynamics necessarily introduce inaccuracies to our innetwork computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for timevarying networks. Evaluations show that our distributed algorithms for both static and timevarying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.
Categories: Scientifical publications
A Linear Source Recovery Method for Underdetermined Mixtures of Uncorrelated ARModel Signals Without SparsenessConventional sparsenessbased approaches for instantaneous underdetermined blind source separation (UBSS) do not take into account the temporal structure of the source signals. In this work, we exploit the source temporal structure and propose a linear source recovery solution for the UBSS problem which does not require the source signals to be sparse. Assuming the source signals are uncorrelated and can be modeled by an autoregressive (AR) model, the proposed algorithm is able to estimate the source AR coefficients from the mixtures given the mixing matrix. We prove that the UBSS problem can be converted into a determined problem by combining the source AR model together with the original mixing equation to form a statespace model. The Kalman filter is then applied to obtain a linear source estimate in the minimum meansquared error sense. Simulation results using both synthetic AR signals and speech utterances show that the proposed algorithm achieves better separation performance compared with conventional sparsenessbased UBSS algorithms.
Categories: Scientifical publications
A DiscretizationFree Sparse and Parametric Approach for Linear Array Signal ProcessingDirection of arrival (DOA) estimation in array processing using uniform/sparse linear arrays is concerned in this paper. While sparse methods via approximate parameter discretization have been popular in the past decade, the discretization may cause problems, e.g., modeling error and increased computations due to dense sampling. In this paper, an exact discretizationfree method, named as sparse and parametric approach (SPA), is proposed for uniform and sparse linear arrays. SPA carries out parameter estimation in the continuous range based on wellestablished covariance fitting criteria and convex optimization. It guarantees to produce a sparse parameter estimate without discretization required by existing sparse methods. Theoretical analysis shows that the SPA parameter estimator is a largesnapshot realization of the maximum likelihood estimator and is statistically consistent (in the number of snapshots) under uncorrelated sources. Other merits of SPA include improved resolution, applicability to arbitrary number of snapshots, robustness to correlation of the sources and no requirement of userparameters. Numerical simulations are carried out to verify our analysis and demonstrate advantages of SPA compared to existing methods.
Categories: Scientifical publications
A Coordinate Descent Algorithm for Complex Joint Diagonalization Under Hermitian and Transpose CongruencesThis paper deals with the problem of joint complex matrix diagonalization by considering both the Hermitian and transpose congruences. We address the general case where the searched diagonalizing matrix is a priori nonunitary. Based on the minimization of a quadratic criterion, we propose a flexible algorithm in the sense that it allows to directly consider a rectangular diagonalizing matrix and to take into consideration both the Hermitian and transpose congruences within the same framework. The proposed algorithm is a coordinate descent algorithm that is based on an approximate criterion leading to the analytical derivation of the minima arguments. Computer simulations are drawn to illustrate the usefulness and performances of the algorithm and a comparison to stateoftheart algorithms is presented. Finally, an application to independent component analysis based on fourthorder statistics is also presented.
Categories: Scientifical publications
Compressive Sparsity Order Estimation for Wideband Cognitive Radio ReceiverCompressive sensing (CS) has been widely investigated in the cognitive radio (CR) literature in order to reduce the hardware cost of sensing wideband signals assuming prior knowledge of the sparsity pattern. However, the sparsity order of the channel occupancy is timevarying and the sampling rate of the CS receiver needs to be adjusted based on its value in order to fully exploit the potential of CSbased techniques. In this context, investigating blind sparsity order estimation (SOE) techniques is an open research issue. To address this, we study an eigenvaluebased compressive SOE technique using asymptotic random matrix theory. We carry out detailed theoretical analysis for the signal plus noise case to derive the asymptotic eigenvalue probability distribution function (aepdf) of the measured signal's covariance matrix for sparse signals. Subsequently, based on the derived aepdf expressions, we propose a technique to estimate the sparsity order of the wideband spectrum with compressive measurements using the maximum eigenvalue of the measured signal's covariance matrix. The performance of the proposed technique is evaluated in terms of normalized SOE Error (SOEE). It is shown that the sparsity order of the wideband spectrum can be reliably estimated using the proposed technique for a variety of scenarios.
Categories: Scientifical publications
Joint Sparse Recovery Method for Compressed Sensing With Structured Dictionary MismatchesIn traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper, we consider a signal model where each column in the dictionary matrix is affected by a structured noise. This formulation is common in directionofarrival (DOA) estimation of offgrid targets, encountered in both radar systems and array processing. We propose to use joint sparse signal recovery to solve the compressed sensing problem with structured dictionary mismatches and also give an analytical performance bound on this joint sparse recovery. We show that, under mild conditions, the reconstruction error of the original sparse signal is bounded by both the sparsity and the noise level in the measurement model. Moreover, we implement fast firstorder algorithms to speed up the computing process. Numerical examples demonstrate the good performance of the proposed algorithm and also show that the jointsparse recovery method yields a better reconstruction result than existing methods. By implementing the joint sparse recovery method, the accuracy and efficiency of DOA estimation are improved in both passive and active sensing cases.
Categories: Scientifical publications
TimeSwitching Uplink NetworkCoded Cooperative Communication With Downlink Energy TransferIn this work, we consider a multiuser cooperative wireless network where the energyconstrained sources have independent information to transmit to a common destination, which is assumed to be externally powered and responsible for transferring energy wirelessly to the sources. The source nodes may cooperate, under either decodeandforward or network codingbased protocols. Taking into account the fact that the energy harvested by the source nodes is a function of the fading realization of interuser channels and userdestination channels, we obtain a closedform approximation for the system outage probability, as well as an approximation for the optimal energy transfer period that minimizes such outage probability. It is also shown that, even though the achievable diversity order is reduced due to wireless energy transfer process, it is very close to the one achieved for a network without energy constraints. Numerical results are also presented to validate the theoretical results.
Categories: Scientifical publications
SuperResolution Reconstruction in FrequencyDomain OpticalCoherence Tomography Using the FiniteRateofInnovation PrincipleThe standard approach to signal reconstruction in frequencydomain opticalcoherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new superresolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finiterateofinnovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the highresolution Prony method and show that highquality, superresolved reconstruction is possible with fewer measurements (about onefourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singularvalue decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the CramérRao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signaltoreconstruction noise offered by the proposed method in comparison with the standard approach.
Categories: Scientifical publications
Optimal Spectrum Leasing and Resource Sharing in TwoWay Relay NetworksAssuming a bidirectional relay assisted network, we study the problem of optimal resource sharing between two transceiver pairs. One pair, referred to as the primary pair, is considered to be the owner of the spectral resources. The rates of the two transceivers in this pair must be guaranteed to be greater than a predefined threshold. The second pair, called the secondary pair, is assumed to own the relay infrastructure. The secondary network allows the primary pair to use the relays to establish a bidirectional communication between its transceivers. In exchange for this cooperation, the primary pair assigns a portion of its resources to the secondary pair, thereby enabling a twoway communication between the secondary transceivers. Assuming amplifyandforward relaying scheme, the relays collectively build two network beamformers each of which enables communication between the two transceivers in one pair. Aiming to optimally calculate the parameters of the two networks, we study three different design problems. The first approach relies on maximizing the smaller of the secondary transceiver rates subject to two separate constraints on the total power levels consumed in the primary and the secondary networks while providing a minimum data rate to the primary pair. In the second approach, we consider a constraint on the average total power consumed in both networks, while maximizing the smaller of the secondary transceiver rates. The third approach extends the second method to materialize a spectrum leasing and sharing scheme for the case when the primary network is active with a certain probability.
Categories: Scientifical publications
Optimal Algorithms for <formula formulatype="inline"> <tex Notation="TeX">$L_{1}$</tex></formula>subspace Signal ProcessingWe describe ways to define and calculate $L_{1}$norm signal subspaces that are less sensitive to outlying data than $L_{2}$ calculated subspaces. We start with the computation of the $L_{1}$ maximumprojection principal component of a data matrix containing $N$ signal samples of dimension $D$. We show that while the general problem is formally NPhard in asymptotically large $N$, $D$, the case of engineering interest of fixed dimension $D$ and asymptotically large sample size $N$ is not. In particular, for the case where the sample size is less than the fixed dimension $(N < D)$, we present in explicit form an optimal algorithm of computational cost $2^{N}$. For the case $N geq D$, we present an optimal algorithm of complexity ${cal O}(N^{D})$ . We generalize to multiple $L_{1}$ maxprojection components and present an explicit optimal $L_{1}$ subspace calculation algorithm of complexity ${cal O}(N^{DKK+1})$ wh
re $K$ is the desired number of $L_{1}$ principal components (subspace rank). We conclude with illustrations of $L_{1}$subspace signal processing in the fields of data dimensionality reduction, directionofarrival estimation, and image conditioning/restoration.
Categories: Scientifical publications
OMP Based Joint Sparsity Pattern Recovery Under Communication ConstraintsWe address the problem of joint sparsity pattern recovery based on multiple measurement vectors (MMVs) in resource constrained distributed networks. We assume that distributed nodes observe sparse signals that share a common (but unknown) sparsity pattern. Each node is assumed to sample the sparse signals via different sensing matrices in general. In many distributed communication networks, it is often required that joint sparse recovery be performed under inherent resource constraints such as communication bandwidth and transmit/processing power. We propose two approaches to take the communication constraints into account while performing joint sparsity pattern recovery. First, we explore the use of a shared multiple access channel (MAC) in forwarding observation vectors from each node to a fusion center. With MAC, while the bandwidth requirement does not depend on the number of nodes, the fusion center has access to only linear combinations of the observations. We discuss the conditions under which the common sparsity pattern can be recovered reliably. Second, we develop two efficient collaborative algorithms based on orthogonal matching pursuit (OMP), to jointly estimate the common sparsity pattern in a decentralized manner with a low communication overhead. In the proposed algorithms, each node collaborates with neighboring nodes by sharing a small amount of information at different stages while estimating the indices of the true sparsity pattern in a greedy manner. The tradeoff between the performance gain and the communication overhead of the proposed algorithms is demonstrated via simulations.
Categories: Scientifical publications
The Restricted Isometry Property for Banded Random MatricesIn this paper, we investigate the problem of determining the conditions under which the restricted isometry property (RIP) is satisfied for a particular type of matrix referred to in here as a banded random matrix (BRM). Such matrices have been recognized as suitable models for a number of compressivesensing based sampling architectures, including the interleaved random demodulator, the random demodulator, the parallel noninterleaved random demodulator, the random sampler, and the periodic nonuniform sampler. It is thus important to establish the conditions under which the BRM satisfies the RIP; to our knowledge, this question has not been theoretically addressed in the literature. If the resulting conditions are satisfied, full signal recovery using a convex optimization algorithm is guaranteed. The specific objective of this research is to determine the conditions under which the RIP is satisfied for two possible sampling matricies: a BRM and a BRM multiplied by the discrete Fourier matrix.
Categories: Scientifical publications
VariableRate Transmission for MIMO TimeCorrelated Channels With Limited FeedbackIn this paper we consider variablerate transmission for timecorrelated MIMO (multiinput multioutput) channels with limited feedback. The number of bits loaded on each subchannel of the MIMO system is dynamically assigned according to the current channel condition and fed back to the transmitter. As the channel is timecorrelated, bit loading is a vector signal that is also timecorrelated. We propose to feedback bit loading using predictive coding, which is known to be a powerful quantization technique when the underlying signal is correlated in time. Assuming the channel is a firstorder GaussMarkov random process, we derive the predictor for the bit loading to be coded and analyze the corresponding prediction error variance when the channel is varying slowly. By exploiting the prediction error variance, we adapt the quantizer of the prediction error to have a smaller quantization error. Furthermore we show that the prediction error variance is proportional to a term that depends only on the timecorrelation coefficient. This leads to the conclusion that, a codebook that is designed for a particular time correlation coefficient can be easily modified to a codebook for a different correlation coefficient without redesign. Simulations are presented to demonstrate that the proposed predictive coding can achieve a very good approximation of the desired transmission rate with a very low feedback rate.
Categories: Scientifical publications
DivergenceBased Soft Decision for Error Resilient Decentralized Signal DetectionIn this paper, we consider decentralized detection where the transmission of local softdecisions of the secondary users (SUs) to the fusion center (FC) is both ratelimited and errorprone. The quantized data to be sent from SUs should not only carry the local information but also need to be resilient to channel errors. With the assumption of independent and identical secondary user observations conditioned on signal hypothesis and binary symmetric channels (BSC) between SUs and the FC, we design local quantizers at a SU, based on two divergence metrics, namely Kullback–Leibler (KL) and Chernoff. Using convex duality, we show that a twostage algorithm can be developed to take care of the quantization thresholding, codeword assignment, and error resilience. Specifically, we obtain the following results. First, we show that the proposed quantizer obtains increased divergence between the distributions of the demodulated data at the FC, when compared to the maximum entropy quantizer design. We also point out the fallacy of previously reported Gray code assignment to quantized data. Second, the quantizer optimally picks the repetition codeword in the case of “ideal” sensing at the sensors. Similar “channel blind” optimal quantizer design was observed in the literature for singlesensor case. Third, we derive new bit error probability (BEP) wall expression for $D$bits softquantization, for specified probabilities of errors at the FC. The new result shows whether and when a majority logic rule is optimal at the FC.
Categories: Scientifical publications
Performance Metrics, Sampling Schemes, and Detection Algorithms for Wideband Spectrum SensingIn this paper, we study the problem of wideband spectrum sensing for cognitive radio networks by partitioning it into four fundamental elements: system modeling, performance metrics, sampling schemes, and detection algorithms. Each element can potentially couple the individual channels so that designs for wideband spectrum sensing should consider the four elements jointly. We propose the $p$sparse model for the primary occupancies and study three uniform sampling schemes for wideband spectrum sensing, specifically, partialband Nyquist sampling, sequential narrowband Nyquist sampling, and integer undersampling. We suggest new performance metrics more appropriate for wideband spectrum sensing, specifically, the probability of insufficient spectrum opportunity and the probability of excessive interference opportunity. We also develop detection algorithms that effectively tradeoff these metrics. Our results indicate that for performance metrics that couple the individual channels, multichannel detection algorithms have a significant advantage over channelbychannel detection algorithms even for wideband Nyquist sampling. Furthermore, integer undersampling, which corresponds to the simplest subNyquist sampling scheme, along with suitable detection algorithms exhibits appealing detection performance in the regime that better protects the primary system.
Categories: Scientifical publications
