This letter addresses the quadratic equality constrained least squares (QEC-LS) problem, a class of non-convex optimization problems that arise in various signal processing and communication applications. We revisit the alternating direction method of multipliers (ADMM) approach to QEC-LS problem and investigate its convergence and efficiency. Despite the inherent non-convexity, the proposed ADMM algorithm is proved to converge globally only requiring the quadratic term equal to a positive constant. Numerical results demonstrate that our method achieves global optimality with significantly reduced complexity compared to existing approaches such as semidefinite relaxation and primal-dual methods.

In recent years, fusing high-resolution multispectral images (HR-MSIs) and low-resolution hyperspectral images (LR-HSIs) has become a widely used approach for hyperspectral image super-resolution (HSI-SR). The deep unfolding framework has attracted significant attention thanks to its ability to formulate the problem into a data module and a prior module. However, there are still two critical issues that hinder the performance enhancement of the existing methods: 1) Parameters in the data module are fixed (though learnable) at each iteration, i.e., lacking the adaptivity to comprehensive data; 2) The Transformer in the prior module cannot effectively capture high-frequency information. To resolve these issues, we propose a Content-Adaptive Unfolding Wavelet Transformer (CAUWT) for HSI-SR, where the parameters are adaptively learned based on the reconstructed HSI at each iteration. Moreover, we propose a novel Wavelet-Assisted Transformer (WAT), by integrating the Discrete Wavelet Transform (DWT) and the Hybrid Spectral-Spatial Attention Block (HSSAB) to further upgrade the high-frequency information quality of HSI at no cost of extra branch structures, where the former is for multi-scale and multi-frequency details and the latter is for correlations between and within sub-band components. Extensive experiments performed on both simulated and real datasets well demonstrate the effectiveness of the proposed method. In comparison with mainstream HSI-SR methods, our method exhibits superior performance and lower computational overhead.

This paper investigates the rate outage constrained (ROC) energy efficiency (EE) under multiple-input single-output (MISO) interference channels, where only channel distribution information (CDI) is available at base stations (BSs). An EE maximization problem is formulated under the constraints of tolerable rate outage probability of each user and the power budget of each BS. Due to the computationally intractable form of the considered problem, two equivalent formulations are derived and four algorithms are proposed, where two are based on the block successive upper bound minimization (BSUM) method and the other two are based on the successive convex approximation (SCA) method. Further, the philosophies behind the BSUM-based algorithms and the SCA-based algorithms are analyzed. Numerical results demonstrate the efficacy of the proposed algorithms, while the BSUM-based algorithms are much more computationally efficient than all the state-of-the-art algorithms, as long as all the coupling requirements on quality of service (like ROC transmission) can be fused into EE. Besides, the impacts of power budget, circuit power and tolerable outage probability on the ROC EE are revealed and discussed.

Federated learning (FL) has been recognized as a rapidly growing research area, where the model is trained over massively distributed clients under the orchestration of a parameter server (PS) without sharing clients’ data. This paper delves into a class of federated problems characterized by non-convex and non-smooth loss functions, that are prevalent in FL applications but challenging to handle due to their intricate non-convexity and non-smoothness nature and the conflicting requirements on communication efficiency and privacy protection. In this paper, we propose a novel federated primal-dual algorithm with bidirectional model sparsification tailored for non-convex and non-smooth FL problems, and differential privacy is applied for privacy guarantee. Its unique insightful properties and some privacy and convergence analyses are also presented as the FL algorithm design guidelines. Extensive experiments on real-world data are conducted to demonstrate the effectiveness of the proposed algorithm and much superior performance than some state-of-the-art FL algorithms, together with the validation of all the analytical results and properties.

In this article, we investigate the federated clustering (FedC) problem, which aims to accurately partition unlabeled data samples distributed over massive clients into finite clusters under the orchestration of a parameter server (PS), meanwhile considering data privacy. Though it is an NP-hard optimization problem involving real variables denoting cluster centroids and binary variables denoting the cluster membership of each data sample, we judiciously reformulate the FedC problem into a nonconvex optimization problem with only one convex constraint, accordingly yielding a soft clustering solution. Then, a novel FedC algorithm using differential privacy (DP) technique, referred to as DP- FedC, is proposed in which partial clients participation (PCP) and multiple local model updating steps are also considered. Furthermore, various attributes of the proposed DP- FedC are obtained through theoretical analyses of privacy protection and convergence rate, especially for the case of nonidentically and independently distributed (non-i.i.d.) data, that ideally serve as the guidelines for the design of the proposed DP- FedC. Then, some experimental results on two real datasets are provided to demonstrate the efficacy of the proposed DP- FedC together with its much superior performance over some state-of-the-art FedC algorithms, and the consistency with all the presented analytical results.

In recent years, fusing high spatial resolution multispectral images (HR-MSIs) and low spatial resolution hyperspectral images (LR-HSIs) has become a widely used approach for hyperspectral image super-resolution (HSI-SR). Various unsupervised HSI-SR methods based on deep image prior (DIP) have gained wide popularity thanks to no pre-training requirement. However, DIP-based methods often demonstrate mediocre performance in extracting latent information from the data. To resolve this performance deficiency, we propose a coupled spatial and spectral deep image priors (CS2DIPs) method for the fusion of an HR-MSI and an LR-HSI into an HR-HSI. Specifically, we integrate the nonnegative matrix-vector tensor factorization (NMVTF) into the DIP framework to jointly learn the abundance tensor and spectral feature matrix. The two coupled DIPs are designed to capture essential spatial and spectral features in parallel from the observed HR-MSI and LR-HSI, respectively, which are then used to guide the generation of the abundance tensor and spectral signature matrix for the fusion of the HSI-SR by mode-3 tensor product, meanwhile taking some inherent physical constraints into account. Free from any training data, the proposed CS2DIPs can effectively capture rich spatial and spectral information. As a result, it exhibits much superior performance and convergence speed over most existing DIP-based methods. Extensive experiments are provided to demonstrate its state-of-the-art overall performance including comparison with benchmark peer methods.

Hyperspectral tensor completion (HTC) for remote sensing, critical for advancing space exploration and other satellite imaging technologies, has drawn considerable attention from recent machine learning community. Hyperspectral image (HSI) contains a wide range of narrowly spaced spectral bands hence forming unique electrical magnetic signatures for distinct materials, and thus plays an irreplaceable role in remote material identification. Nevertheless, remotely acquired HSIs are of low data purity and quite often incompletely observed or corrupted during transmission. Therefore, completing the 3-D hyperspectral tensor, involving two spatial dimensions and one spectral dimension, is a crucial signal processing task for facilitating the subsequent applications. Benchmark HTC methods rely on either supervised learning or nonconvex optimization. As reported in recent machine learning literature, John ellipsoid (JE) in functional analysis is a fundamental topology for effective hyperspectral analysis. We therefore attempt to adopt this key topology in this work, but this induces a dilemma that the computation of JE requires the complete information of the entire HSI tensor that is, however, unavailable under the HTC problem setting. We resolve the dilemma, decouple HTC into convex subproblems ensuring computational efficiency, and show state-of-the-art HTC performances of our algorithm. We also demonstrate that our method has improved the subsequent land cover classification accuracy on the recovered hyperspectral tensor.

This paper investigates the system model and the transmit beamforming design for the Cell-Free massive multi-input multi-output (MIMO) integrated sensing and communication (ISAC) system. The impact of the uncertainty of the target locations on the propagation of wireless signals is considered during both uplink and downlink phases, and especially, the main statistics of the MIMO channel estimation error are theoretically derived in the closed-form fashion. A fundamental performance metric, termed communication-sensing (C-S) region, is defined for the considered system via three cases, i.e., the sensing-only case, the communication-only case and the ISAC case. The transmit beamforming design problems for the three cases are respectively carried out through different reformulations, e.g., the Lagrangian dual transform and the quadratic fractional transform, and some combinations of the block coordinate descent method and the successive convex approximation method. Numerical results present a 3-dimensional C-S region with a dynamic number of access points to illustrate the trade-off between communication and radar sensing. The advantage for radar sensing of the Cell-Free massive MIMO system is also studied via a comparison with the traditional cellular system. Finally, the efficacy of the proposed beamforming schemes is validated in comparison with zero-forcing and maximum ratio transmission schemes.

This paper investigates space-aerial assisted mixed cloud-edge computing services for space-aerial integrated networks, where unmanned aerial vehicles (UAVs) provide edge computing services and one satellite (SAT) provides ubiquitous cloud computing services. To effectively and efficiently schedule such services under constraints on the available resources of computational capacity, energy, and communications of UAVs and the SAT, a problem for minimizing the total computing and offloading delay is formulated. A learning algorithm for handling the reformulated problem is proposed that alternatively performs convex optimization based computation capacity allocation (involving real variables) and double deep Q-learning (DDQL) based task assignment (involving binary variables) among all UAVs and the SAT. Extensive simulation results are presented to demonstrate that the efficacy of the proposed algorithm is significantly superior over some state-of-the-art reinforcement learning-based methods in terms of the algorithm running time and system scalability in the training stage and total computing and offloading delay in the testing stage.

Over the past decade, many low-rank models, factorizations, or approximations have been applied to the restoration of hyperspectral images (HSIs) (e.g., denoising, inpainting, and super-resolution) from their incomplete and/or noisy measurements. Recently, deep learning (DL) has been shown to be a powerful method for solving inverse problems (including HSI restoration), but a large amount of training data is required. Since this is not possible for HSIs, unlike red green blue (RGB) images, in this work, a novel unsupervised framework for hyperspectral inpainting (HI) is proposed that can be implemented using an untrained convolutional neural network (CNN) for deep image prior (DIP), together with a recently reported differentiable regularization for the data rank and$\ell _{2}$-norm squared loss function. Based on the proposed framework, we come up with a novel HI algorithm [denoted as deep low-rank hyperspectral inpainting (DLRHyIn)] and a robust DLRHyIn (denoted as R-DLRHyIn) which is robust against outliers, where the latter differs from the former only in the Huber loss function (HLF) (which has been justified robust to mixed noise) used instead. Then some simulation results and real-data experiments are provided to demonstrate the effectiveness of the proposed DLRHyIn and R-DLRHyIn. Finally, we draw some conclusions.

For multi-user satellite Internet of Things (IoT) systems operating at lower signal-to-noise ratio, spread spectrum techniques are usually used to combat narrowband interference. In addition, the communication performance in the spread spectrum system depends on the anti-jamming ability of the spreading codes (SCs). Therefore, how to design the SCs scheduling strategies under users' requirements and resource constraints has become a crucial problem for satellite IoT systems. In this paper, communication rewards and scheduling delays are introduced as gauges to measure the scheduling performance of the satellite gateway station control center (SGSCC). Specifically, SGSCC must efficiently and effectively allocate limited available SCs over terminal gateways under request at each transmission time slot. The SCs scheduling problem is formulated as a Markov Decision Process (MDP) along with the observed environments composed of resource status and user request status. Then a deep reinforcement learning scheduling algorithm is devised by embedding the idea of Long Short-Term Memory (LSTM) in the standard Double Deep Q-learning (DDQN). Simulation results show that the proposed algorithm can achieve much better performance than traditional algorithms in terms of communication rewards and scheduling delays. Finally, we draw some conclusions.

Distributed clustering is emerging along with the advent of the era of big data. However, most existing established distributed clustering methods focus on problems caused by a large amount of data rather than caused by the large dimension of data. Consequently, they suffer the “curse” of dimensionality (e.g., poor performance and heavy network overhead) when high-dimensional (HD) data are clustered. In this article, we propose a distributed algorithm, referred to as Local Density Subspace Distributed Clustering (LDSDC) algorithm, to cluster large-scale HD data, motivated by the idea that a local dense region of a HD dataset is usually distributed in a low-dimensional (LD) subspace. LDSDC follows a local-global-local processing structure, including grouping of local dense regions (atom clusters) followed by subspace Gaussian model (SGM) fitting (flexible and scalable to data dimension) at each sub-site, merging of atom clusters at every sub-site according to the merging result broadcast from the global site. Moreover, we propose a fast method to estimate the parameters of SGM for HD data, together with its convergence proof. We evaluate LDSDC on both synthetic and real datasets and compare it with four state-of-the-art methods. The experimental results demonstrate that the proposed LDSDC yields best overall performance.

Change detection (CD), enabled by multitemporal multispectral satellite imagery, has many important Earth observation missions such as land cover/use monitoring, for which we observe that change regions are relatively smaller than those caused by disaster (e.g., forest fire) with patterns typically composed of a number of smooth regions. These observations are considered in our new CD criterion, which can effectively mitigate the artifacts and speckle noise suffered by existing statistic-based and difference image (DI) analysis based methods. The proposed CD criterion amounts to a large-scale non-convex optimization, which is first reformulated using the convex relaxation trick with associated change map interpreted in the probability sense, followed by adopting an efficient convex solver known as alternating direction method of multipliers (ADMM). The resulted probabilistic change map would be more practical, and can be thresholded at 0.5 to yield the conventional binary-valued one. We also reveal a link between the proposed criterion and the DI-based criterion, and demonstrate the outstanding performance of our fully unsupervised CD algorithm qualitatively and quantitatively.

Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral unmixing in remote sensing and topic discovery in machine learning, to name a few. In this paper we develop a new theoretical SSMF framework whose idea is to study a maximum volume ellipsoid inscribed in the convex hull of the data points. This maximum volume inscribed ellipsoid (MVIE) idea has not been attempted in prior literature, and we show a sufficient condition under which the MVIE framework guarantees exact recovery of the factors. The sufficient recovery condition we show for MVIE is much more relaxed than that of separable nonnegative matrix factorization (or pure-pixel search); coincidentally, it is also identical to that of minimum volume enclosing simplex, which is known to be a powerful SSMF framework for nonseparable problem instances. We also show that MVIE can be practically implemented by performing facet enumeration and then by solving a convex optimization problem. The potential of the MVIE framework is illustrated by numerical results.

Fusing a low-spatial-resolution hyperspectral data with a high-spatial-resolution (HSR) multispectral data has been recognized as an economical approach for obtaining HSR hyperspectral data, which is important to accurate identification and classification of the underlying materials. A natural and promising fusion criterion, called coupled nonnegative matrix factorization (CNMF), has been reported that can yield high-quality fused data. However, the CNMF criterion amounts to an ill-posed inverse problem, and hence, advisable regularization can be considered for further upgrading its fusion performance. Besides the commonly used sparsity-promoting regularization, we also incorporate the well-known sum-of-squared-distances regularizer, which serves as a convex surrogate of the volume of the simplex of materials’ spectral signature vectors (i.e., endmembers), into the CNMF criterion, thereby leading to a convex formulation of the fusion problem. Then, thanks to the biconvexity of the problem nature, we decouple it into two convex subproblems, which are then, respectively, solved by two carefully designed alternating direction method of multipliers (ADMM) algorithms. Closed-form expressions for all the ADMM iterates are derived via convex optimization theories (e.g., Karush–Kuhn–Tucker conditions), and furthermore, some matrix structures are employed to obtain alternative expressions with much lower computational complexities, thus suitable for practical applications. Some experimental results are provided to demonstrate the superior fusion performance of the proposed algorithm over state-of-the-art methods.

While non-negative blind source separation (nBSS) has found many successful applications in science and engineering, model order selection, determining the number of sources, remains a critical yet unresolved problem. Various model order selection methods have been proposed and applied to real-world data sets but with limited success, with both order over- and under-estimation reported. By studying existing schemes, we have found that the unsatisfactory results are mainly due to invalid assumptions, model oversimplification, subjective thresholding, and/or to assumptions made solely for mathematical convenience. Building on our earlier work that reformulated model order selection for nBSS with more realistic assumptions and models, we report a newly and formally revised model order selection criterion rooted in the minimum description length (MDL) principle. Adopting widely invoked assumptions for achieving a unique nBSS solution, we consider the mixing matrix as consisting of deterministic unknowns, with the source signals following a multivariate Dirichlet distribution. We derive a computationally efficient, stochastic algorithm to obtain approximate maximum-likelihood estimates of model parameters and apply Monte Carlo integration to determine the description length. Our modeling and estimation strategy exploits the characteristic geometry of the data simplex in nBSS. We validate our nBSS-MDL criterion through extensive simulation studies and on four real-world data sets, demonstrating its strong performance and general applicability to nBSS. The proposed nBSS-MDL criterion consistently detects the true number of sources, in all of our case studies.

In this paper, we consider a decode-and-forward (DF) full-duplex relay (FDR)-aided downlink wireless communication system consisting of one base station (BS) equipped with large scale antennas and multiple MIMO FDRs, which have been recognized as essential techniques in the fifth generation (5G) wireless communications. In view of the system performance not only limited by self-interference (SI) and inter-relay interference (IRI) caused by FDRs but also by channel state information uncertainty, a distributed worst-case robust design of FDR beamforming and total power minimization for downlink transmission is proposed subject to relays' and users' target rates, a centralized solution is presented, and then its distributed implementation using alternating direction method of multipliers (ADMM) is presented as well. Finally, some simulation results are provided to demonstrate the efficacy of the proposed algorithm.

Heterogeneous network (HetNet), employing massive multiple-input multiple-output (MEMO), has been recognized as a promising technique to enhance network capacity, and to improve energy efficiency for fifth generation (5G) of wireless communications. However, most existing schemes for coordinated beamforming (CoBF) for a massive MIMO HetNet unrealistically assume the availability of perfect channel state information (CSQ on one hand, and cascade of each antenna with a distinct radio frequency (RF) chain in massive MEMO is neither power nor cost efficient on the other hand. In this paper, we consider a massive MEMO enabled HetNet framework, consisting of one macrocell base station (MBS) equipped with an analog beamformer, followed by a digital beamformer, and one femtocell base station (FBS) equipped with a digital beamformer. In the presence of Gaussian CSI errors, we propose a robust hybrid CoBF (HyCoBF) design, including an analog beamforming design for MBS and a digital CoBF design for both MBS and FBS. To this end, an outage probability constrained robust HyCoBF problem is formulated by minimizing the total transmit power. The analog beamforming mechanism at MBS is a newly devised low-complexity beam selection scheme by selecting analog beams from a discrete Fourier transform (DFT) matrix codebook. Then a conservative approximate CoBF solution is obtained via semidefinite relaxation (SDR) and an extended Bernsteintype inequality. Finally, numerical simulations are provided to demonstrate the efficacy of the proposed HyCoBF algorithm.

Optimizing the system performance of a wireless powered communication network (WPCN) has been extensively studied recently, by incorporating space, frequency and/or time diversity of the channel, etc. However, the time diversity, inherently imposes the causality constraint on the channel state information (CSI) in the system design. Hence development of effective and efficient online algorithms for optimizing the system performance is essential but challenging. In this paper, a WPCN with two single-antenna access points (APs) and a single-antenna user, wherein the "harvest and then transmit" over multiple time blocks is considered for the resource allocation (time and power in each time block) by maximizing the system throughput rate. To this end, a low-complexity online algorithm is proposed. Some simulation results are provided to support its efficacy.

This paper considers the energy-efficient precoding matrix design for relay-aided multiuser downlink multiple-input single-output wireless systems. The precoders of the base station (BS) and the relay station (RS) are designed to maximize the transmit energy efficiency, defined as the ratio between the system sum rate and the total power consumption, under the quality-of-service constraints of the users and the transmit power constraints on the BS and the RS. In view of the fact that this precoder design problem is a nonconvex fractional programming, a successive Dinkelbach and convex approximation (SDCA) algorithm is proposed to handle this problem. Simulation results are provided to demonstrate the effectiveness of the proposed SDCA algorithm, and significant EE improvement as the number of antennas at the BS and the RS increases.

Hyperspectral unmixing (HU) is an essential signal processing procedure for blindly extracting the hidden spectral signatures of materials (or endmembers) from observed hyperspectral imaging data. Craig's criterion, stating that the vertices of the minimum volume enclosing simplex (MVES) of the data cloud yield high-fidelity endmember estimates, has been widely used for designing endmember extraction algorithms (EEAs) especially in the scenario of no pure pixels. However, most Craig-criterion-based EEAs generally suffer from high computational complexity due to heavy simplex volume computations, and performance sensitivity to random initialization, etc. In this work, based on the idea that Craig's simplex with N vertices can be defined by N associated hyperplanes, we develop a fast and reproducible EEA by identifying these hyperplanes from N(N - 1) data pixels extracted via simple and effective linear algebraic formulations, together with endmember identifiability analysis. Some Monte Carlo simulations are provided to demonstrate the superior efficacy of the proposed EEA over state-of-the-art Craig-criterion-based EEAs in both computational efficiency and estimation accuracy.

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no-pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are supported by numerical simulation results.

Max-min-fairness (MMF), which concerns optimizing the worst signal-to-interference-plus-noise ratio (SINR) performance of receivers, is a popular transmitter design criterion in multiuser communications. In the single-input single-output (SISO), multiple-input single-output (MISO), and single-input multiple-output (SIMO) interference channels with perfect channel state information at the transmitters, it has been shown that the MMF power allocation and beamforming design problems are polynomial-time solvable, and efficient optimization algorithms exist. In this paper, we assume that the transmitters have channel distribution information only, and study the MMF coordinated beamforming design problem under probabilistic SINR outage constraints. While such a problem is non-convex, it was not clear if it is polynomial-time solvable. We propose a complexity analysis, showing that the SINR outage constrained MMF problem is polynomial-time solvable in the SISO scenario whereas it is NP-hard in the MISO scenario. The NP-hardness is established by showing that the MISO MMF problem is at least as difficult as the 3-satisfiability problem which is NP-complete.

This paper considers beamforming designs for weighted sum rate maximization (WSRM) in a multiple-input single-output interference channel subject to probability constraints on the rate outage. We claim that the outage probability constrained WSRM problem is an NP-hard problem, and therefore focus on devising efficient approximation methods. In particular, inspired by an insightful problem reformulation, a pricing-based sequential optimization (PSO) algorithm is proposed for efficiently handling the considered outage constrained WSRM problem. We show that the proposed PSO algorithm has semi-analytical beamforming solutions in each iteration, and hence can be efficiently implemented. Moreover, the PSO algorithm upon convergence attains a point satisfying Karush-Kuhn-Tucker (KKT) conditions of the original outage constrained problem. Simulation results demonstrate that the proposed PSO algorithm not only yields competing weighted sum rate performance, but also is computationally more efficient than the existing method [1].

Hyperspectral unmixing (HU) is a process to extract the underlying endmember signatures (or simply endmembers) and the corresponding proportions (abundances) from the observed hyperspectral data cloud. The Craig's criterion (minimum volume simplex enclosing the data cloud) and the Winter's criterion (maximum volume simplex inside the data cloud) are widely used for HU. For perfect identifiability of the endmembers, we have recently shown in [1] that the presence of pure pixels (pixels fully contributed by a single endmember) for all endmembers is both necessary and sufficient condition for Winter's criterion, and is a sufficient condition for Craig's criterion. A necessary condition for endmember identifiability (EI) when using Craig's criterion remains unsolved even for three-endmember case. In this work, considering a three-endmember scenario, we endeavor a statistical analysis to identify a necessary and statistically sufficient condition on the purity level (a measure of mixing levels of the endmembers) of the data, so that Craig's criterion can guarantee perfect identification of endmembers. Precisely, we prove that a purity level strictly greater than 1/√(2) is necessary for EI, while the same is sufficient for EI with probability-1. Since the presence of pure pixels is a very strong requirement which is seldom true in practice, the results of this analysis foster the practical applicability of Craig's criterion over Winter's criterion, to real-world problems.

In this paper, we consider a two-tier heterogeneous network that locally consists of a multi-antenna macrocell base station and a multi-antenna femtocell base station (FBS) each serving separate single-antenna users. We investigate an optimal transmission strategy with maximum degree of freedom for transmit power minimization of the FBS under outage-based quality-of-service (QoS) constraints for the femtocell user equipment (FUE) and macrocell user equipment (MUE). Specifically, we examine the scenario that the FBS receives no instantaneous channel estimate from the FUE, and relies on only statistical information of downlink multiple-input single-output (MISO) channels. Although the outage constrained problem has no closed-form probabilistic constraints and may not be convex in general, we propose a transmission strategy and prove its optimality under a given condition. Our simulation results also demonstrate that the proposed transmission strategy can significantly save power compared to beamforming strategies.

This work considers worst-case utility maximization (WCUM) problem for a downlink wireless system where a multiantenna base station communicates with multiple single-antenna users. Specifically, we jointly design transmit covariance matrices for each user to robustly maximize the worst-case (i.e., minimum) system utility function under channel estimation errors bounded within a spherical region. This problem has been shown to be NP-hard, and so any algorithms for finding the optimal solution may suffer from prohibitively high complexity. In view of this, we seek an efficient and more accurate suboptimal solution for the WCUM problem. A low-complexity iterative WCUM algorithm is proposed for this nonconvex problem by solving two convex problems alternatively. We also show the convergence of the proposed algorithm, and prove its Pareto optimality to the WCUM problem. Some simulation results are presented to demonstrate its substantial performance gain and higher computational efficiency over existing algorithms.

Hyperspectral endmember extraction is a process to estimate endmember signatures from the hyperspectral observations, in an attempt to study the underlying mineral composition of a landscape. However, estimating the number of endmembers, which is usually assumed to be known a priori in most endmember estimation algorithms (EEAs), still remains a challenging task. In this paper, assuming hyperspectral linear mixing model, we propose a hyperspectral data geometry-based approach for estimating the number of endmembers by utilizing successive endmember estimation strategy of an EEA. The approach is fulfilled by two novel algorithms, namely geometry-based estimation of number of endmembers—convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The GENE-CH and GENE-AH algorithms are based on the fact that all the observed pixel vectors lie in the convex hull and affine hull of the endmember signatures, respectively. The proposed GENE algorithms estimate the number of endmembers by using the Neyman–Pearson hypothesis testing over the endmember estimates provided by a successive EEA until the estimate of the number of endmembers is obtained. Since the estimation accuracies of the proposed GENE algorithms depend on the performance of the EEA used, a reliable, reproducible, and successive EEA, called$p$-norm-based pure pixel identification (TRI-P) algorithm is then proposed. The performance of the proposed TRI-P algorithm, and the estimation accuracies of the GENE algorithms are demonstrated through Monte Carlo simulations. Finally, the proposed GENE and TRI-P algorithms are applied to real AVIRIS hyperspectral data obtained over the Cuprite mining site, Nevada, and some conclusions and future directions are provided.

Hyperspectral endmember extraction is to estimate endmember signatures (or material spectra) from the hyperspectral data of an area for analyzing the materials and their composition therein. The presence of noise and outliers in the data poses a serious problem in endmember extraction. In this paper, we handle the noise- and outlier-contaminated data by a two-step approach. We first propose a robust-affine-set-fitting algorithm for joint dimension reduction and outlier removal. The idea is to find a contamination-free data-representative affine set from the corrupted data, while keeping the effects of outliers minimum, in the least squares error sense. Then, we devise two computationally efficient algorithms for extracting endmembers from the outlier-removed data. The two algorithms are established from a simplex volume max-min formulation which is recently proposed to cope with noisy scenarios. A robust algorithm, called worst case alternating volume maximization (WAVMAX), has been previously developed for the simplex volume max-min formulation but is computationally expensive to use. The two new algorithms employ a different kind of decoupled max-min partial optimizations, wherein the design emphasis is on low-complexity implementations. Some computer simulations and real data experiments demonstrate the efficacy, the computational efficiency, and the applicability of the proposed algorithms, in comparison with the WAVMAX algorithm and some benchmark endmember extraction algorithms.

Most of the existing works on two-way frequency division multiplexing (OFDM) relay channels was centered on per-subcarrier decode-and-forward (DF) relaying, where each subcarrier is treated as a separate channel, and channel coding is performed separately over each subcarrier. In this paper, we show that this per-subcarrier DF relay strategy is suboptimal. More specifically, we present a multi-subcarrier DF relay strategy which achieves a larger rate region by adopting cross-subcarrier channel coding. Then we develop an optimal resource allocation algorithm to characterize the achievable rate region of the proposed multi-subcarrier DF relay strategy. Compared to standard Lagrangian duality optimization algorithms, our algorithm has a much smaller computational complexity due to the use of the structure property of the optimal resource allocation solution. We further prove that our multi-subcarrier DF relay strategy tends to achieve the capacity region of the two-way OFDM relay channels in the low signal-to-noise ratio (SNR) regime, and the amplify-and-forward (AF) relay strategy tends to achieve the multiplexing gain region of the two-way OFDM relay channels in the high SNR regime. Our theoretical analysis and numerical results demonstrate that DF relaying has better performance in the low to moderate SNR regime, while AF relaying is more appropriate in the high SNR regime.

Optimal power allocation for orthogonal frequency division multiplexing (OFDM) wiretap channels with Gaussian channel inputs has already been studied in some previous works from an information theoretical viewpoint. However, these results are not sufficient for practical system designs. One reason is that discrete channel inputs, such as quadrature amplitude modulation (QAM) signals, instead of Gaussian channel inputs, are deployed in current practical wireless systems to maintain moderate peak transmission power and receiver complexity. In this paper, we investigate the power allocation and artificial noise design for OFDM wiretap channels with discrete channel inputs. We first prove that the secrecy rate function for discrete channel inputs is nonconcave with respect to the transmission power. To resolve the corresponding nonconvex secrecy rate maximization problem, we develop a low-complexity power allocation algorithm, which yields a duality gap diminishing in the order of O(1/√N), where N is the number of subcarriers of OFDM. We then show that independent frequency-domain artificial noise cannot improve the secrecy rate of single-antenna wiretap channels. Towards this end, we propose a novel time-domain artificial noise design which exploits temporal degrees of freedom provided by the cyclic prefix of OFDM systems to jam the eavesdropper and boost the secrecy rate even with a single antenna at the transmitter. Numerical results are provided to illustrate the performance of the proposed design schemes.

To improve wireless heterogeneous network service via macrocell and femtocells that share certain spectral resources, this paper studies the transmit beamforming design for femtocell base station (FBS), equipped with multiple antennas, under an outage-based quality-of-service (QoS) constraint at the single-antenna femtocell user equipment characterized by its signal-to-interference-plus-noise ratio. Specifically, we focus on the practical case of imperfect downlink multiple-input single-output (MISO) channel state information (CSI) at the FBS due to limited CSI feedback or CSI estimation errors. By characterizing the CSI uncertainty probabilistically, we formulate an outage-based robust beamforming design. This nonconvex optimization problem can be relaxed into a convex semidefinite programming problem, which reduces to a power control problem when all CSI vectors are independent and identically distributed. We also investigate the performance gap between the optimal transmission strategy (that allows maximum transmission degrees of freedom (DoF) equal to the number of transmit antennas) and the proposed optimal beamforming design (with the DoF equal to one) and provide some feasibility conditions, followed by their performance evaluation and trade-off through simulation results.

This paper considers robust multi-cell coordinated beamforming (MCBF) design for downlink wireless systems, in the presence of channel state information (CSI) errors. By assuming that the CSI errors are complex Gaussian distributed, we formulate a chance-constrained robust MCBF design problem which guarantees that the mobile stations can achieve the desired signal-to-interference-plus-noise ratio (SINR) requirements with a high probability. A convex approximation method, based on semidefinite relaxation and tractable probability approximation formulations, is proposed. The goal is to solve the convex approximation formulation in a distributed manner, with only a small amount of information exchange between base stations. To this end, we develop a distributed implementation by applying a convex optimization method, called weighted variable-penalty alternating direction method of multipliers (WVP-ADMM), which is numerically more stable and can converge faster than the standard ADMM method. Simulation results are presented to examine the chance-constrained robust MCBF design and the proposed distributed implementation algorithm.

Hyperspectral unmixing is a process of decomposing the hyperspectral data cube into endmember signatures and their corresponding abundance maps. For the unmixing results to be completely interpretable, the number of materials (or endmembers) present in that area should be known a priori, which however is unknown in practice. In this work, we use hyperspectral data geometry and successive endmember estimation strategy of an endmember extraction algorithm (EEA) to develop two novel algorithms for estimating the number of endmembers, namely geometry based estimation of number of endmembers - convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The proposed GENE algorithms estimate the number of endmembers by using Neyman-Pearson hypothesis testing over the endmembers sequentially estimated by an EEA until the estimate of the number of endmembers is obtained. Monte- Carlo simulations demonstrate the efficacy of the proposed GENE algorithms, compared to some existing benchmark methods for estimating number of endmembers.

Hyperspectral endmember extraction (EE) is to estimate endmember signatures (or material spectra) from the hyperspectral data of an unexplored area for analyzing the materials and their composition therein. However, the presence of noise in the data posts a serious problem for EE. Recently, robustness against noise has been taken into account in the design of EE algorithms. The robust maximum-volume simplex criterion [1] has been shown to yield performance improvement in the noisy scenario, but its real applicability is limited by its high implementation complexity. In this paper, we propose two fast algorithms to approximate this robust criterion [1], which turns out to deal with a set of partial max-min optimization problems in alternating manner and successive manner, respectively. Some Monte Carlo simulations demonstrate the superior computational efficiency and efficacy of the proposed robust algorithms in the noisy scenario over the robust algorithm in [1] and some benchmark EE algorithms.

In this paper, we consider a single-user multiple-input single-output (MISO) fading channel with training, and investigate optimal training and data transmission strategies for outage rate maximization. The receiver obtains instantaneous channel estimates through training; while the transmitter knows only the statistical information of the channel. We present analytical, closed-form solutions for the optimal training power and optimal data transmit covariance matrix. In particular, explicit numbers of antennas required for optimal data transmission are analyzed. Numerical results are presented to validate our analysis.

The combination of bit-interleaved coded modulation (BICM), orthogonal space-time block coding (OSTBC) and orthogonal frequency division multiplexing (OFDM) has been shown recently to be able to achieve maximum spatial-frequency diversity in frequency selective multi-path fading channels, provided that perfect channel state information (CSI) is available to the receiver. In view of the fact that perfect CSI can be obtained only if a sufficient amount of resource is allocated for training or pilot data, this paper investigates pilot-efficient noncoherent decoding methods for the BICM-OSTBC-OFDM system. In particular, we propose a noncoherent maximum-likelihood (ML) decoder that uses only one OSTBC-OFDM block. This block-wise decoder is suitable for relatively fast fading channels whose coherence time may be as short as one OSTBC-OFDM block. Our focus is mainly on noncoherent diversity analysis. We study a class of carefully designed transmission schemes, called perfect channel identifiability (PCI) achieving schemes, and show that they can exhibit good diversity performance. Specifically, we present a worst-case diversity analysis framework to show that PCI-achieving schemes can achieve the maximum noncoherent spatial-frequency diversity of BICM-OSTBC-OFDM. The developments are further extended to a distributed BICM-OSTBC-OFDM scenario in cooperative relay networks. Simulation results are presented to confirm our theoretical claims and show that the proposed noncoherent schemes can exhibit near-coherent performance.

Endmember extraction is of prime importance in the process of hyperspectral unmixing so as to study the mineral composition of a landscape from its hyperspectral observations. Though, a whole bunch of pure-pixel based endmember extraction algorithms exists, the quest for a reliable, repeatable, and computationally efficient endmember extraction algorithm still prevails. In this work, we propose two pure-pixel based endmember extraction algorithms called simplex estimation by projection (SIMPLE-Pro) algorithm and p-norm based pure pixel identification (TRI-P) algorithm. The end member identifiability of the proposed two algorithms is theoretically proved under the pure pixel assumption. Both algorithms never require any initializations and hence they are repeatable. Monte Carlo simulations are performed to demonstrate the superior efficacy and computational efficiency of the proposed two algorithms over some existing benchmark endmember extraction algorithms.

This paper considers weighted sum rate maximization of multiuser multiple-input single-output interference channel (MISO-IFC) under outage constraints. The outage-constrained weighted sum rate maximization problem is a nonconvex optimization problem and is difficult to solve. While it is possible to optimally deal with this problem in an exhaustive search manner by finding all the Pareto-optimal rate tuples in the (discretized) outage-constrained achievable rate region, this approach, however, suffers from a prohibitive computational complexity and is feasible only when the number of transmitter-receive pairs is small. In this paper, we propose a convex optimization based approximation method for efficiently handling the outage-constrained weighted sum rate maximization problem. The proposed approximation method consists of solving a sequence of convex optimization problems, and thus can be efficiently implemented by interior-point methods. Simulation results show that the proposed method can yield near-optimal solutions.

Recently, robust transmit beamforming has drawn considerable attention because it can provide guaranteed receiver performance in the presence of channel state information (CSI) errors. Assuming complex Gaussian distributed CSI errors, this paper investigates the robust beamforming design problem that minimizes the transmission power subject to probabilistic signal-to-interference-plus-noise ratio (SINR) constraints. The probabilistic SINR constraints in general have no closed-form expression and are difficult to handle. Based on a Bernstein-type inequality for quadratic forms of complex Gaussian random variables, we propose a conservative formulation to the robust single-cell beamforming design problem. The semidefinite relaxation technique can be applied to efficiently handle the proposed conservative formulation. Simulation results show that, in comparison with existing methods, the proposed method is more power efficient and is able to support higher target SINR values for receivers.

Recently, in multi-antenna wireless systems, the use of artificial noise (AN) in training and data transmission phases has been respectively proposed to achieve performance discrimination between a legitimate receiver (LR) and an unauthorized receiver (UR). For data transmission, an AN-aided beamforming (ANBF) scheme has been proposed where the message is sent towards LR using beamforming while AN is imposed in the null space of LR's channel to disrupt UR's reception. For channel estimation, the so-called discriminatory channel estimation (DCE) scheme has been proposed where a multi-stage training scheme is employed and AN is imposed in the null space of the estimated LR's channel obtained in previous stages to degrade the channel estimation performance of UR. In this work, the optimal power allocation between DCE and ANBF (as well as AN in both phases) is derived with the goal of maximizing the receive signal-to-interference-plus-noise ratio (SINR) of LR subject to a constraint on the maximum achievable SINR of UR. The simulation results show that, with the joint power allocation of DCE and ANBF, the SINR at LR and UR can be effectively discriminated even when UR is equipped with more antennas than the transmitter. Moreover, it is observed that the proposed joint DCE and ANBF scheme would allocate more power to the channel estimation phase compared with that using conventional channel estimation (without considering URs) in the training phase.

Multicell coordinated beamforming (MCBF) has been recognized as a promising approach to enhancing the system throughput and spectrum efficiency of wireless cellular systems. In contrast to the conventional single-cell beamforming (SBF) design, MCBF jointly optimizes the beamforming vectors of cooperative base stations (BSs) (via a central processing unit (CPU)) in order to mitigate the intercell interference. While most of the existing designs assume that the CPU has the perfect knowledge of the channel state information (CSI) of mobile stations (MSs), this paper takes into account the inevitable CSI errors at the CPU, and study the robust MCBF design problem. Specifically, we consider the worst-case robust design formulation that minimizes the weighted sum transmission power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on MSs. The associated optimization problem is challenging because it involves infinitely many nonconvex SINR constraints. In this paper, we show that the worst-case SINR constraints can be reformulated as linear matrix inequalities, and the approximation method known as semidefinite relation can be used to efficiently handle the worst-case robust MCBF problem. Simulation results show that the proposed robust MCBF design can provide guaranteed SINR performances for the MSs and outperforms the robust SBF design.

In this paper, we describe a continuous optimization perspective on Winter's simplex volume maximization belief for endmember ex traction in hyperspectral remote sensing. Winter's belief, proposed in the late 90's, is very insightful and has led to one of the most widely used class of endmember extraction algorithms nowadays- N-FINDR. Our endeavor to revisit this problem is to provide an al ternative, systematic, framework of formulating and understanding Winter's belief. Under the continuous optimization formulation of Winter's belief, we show a fundamental result that the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers, but also necessary. Then, we derive two Winter-based algorithms based on two different optimization strategies. Interestingly, the resulting algorithms are found to be similar to an N-FINDR variant and the vertex component analysis (VCA) algorithm. Hence, the developed framework provides linkage and alternative interpretations to these existing algorithms. Simulation results are also presented to compare the derived Winter algorithms and several existing algorithms.

SUMMARY: In vivo dynamic contrast-enhanced imaging tools provide non-invasive methods for analyzing various functional changes associated with disease initiation, progression and responses to therapy. The quantitative application of these tools has been hindered by its inability to accurately resolve and characterize targeted tissues due to spatially mixed tissue heterogeneity. Convex Analysis of Mixtures - Compartment Modeling (CAM-CM) signal deconvolution tool has been developed to automatically identify pure-volume pixels located at the corners of the clustered pixel time series scatter simplex and subsequently estimate tissue-specific pharmacokinetic parameters. CAM-CM can dissect complex tissues into regions with differential tracer kinetics at pixel-wise resolution and provide a systems biology tool for defining imaging signatures predictive of phenotypes. AVAILABILITY: The MATLAB source code can be downloaded at the authors' website www.cbil.ece.vt.edu/software.htm CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in remote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig's criterion, which states that the vertices of the minimum-volume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signatures associated with the data cloud. Recently, we have developed a minimum-volume enclosing simplex (MVES) algorithm based on Craig's criterion and validated that the MVES algorithm is very useful to unmix highly mixed hyperspectral data. However, the presence of noise in the observations expands the actual data cloud, and as a consequence, the endmember estimates obtained by applying Craig-criterion-based algorithms to the noisy data may no longer be in close proximity to the true endmember signatures. In this paper, we propose a robust MVES (RMVES) algorithm that accounts for the noise effects in the observations by employing chance constraints. These chance constraints in turn control the volume of the resulting simplex. Under the Gaussian noise assumption, the chance-constrained MVES problem can be formulated into a deterministic nonlinear program. The problem can then be conveniently handled by alternating optimization, in which each subproblem involved is handled by using sequential quadratic programming solvers. The proposed RMVES is compared with several existing benchmark algorithms, including its predecessor, the MVES algorithm. Monte Carlo simulations and real hyperspectral data experiments are presented to demonstrate the efficacy of the proposed RMVES algorithm.

In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximum-volume simplex whose vertices are drawn from the pixel vectors. Winter's belief has stimulated much interest, resulting in many different variations of pixel search algorithms, widely known as N-FINDR, being proposed. In this paper, we take a continuous optimization perspective to revisit Winter's belief, where the aim is to provide an alternative framework of formulating and understanding Winter's belief in a systematic manner. We first prove that, fundamentally, the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the ground-truth endmembers but also necessary. Then, under the umbrella of the Winter problem, we derive two methods using two different optimization strategies. One is by alternating optimization. The resulting algorithm turns out to be an N-FINDR variant, but, with the proposed formulation, we can pin down some of its convergence characteristics. Another is by successive optimization; interestingly, the resulting algorithm is found to exhibit some similarity to vertex component analysis. Hence, the framework provides linkage and alternative interpretations to these existing algorithms. Furthermore, we propose a robust worst case generalization of the Winter problem for accounting for perturbed pixel effects in the noisy scenario. An algorithm combining alternating optimization and projected subgradients is devised to deal with the problem. We use both simulations and real data experiments to demonstrate the viability and merits of the proposed algorithms.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.

The impact of quantized channel direction information (CDI) on the achievable secrecy rate is studied for multiple antenna wiretap channels. By assuming that the eavesdropper's channel is unknown at the transmitter, we adopt the transmission scheme where artificial noise (AN) is imposed in the null space of the legitimate receiver's channel to disrupt the eavesdropper's reception. It has been shown that, in the ideal case where perfect CDI is available at the transmitter, the achievable secrecy rate can be made arbitrarily large by increasing the transmission power. However, when only quantized CDI is available, the AN that was originally intended to jam the eavesdropper may now leak into the legitimate receiver's channel, causing significant secrecy rate loss. For a given number of feedback bits B and transmission power P, we derive the optimal power allocation among the message-bearing signal and the AN to maximize the secrecy rate under AN leakage. We show that, when B is sufficiently large, one should allocate power evenly among the message-bearing signal and the AN; whereas when B is small, one should be more conservative in allocating power to the AN. Moreover, by showing that the achievable secrecy rate under quantized CDI is bounded by a constant, we derive a scaling law between B and P that is necessary to maintain a constant secrecy rate loss compared to the perfect CDI case. The scaling of B is shown to be logarithmic of P. These results are first derived for the multiple-input single-output single-antenna-eavesdropper scenario and are later extended to the multiple-input multiple-output multiple-antenna-eavesdropper case. Numerical simulations are provided to verify our theoretical claims.

Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and the corresponding proportions (or abundances) of a scene, from its hyperspectral observations. Motivated by Craig's belief, we recently proposed an alternating linear programming based hyperspectral unmixing algorithm called minimum volume enclosing simplex (MVES) algorithm, which can yield good unmixing performance even for instances of highly mixed data. In this paper, we propose a robust MVES algorithm called RMVES algorithm, which involves probabilistic reformulation of the MVES algorithm, so as to account for the presence of noise in the observations. The problem formulation for RMVES algorithm is manifested as a chance constrained program, which can be suitably implemented using sequential quadratic programming (SQP) solvers in an alternating fashion. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RMVES algorithm over several existing benchmark hyperspectral unmixing methods, including the original MVES algorithm.

This paper considers a downlink wireless system where a multiple-antenna transmitter (Alice) aims to discriminate the reception performances between a legitimate receiver (Bob) and a set of unauthorized receivers (Eves). To this end, there has been great interest in the use of artificial noise (AN) together with transmit beamforming in order to effectively interfere Eves' reception. However, most of the existing works do not optimize the AN but simply allocate it in the left null space of the Alice-to-Bob channel. In the paper, we propose to jointly optimize the beamforming vector and the AN covariance matrix by minimizing the total transmit power subject to a target signal-to-interference-plus-noise ratio (SINR) constraint on Bob and limited SINR constraints on all Eves. While the considered beamforming problem is not convex and may be difficult to solve in general, it can be effectively handled by a convex approximation method called semidefinite program (SDP) relaxation. In addition to showing how SDP relaxation can be applied to this problem, we prove using the KKT optimality that SDP relaxation provides a global optimum solution of the proposed beamforming problem when Alice has perfect information of the channel from Alice to Bob. Simulation results are presented to demonstrate the effectiveness of the proposed beamforming method.

In this work, we examine the impact of quantized channel direction feedback on the achievable secrecy rate of multiple-antenna wiretap channels. To guarantee secrecy without knowledge of the eavesdropper's channel, we consider the transmission scheme proposed by Goel and Negi where artificial noise (AN) is imposed in the null space of the legitimate receiver's channel to disrupt the eavesdropper's reception. When perfect knowledge of the legitimate receiver's channel direction information (CDI) is available at the transmitter, the secrecy rate can be made arbitrarily large by increasing the transmission power. However, perfect CDI is difficult to achieve in practice due to rate-limitations on the feedback channel. When only quantized CDI is available at the transmitter, the AN that is only intended to disrupt the eavesdropper's reception may leak into the legitimate receiver's channel, causing significant loss in secrecy rate. In fact, we show that the achievable secrecy rate under quantized CDI is bounded by a constant even as the transmission power increases. To guarantee a constant rate loss compared to the perfect CDI case, we show that the number of feedback bits must scale at least logarithmically with the transmission power. These theoretical claims are verified by computer simulations.

Although significant efforts have been made in developing nonnegative blind source separation techniques, accurate separation of positive yet dependent sources remains a challenging task. In this paper, a joint correlation function of multiple signals is proposed to reveal and confirm that the observations after nonnegative mixing would have higher joint correlation than the original unknown sources. Accordingly, a new nonnegative least-correlated component analysis (n/LCA) method is proposed to design the unmixing matrix by minimizing the joint correlation function among the estimated nonnegative sources. In addition to a closed-form solution for unmixing two mixtures of two sources, the general algorithm of n/LCA for the multisource case is developed based on an iterative volume maximization (IVM) principle and linear programming. The source identifiability and required conditions are discussed and proven. The proposed n/LCA algorithm, denoted by n/LCA-IVM, is evaluated with both simulation data and real biomedical data to demonstrate its superior performance over several existing benchmark methods.

Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing approaches to hyperspectral unmixing rely on the pure-pixel assumption, which may be violated for highly mixed data. A heuristic unmixing criterion without requiring the pure-pixel assumption has been reported by Craig: The endmember estimates are determined by the vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, using convex analysis, we show that the hyperspectral unmixing by Craig's criterion can be formulated as an optimization problem of finding a minimum-volume enclosing simplex (MVES). An algorithm that cyclically solves the MVES problem via linear programs (LPs) is also proposed. Some Monte Carlo simulations are provided to demonstrate the efficacy of the proposed MVES algorithm.

This paper considers maximum-likelihood (ML) detection of orthogonal space-time block coded OFDM (OSTBC-OFDM) systems without channel state information. Our previous work has shown an interesting identifiability result, that the whole time-domain channel can be uniquely identified by only having one subchannel to transmit pilots. However, this identifiability is in a probability-one sense, under some mild assumptions on the channel statistics. In this paper we establish a “perfect” channel identifiability (PCI) condition under which the channel is always uniquely identifiable. It is shown that PCI can be achieved by judiciously applying the so-called non-intersecting subspace OSTBCs. The resultant PCI achieving scheme has its number of pilots larger than that used in the previous probability-one identifiability achieving scheme, but smaller than that required in conventional pilot-aided channel estimation. Simulation results are presented to show that the proposed scheme can provide a better performance than the other schemes.

This paper addresses the problem of direction-of-arrival (DOA) estimation of quasi-stationary signals, which finds applications in array processing of speech and audio. By studying the subspace structures of the local second-order statistics (SOSs) of quasi-stationary signals, we develop a Khatri-Rao (KR) subspace approach that has two notable advantages. First, the approach can operate in underdetermined cases. It is proven that if N is the number of sensors in the array, then the proposed approach can identify up to 2N - 2 source DOAs in an unambiguous fashion. Second, the approach can handle the problem of unknown noise covariance. Essentially, the KR subspace formulation is found to provide a simple and effective way of annihilating the (unknown) noise covariance from the observed signal SOSs. Simulation results, with an emphasis on underdetermined and colored-noise cases, illustrate that the KR subspace approach provides promising mean square estimation error performance.

Physical-layer secrecy in wireless fading channels has been studied extensively in recent years to ensure reliable communication between the transmitter and the receiver subject to constraints on the information attainable by the eavesdropper. With multiple antennas at the transmitter, Goel and Negi proposed the use of artificial noise (AN) in the null space of the receiver's channel to corrupt the eavesdropper's reception, which helps guarantee secrecy without knowledge of the eavesdropper's channel. It has been shown that the secrecy capacity can be made arbitrarily large by increasing the transmission power, when perfect knowledge of the receiver's channel direction information (CDI) is available. However, in practice, this is not possible due to rate-limitations on the feedback channel. This paper studies the impact of quantized channel feedback on the secrecy capacity achievable with artificial noise.We show that, with imperfect CDI at the transmitter, the AN that was originally intended only for the eavesdropper may leak into the receiver's channel and limit the achievable secrecy rate. To maintain a constant performance degradation, the number of feedback bits must increase at least logarithmically with the transmission power. Moreover, we observe that the portion of power allocated to the transmission of AN should decrease as the number of quantization bits decreases to alleviate the degradation due to noise leakage.

To meet the demand of high data rate transmissions for multimedia wireless communications, orthogonal frequency division multiplexing (OFDM) systems in conjunction with multiple-input multiple-output (MIMO) signal processing have been considered one of the central techniques in advanced wireless communications. In the paper, two semiblind channel estimation algorithms are proposed for the uplink multiuser OFDM systems with insufficient guard interval, in contrast to sufficient guard interval assumed in most of the prior works. A zero-padding OFDM system, which zero-pads rather than cyclicly prefixing each block, is considered in this paper. By utilizing the relation between the linear prediction error filters (LPEFs) of the received signal with multiple prediction orders and the transmitted data sequence, the first proposed algorithm, namely the multistage LP (MLP) based algorithm, can estimate the MIMO channel coefficients, with only a single pilot OFDM block used. To reduce the sensitivity of the proposed algorithms to the channel order overestimation, it is proposed to implement the LPEFs with a QR-decomposition based approach. This QRdecomposition based approach alternatively computes the LPEFs without direct inversion of the received signal correlation matrix, thus exhibiting robustness against channel order overestimation. Some simulation results are presented to demonstrate the effectiveness and robustness of the proposed algorithms.

We recently reported a criterion for blind separation of non-negative sources, using a new concept called convex analysis for mixtures of non-negative sources (CAMNS). Under some assumptions that are considered realistic for sparse or high-contrast signals, the criterion is that the true source signals can be perfectly recovered by finding the extreme points of some observation-constructed convex set. In our last work we also developed methods for fulfilling the CAMNS criterion, but only for two to three sources. In this paper we propose a systematic linear programming (LP) based method that is applicable to any number of sources. The proposed method has two advantages. First, its dependence on LP means that the method does not suffer from local minima. Second, the maturity of LP solvers enables efficient implementation of the proposed method in practice. Simulation results are provided to demonstrate the efficacy of the proposed method.

In this paper, we develop a new class of parameter estimation techniques for the Gaussian Continuous-Density Hidden Markov Model (CDHMM), where the discriminative margin among a set of HMMs is used as the objective function for optimization. In addition to optimizing the mean parameters of the large-margin CDHMM, which was attempted in the past, our new technique is able to optimize the variance parameters as well. We show that the joint mean and variance estimation problem is a difficult optimization problem but can be approximated by a convex relaxation method. We provide some simulation results using synthetic data which possess key properties of speech signals to validate the effectiveness of the new method. In particular, we show that with joint optimization of the mean and variance parameters, the CDHMMs under model mismatch are much more discriminative than with only the mean parameters.

Semidefinite relaxation (SDR) is a high-performance efficient approach to MIMO detection especially for the BPSK or QPSK constellations. Recently, a number of research endeavors have focused on extending SDR to the case of 16-QAM constellations. This paper reports two interesting and useful results on this problem. First, we show that two of the existing 16-QAM SDR receivers, namely the polynomial-inspired SDR (PI-SDR) and bound-constrained SDR (BC-SDR) methods, are equivalent. Second, we develop a specialized interior-point algorithm for the implementation of BCSDR. The proposed algorithm is computationally efficient exploiting the BC-SDR structures, and enables us to handle larger problem sizes in practice.

The blind maximum-likelihood (ML) detection of orthogonal space-time block codes (OSTBCs) is a computationally challenging optimization problem. Fortunately, for BPSK and QPSK OSTBCs, it has been shown that the blind ML detection problem can be efficiently and accurately approximated by a semideflnite relaxation (SDR) approach [1]. This paper considers the situation where the 16-QAM signals are employed. Due to the nonconstant modulus nature of 16-QAM signals, the associated blind ML OSTBC detection problem has its objective function exhibiting a Rayleigh quotient structure, which makes the SDR approach not directly applicable. In the paper, a linear fractional SDR (LF-SDR) approach is proposed for efficient approximation of the optimum blind ML solution. In this approach, the blind ML 16-QAM OSTBC detection problem is first approximated by a quasi-convex relaxation problem. Generally quasi-convex problems may be computationally more complex to handle than convex problems, but we show that the optimum solution of our quasi-convex problem can be efficiently obtained by solving a convex problem, namely a semideflnite program. Simulation results demonstrate that the proposed LF-SDR based blind ML detector outperforms the norm relaxed blind ML detector and the blind subspace channel estimator [2], especially in the one- receive-antenna scenario.

Chi et al. proposed a computationally efficient fast kurtosis maximization algorithm for blind equalization of multiple-input multiple-output linear time-invariant systems. This algorithm is also an iterative batch processing algorithm and has been applied to blind source separation. This paper considers blind beamforming of multiuser orthogonal frequency division multiplexing (OFDM) systems. Assuming that the channel is static within one OFDM block, a blind post-FFT multistage beamforming algorithm (MSBFA) based on subcarrier averaging is proposed. The algorithm basically comprises:( i) source (path signal) extraction using a hybrid beamforming algorithm composed of a Fourier beamformer and a kurtosis maximization beamformer, (ii) time delay estimation and compensation, (iii) classification (path-to-user association) and blind maximum ratio combining (of path signals). The designed beamformer is exactly the same for all the subcarriers, effectively utilizes multipath diversity for performance gain, and works well even in an environment with spatially correlated sources. Some simulation results are presented to demonstrate the effectiveness of the proposed MSBFA.

In this paper, we apply convex analysis to the problem of blind source separation (BSS) of non-negative signals. Under realistic assumptions applicable to many real-world problems such as multichannel biomedical imaging, we formulate a new BSS criterion that does not require statistical source independence, a fundamental assumption to many existing BSS approaches. The new criterion guarantees perfect separation (in the absence of noise), by constructing a convex set from the observations and then finding the extreme points of the convex set. Some experimental results are provided to demonstrate the efficacy of the proposed method.

This paper presents a semiblind maximum-likelihood (ML) detector for the orthogonal space-time block coded orthogonal frequency division multiplexing (OSTBC-OFDM) system. Many existing blind/ semiblind OSTBC-OFDM receivers typically require that the channel is static over a multitude of OSTBC-OFDM blocks. The proposed method is specifically for detection over one OSTBC-OFDM block only, and hence is well suited to block fading channels. The presented identifiability analysis shows that the data can be uniquely identified in a probability one sense by using one pilot code only, in contrast to the pilot-based least-squares channel estimator which requires at least L pilot codes where L is the channel length. Simulation examples are then presented to show the efficacy of the proposed detector.

In this paper we propose an extended differential unitary space-time modulation (xDUSTM) scheme that can offer improved error performance over the differential unitary space-time modulation (DUSTM) scheme. DUSTM is well suited to rapidly time-varying unknown channels. It has a simple structure, but incurs an error performance penalty of about 3dB compared to its coherent counterpart. The xDUSTM scheme considers moderately fast time-varying channels, and is designated to exploit such a characteristic for performance improvement. In xDUSTM, a problem that needs to be addressed is the complexity of its non-coherent maximum-likelihood (ML) receiver. We show that by choosing the orthogonal space-time block code (OSTBC) designs, the ML problem can be reduced to a Boolean quadratic program for which highly effective algorithms are available. Simulation results illustrate that the error performance penalty in xDUSTM can be reduced to 1dB.

Higher-order statistics based inverse filter criteria (HOS-IFC) proposed by Tugnait (1997) and Chi et al. (2002) have been widely used for blind identification and deconvolution of multiple-input multiple-output (MIMO) linear time-invariant systems with a set of nonGaussian measurements. Based on a relationship, that holds true for finite signal-to-noise ratio, between the optimum inverse filter associated with the HOS-IFC and the unknown MIMO system, an iterative FFT-based blind system identification (BSI) algorithm for MIMO systems is proposed in this paper, for which common subchannel zeros are allowed and the system order information is never needed, and meanwhile its performance is superior to the performance of Tugnait's HOS-IFC approach. Some simulation results are presented to support the efficacy of the proposed BSI algorithm.

In this paper, we present the formulation of the super-exponential blind adaptive beamforming algorithm; which is an extension of the cumulant-based super-exponential blind deconvolution theory presented by Shalvi and Weinstein. Simulation results show the efficacy of the algorithm.

Cumulant (higher-order statistics) based inverse filter criteria maximizing J/sub r,m/=|C/sub m/|/sup r//|C/sub r/|/sup m/, where m/spl ne/r and C/sub m/ (C/sub r/) denotes the mth-order (rth-order) cumulant of the inverse filter output, have been proposed for blind deconvolution and equalization with only non-Gaussian output measurements of an unknown linear time-invariant (LTI) system. This paper shows that the maximum of J/sub r,m/ associated with the true inverse filter of the unknown LTI system, exists only for r to be even and m>r, otherwise, J/sub r,m/ is unbounded. The admissible values for (r,m)=(2s,l+s) where l>s/spl ges/1 include (2,3), (2,4) and (4,6) proposed by Tugnait (see IEEE Trans. Signal Processing, vol.41, no.11, p.3196-3199, 1993), Wiggins (1978), and Shalvi and Weinstein (see IEEE Trans. Information Theory, vol.36, p.312-321, 1990) in addition to more new ones such as (2,5), (2,6) and (4,5). Some simulation results for the inverse filter criteria J/sub r,m/ with the proposed admissible values of (r,m) are then provided. Finally, we draw some conclusions.

In this paper, a new nonlinear parameter estimation method for a noncausal autoregressive (AR) system based on a new quadratic equation relating the unknown AR parameters to higher-order (/spl ges/3) cumulants of non-Gaussian output measurements in the presence of additive Gaussian noise, is described. It is applicable no matter whether or not the order of the system is known in advance; it is also applicable for the case of causal AR system. Some simulation results are offered to justify that the proposed method is effective.>

J.P. Todoeschuck and O.G. Jensen (Geophysics, vol.53, no.11, p.1410-14, 1988) recently reported that some reflectivity sequences denoted mu (k), calculated from sonic logs, are not white and have a power spectral density approximately proportional to frequency, which is called a Joseph spectrum. A robustness test is now presented for the case of mu (k) having a Joseph spectrum for the minimum-variance deconvolution (MVD) filter and the maximum-likelihood deconvolution (MLD) algorithm, which were developed based on the whiteness assumption about mu (k). From the simulations performed, it is concluded that the possible Joseph spectrum of mu (k) is not a concern when applying the MVD filter and MLD algorithm towards estimating mu (k) from seismic data.>

We derive and implement a maximum-likelihood detection and estimation algorithm based on the same channel and statistical models used by Kormylo and Mendel [1], that leads to less computations than the approach presented by Chi, Mendel and Hampson [2]. We introduce a single generalized likelihood function and we develop the Multiple-Most-Likely Replacement (MMLR) detector. This detector is computationally faster compared with the Single-Most-Likely Replacement (SMLR) detector developed by Kormylo and Mendel [3]. We demonstrate good performance of our algorithm for a synthetic data example.

Recently, we observed zero phase and undershoot patterns in data processed by a minimum-variance deconvolution (MVD) filter. These observations motivated a careful analys is of the MVD filter, which, as we demonstrate in this paper, explains both the zero phase and undershoot patterns. This analysis also connects the MVD filter with the well-known prediction-error filter [6], and Berkhout's two-sided least-squares inverse filter [7]. We show that the performance of the MVD filter depends heavily on the bandwidth of the source wavelet, and signal-to-noise ratio, and only slightly on data length.

When a wavelet to be estimated is not spiky, then a single most likely replacement (SMLR) detector, which is used to detect randomly located impulsive events that have Gaussian-distributed amplitudes, may split a large spike into two smaller ones and may also detect some spikes at wrong locations, although these locations are very close to their true ones. Presented here are two new detection algorithms, namely a single-spike-shift (SSS) detector and an SSS-SMLR detector both of which help correct the SMLR detector's spike-splitting and shifting problem.