Given an undirected graph and a size parameter k, the Densest k-Subgraph (DkS) problem extracts the subgraph on k vertices with the largest number of induced edges. While DkS is NP--hard and difficult to approximate, penalty-based continuous relaxations of the problem have recently enjoyed practical success for real-world instances of DkS. In this work, we propose a scalable and exact continuous penalization approach for DkS using the error bound principle, which enables the design of suitable penalty functions. Notably, we develop new theoretical guarantees ensuring that both the global and local optima of the penalized problem match those of the original problem. The proposed penalized reformulation enables the use of first-order continuous optimization methods. In particular, we develop a non-convex proximal gradient algorithm, where the non-convex proximal operator can be computed in closed form, resulting in low per-iteration complexity. We also provide convergence analysis of the algorithm. Experiments on large-scale instances of the DkS problem and one of its variants, the Densest (k1, k2) Bipartite Subgraph (Dk1k2BS) problem, demonstrate that our method achieves a favorable balance between computation cost and solution quality.

Dual-functional radar-communication (DFRC) signal design has received much attention lately. We consider the scenario of one-bit massive multi-input multi-output (MIMO) wherein one-bit DACs are employed for the sake of saving hardware costs. Specifically, a spatial Sigma-Delta$(\Sigma \Delta)$modulation scheme is proposed for one-bit MIMO-DFRC waveform design. Unlike the existing approaches which require large-scale binary optimization, the proposed scheme performs$\Sigma \Delta$modulation on a continuous-valued DFRC signal. The subsequent waveform design is formulated as a constrained least square problem, which can be efficiently solved. Moreover, we leverage quantization noise for radar probing purposes, rather than treating it as unwanted noise. Numerical results demonstrate that the proposed scheme performs well in both radar probing and downlink precoding.

Multilayer matrix factorization (MMF) has recently emerged as a generalized model of, and potentially a more expressive approach than, the classic matrix factorization. This paper considers MMF under a probabilistic formulation, and our focus is on inference methods under variational inference. The challenge in this context lies in determining a variational process that leads to a computationally efficient and accurate approximation of the maximum likelihood inference. One well-known example is the variational autoencoder (VAE), which uses neural networks for the variational process. In this work, we take insight from variational diffusion models in the context of generative models to develop variational inference for MMF. We propose a dimension-reducing diffusion process that results in a new way to interact with the layered structures of the MMF model. Experimental results demonstrate that the proposed diffusion variational inference method leads to improved performance scores compared to several existing methods, including the VAE.

Transmitting data using the phases on reconfigurable intelligent surfaces (RIS) is a promising solution for future energy-efficient communication systems. Recent work showed that a virtual phased massive multiuser multiple-input-multiple-out (MIMO) transmitter can be formed using only one active antenna and a large passive RIS. In this paper, we are interested in using such a system to perform MIMO downlink precoding. In this context, we may not be able to apply conventional MIMO precoding schemes, such as the simple zero-forcing (ZF) scheme, and we typically need to design the phase signals by solving optimization problems with constant modulus constraints or with discrete phase constraints, which pose challenges in terms of incurring high computational costs. In this work, we propose an alternative approach based on Sigma-Delta (Σ∆) modulation, which is classically famous for its noise-shaping ability. Specifically, first-order Σ∆ modulation is applied in the spatial domain to handle phase quantization in generating constant envelope signals. Under some mild assumptions, the proposed phased Σ∆ modulator allows us to use the ZF scheme to synthesize the RIS reflection phases in a low complexity fashion. The proposed approach is empirically shown to achieve comparable bit error rate performance to the unquantized ZF scheme.

The present work studies symbol-level precoding (SLP) for multiuser multi-input single-output (MISO) downlink channels and with imperfect channel state information (CSI) at the transmitter. SLP has gained significant interest in recent years because it is capable of enhancing symbol-level performance, such as symbol error probability (SEP), in a direct manner. Lately it has been shown that under a design formulation of SEP-constrained total power minimization, SLP can be regarded as a zero-forcing precoding scheme with appropriate symbol perturbations. That result is obtained under the perfect CSI assumption. In this paper we illustrate that, for the imperfect CSI case and under a worst-case SEP-constrained total power minimization formulation, SLP can also be regarded as a symbol-perturbed ZF scheme. Following such observation, we further establish an algorithm customized for our robust SLP formulation. Numerical results are presented to demonstrate the performance of our robust SLP design.

Simplex component analysis (SCA) aims to estimate the vertices of the convex hull where data samples reside in. SCA finds various applications in signal processing, e.g., hyperspectral unmixing and noisy label learning. Recent works proposed to tackle SCA from a probabilistic viewpoint using variational inference (VI) tools, which fends against noise more effectively relative to the deterministic counterparts. However, the computational efficiency of VI for SCA hinges on the use of the Dirichlet variational posterior. Such variational posterior appears to lack expressiveness—making the SCA performance limited if the true posterior is complex. This work proposes to employ a logistic-normal variational posterior, which exhibits enhanced expressive power. To circumvent the computational bottleneck, a neural representation-based inference algorithm is proposed—which exploits a connection between the logistic-normal distribution and variational auto-encoding. Numerical experiments using simulated and semi-real data are conducted to showcase the effectiveness of our algorithm design.

Cardinality-constrained binary quadratic optimization appears in various applications such as finding a densest size-constrained subgraph from a graph. It is a challenging combinatorial problem, and in this paper we tackle the problem by a continuous optimization approach. Our method, called the extreme point pursuit, works by relaxing the cardinality-constrained binary set to its corresponding convex hull, and then by adding an appropriate penalty function to encourage the solution to be an extreme point of the convex hull. The resulting extreme-point pursuit formulation is non-convex. As an intuitive strategy to try to avoid poor local minima, we adopt a homotopy optimization method wherein we start with an easy convex problem and gradually change the landscape of the problem to approach the extreme-point pursuit formulation. Experiments based on real-world large-scale graph data are performed to demonstrate the performance and efficiency of our method.

In this paper we develop a simple scheme for a coupled matrix factorization problem arising in the topic of hyperspectral super-resolution (HSR). HSR considers the problem of recovering a super-resolution image from a multispectral image and a hyperspectral image, which have lower spectral and spatial resolutions, respectively, and it is a motivated topic in the domain of remote sensing. The challenge with coupled factorization (COFAC) is that we are required to simultaneously factorize two data matrices, with their factors being interrelated. We adopt a separable COFAC strategy, in which we first factorize one data matrix, and then use the retrieved factors and the coupled factor relationship to help us factorize another matrix; the merit is that it may lead to simple COFAC schemes. Our scheme is based on the simplex-structured factorization model, which is commonly used in HSR, and a sparse factor assumption. In particular, we leverage the coupled factor structure to exploit sparsity in an easy way; we solve simple constrained least squares problems, and we sidestep the need to do sparse optimization. Numerical results show that our proposed scheme works reasonably on both semi-real data and synthetic data, and it runs much faster than some state-of-the-art COFAC schemes.

Symbol-level precoding (SLP) has received tremendous interest in MIMO communications in recent years. In particular, much attention has been paid to the formulation and optimization aspects. In this paper we contribute to these aspects by drawing a connection between SLP and a seemingly unrelated topic—namely, parameter estimation from quantized data. Specifically, we illustrate that the maximum detection probability formulation for SLP is basically the same as the maximum likelihood estimation formulation for quantized linear regression (QLR). This dual relationship is not just an interesting fundamental result. Using this relationship, we show how the expectation maximization (EM) method for QLR, a popular way to deal with QLR, can be repurposed to perform optimization for SLP. Our numerical results suggest that the accelerated EM method for SLP, as a new possibility, is highly efficient.

In this paper we examine the application of variational inference (VI) to MIMO detection. Our study is motivated by the recent interest in applying machine learning concepts to signal processing. VI is an approach for providing friendly approximations of certain intractable posterior probabilities in statistics, and it has been popularly used in machine learning. In MIMO detection we also have a similar problem; specifically, we want to evaluate the posterior symbol probabilities for detection, but they are computationally too expensive to evaluate when the problem size and/or the constellation size are large. By approximating the discrete symbol prior by a continuous Gaussian mixture model, we show how the notion of VI can be used to derive an iterative MIMO detector. Interestingly, the detector resembles the MMSE detector in structure. The performance of the proposed detector is demonstrated by simulations.

Unit-modulus constrained optimization is frequently encountered in many engineering problems. In our recent study for massive MIMO precoding, we devised a penalty method for unit-modulus optimization. In this paper, we revisit this penalty method in several other unit-modulus applications in signal processing. Moreover, as a new result, we show that the concept of our penalty method can be generalized to handle a much broader class of problems, such as those with semi-orthogonal matrix constraints. The rationale is to relax the constraint set as its convex hull, and at the same time, we add a penalty function to force the solution to be an extreme point—which lies in the original constraint set. We show conditions under which the penalty formulation is equivalent to the original problem. We test the penalty method on classic and one-bit MIMO detection under M-PSK constraints, and on phase retrieval. Simulation results indicate that the penalty method yields competitive performance on the aforementioned applications.

Simplex identification via split augmented Lagrangian (SISAL) is a popularly used algorithm in blind unmixing of hyperspectral images. Developed by José M. Bioucas-Dias in 2009, the algorithm is fundamentally relevant to tackling simplex-structured matrix factorization and, by extension, nonnegative matrix factorization, which have many applications under their umbrellas. In this article, we revisit SISAL and provide new meanings to this quintessential algorithm. The formulation of SISAL was motivated from a geometric perspective, with no noise. We show that SISAL can be explained as an approximation scheme from a probabilistic simplex component analysis framework, which is statistical and is principally more powerful in accommodating the presence of noise. The algorithm for SISAL was designed based on a successive convex approximation method, with a focus on practical utility. It was not known, by analyses, whether the SISAL algorithm has any kind of guarantee of convergence to a stationary point. By establishing associations between the SISAL algorithm and a line search--based proximal gradient method, we confirm that SISAL can indeed guarantee convergence to a stationary point. Our re-explanation of SISAL also reveals new formulations and algorithms. The performance of these new possibilities is demonstrated by numerical experiments.

In federated learning, models are learned from users’ data that are held private in their edge devices, by aggregating them in the service provider’s “cloud” to obtain a global model. Such global model is of great commercial value in, e.g., improving the customers’ experience. In this paper we focus on two possible areas of improvement of the state of the art. First, we take the difference between user habits into account and propose a quadratic penalty-based formulation, for efficient learning of the global model that allows to personalize local models. Second, we address the latency issue associated with the heterogeneous training time on edge devices, by exploiting a hierarchical structure modeling communication not only between the cloud and edge devices, but also within the cloud. Specifically, we devise a tailored block coordinate descent-based computation scheme, accompanied with communication protocols for both the synchronous and asynchronous cloud settings. We characterize the theoretical convergence rate of the algorithm, and provide a variant that performs empirically better. We also prove that the asynchronous protocol, inspired by multi-agent consensus technique, has the potential for large gains in latency compared to a synchronous setting when the edge-device updates are intermittent. Finally, experimental results are provided that corroborate not only the theory, but also show that the system leads to faster convergence for personalized models on the edge devices, compared to the state of the art.

Adopting one-bit analog-to-digital convertors (ADCs) for massive multiple-input multiple-output (MIMO) implementations has great potential in reducing the hardware cost and power consumption. However, distortions caused by quantization raise great challenges. In MIMO orthogonal frequency-division modulation (OFDM) detection, coarse quantization renders the orthogonal separation among subcarriers inapplicable, forcing us to deal with a problem that has a very large problem size. In this paper we study the expectation-maximization (EM) approach for one-bit MIMO-OFDM detection. The idea is to iteratively decouple the MIMO-OFDM detection problem among subcarriers. Using the perspective of block coordinate descent, we describe inexact variants of the classical EM method for providing more flexible and computationally efficient designs. Simulation results are provided to illustrate the potential of the divide-and-conquer strategy enabled by EM.

In this article the author reviews Jose Bioucas-Dias' key contributions to hyperspectral unmixing (HU), in memory of him as an influential scholar and for his many beautiful ideas introduced to the hyperspectral community. Our story will start with vertex component analysis (VCA)—one of the most celebrated HU algorithms, with more than 2,000 Google Scholar citations. VCA was pioneering, invented at a time when HU research just began to emerge, and it shows sharp insights on a then less-understood subject. Then we will turn to SISAL, another widely-used algorithm. SISAL is not only a highly successful algorithm, it is also a demonstration of its inventor's ingenuity on applied optimization and on smart formulation for practical noisy cases. Our tour will end with dependent component analysis (DECA), perhaps a less well-known contribution. DECA adopts a statistical inference framework, and the author's latest research indicates that such framework has great potential for further development, e.g., there are hidden connections between SISAL and DECA. The development of DECA shows foresight years ahead, in that regard.

Consider a robust multiple-input single-output downlink beamforming optimization problem in a frequency division duplexing system. The base station (BS) sends training signals to the users, and every user estimates the channel coefficients, quantizes the gain and the direction of the estimated channel and sends them back to the BS. Suppose that the channel state information at the transmitter is imperfectly known mainly due to the channel direction quantization errors, channel estimation errors and outdated channel effects. The actual channel is modeled as in an uncertainty set composed of two inequality homogeneous and one equality inhomogeneous quadratic constraints, in order to account for the aforementioned errors and effects. Then the transmit power minimization problem is formulated subject to robust signal-to-noise-plus-interference ratio constraints. Each robust constraint is transformed equivalently into a quadratic matrix inequality (QMI) constraint with respect to the beamforming vectors. The transformation is accomplished by an equivalent phase rotation process and the strong duality result for a quadratically constrained quadratic program. The minimization problem is accordingly turned into a QMI problem, and the problem is solved by a restricted linear matrix inequality relaxation with additional valid convex constraints. Simulation results are presented to demonstrate the performance of the proposed method, and show the efficiency of the restricted relaxation.

This paper studies nonconvex quadratically constrained quadratic program (QCQP), which is known to be NP-hard in general. In the past decades, various approximate approaches have been developed to tackle the QCQP, including semidefinite relaxation (SDR), successive convex approximation (SCA), the variable splitting approach, to name a few. While these approaches are effective under some circumstances, they have to either lift the variable dimension or require a feasible starting point, thereby not suitable for the large-scale QCQP or lack of a feasible starting point. In light of this, this work aims at developing an efficient approach to the QCQP without the above mentioned drawbacks. The crux of our approach is the proximal distance algorithm (PDA), which merges the idea of the penalty method and majorization minimization (MM) to provide an efficient (closed-form) iterative algorithm. To demonstrate the effectiveness of the PDA, we test it on the multicast beamforming applications in wireless communications. Simulation results show that the PDA outperforms state-of-the-art algorithms in terms of delivering a better solution with much less running time.

Hyperspectral unmixing (HU) is a problem of blindly identifying the underlying materials, in form of spectral signatures, in the captured hyperspectral image. HU has received tremendous interest in remote sensing, and fundamentally the problem can be regarded as solving a simplex-structured matrix factorization problem. The majority of HU research has been focused on the linear mixture model. On the other hand, remote sensing research has long indicated that real-life hyperspectral images can exhibit spatial variant and nonlinear effects. In this study we introduce a probabilistic approach for HU under two different models, namely, the normal composition model for modeling spatial endmember variability and the generalized bilinear model for modeling multi-path nonlinear effects. Our approach formulates HU as a maximum-likelihood (ML) model parameter estimation problem, and we demonstrate that the ML formulation can flexibly handle the two models. The ML problem is technical challenging, and we apply a combination of techniques, namely, sample average approximation, block coordinate descent and majorization minimization, to tackle the problem. Our empirical study suggests that the ML method gives competitive recovery performance.

Massive MIMO using low-resolution digital-to-analog converters (DACs) at the base station (BS) is an attractive downlink approach for reducing hardware overhead and for reducing power consumption, but managing the large quantization noise effect is a challenge. Spatial Sigma-Delta (ΣΔ) modulation is a recently emerged technique for tackling the aforementioned effect. Assuming a uniform linear array at the BS, it works by shaping the quantization noise as high spatial-frequency, or angle, noise. By restricting the user-serving region to be within a smaller angular region, the quan-tization noise incurred by the users can be effectively reduced. We previously showed that, under the one-bit DAC case, the quantization noise can be satisfactorily contained using a simple first-order ΣΔ modulation scheme. In this work we study the potential of spatial ΣΔ modulation in the two-bit DAC case and under second-order modulation. Our empirical results indicate that second-order spatial ΣΔ modulation provides better quantization noise suppression.

A family of computationally efficient DOA estimators under the partial relaxation framework has recently been proposed. In this framework, the manifold structure of the "interfering" signals is relaxed, and only the manifold structure of one desired signal is retained. This particular type of relaxation results in closed-form estimates for the interference parameters and enhances the estimation performance compared to the conventional spectral-search methods. By adopting the principle of the partial relaxation approach, in this paper, a modification of the Orthogonal Matching Pursuit algorithm is proposed and applied to the Direction-of-Arrival estimation problem. In each iteration of the proposed partial relaxation-based orthogonal matching pursuit (PR-OMP) algorithm, the impact on the receive signal from the previously-estimated directions and the remaining direction with the relaxed steering structure are considered. Simulations show that the proposed PR-OMP algorithm outperforms conventional estimators in the case of low Signal-to-Noise-Ratio or small number of snapshots.

Hyperspectral super-resolution (HSR) is a problem that aims to estimate an image of high spectral and spatial resolutions from a pair of coregistered multispectral (MS) and hyperspectral (HS) images, which have coarser spectral and spatial resolutions, respectively. In this article, we pursue a lowrank matrix estimation approach for HSR. We assume that the spectral-spatial matrices associated with the whole image and the local areas of the image have low-rank structures. The local low-rank assumption, in particular, has the aim of providing a more flexible model for accounting for local variation effects due to endmember variability. We formulate the HSR problem as a global-local rank-regularized least-squares problem. By leveraging on the recent advances in nonconvex large-scale optimization, namely the smooth Schatten-p approximation and the accelerated majorization-minimization method, we develop an efficient algorithm for the global-local low-rank problem. Numerical experiments on synthetic, semi-real, and real data show that the proposed algorithm outperforms a number of benchmark algorithms in terms of recovery performance.

Hyperspectral image unmixing has proven to be a useful technique to interpret hyperspectral data, and is a prolific research topic in the community. Most of the approaches used to perform linear unmixing are based on convex geometry concepts, because of the strong geometrical structure of the linear mixing model. However, many algorithms based on convex geometry are still used in spite of the underlying model not considering the intra-class variability of the materials. A natural question is to wonder to what extent these concepts and tools (Intrinsic Dimensionality estimation, endmember extraction algorithms, pixel purity) are still relevant when spectral variability comes into play. In this paper, we first analyze their robustness in a case where the linear mixing model holds in each pixel, but the endmembers vary in each pixel according to a prescribed variability model. In the light of this analysis, we propose an integrated unmixing chain which tries to adress the shortcomings of the classical tools used in the linear case, based on our previously proposed extended linear mixing model. We show the interest of the proposed approach on simulated and real datasets.

This paper considers symbol-level precoding (SLP) for the multiuser multiple-input single-output (MISO) downlink scenario. By exploiting symbol constellation information, SLP has the ability to achieve much better performance than traditional linear beamforming schemes. In this work, we propose an SLP design formulation under quadrature amplitude modulation (QAM) constellations. The objective of the design is to minimize the peak transmission energy over symbol time slots, while, at the same time, satisfying pre-specified symbol error probability (SEP) requirements of all the users. This kind of design can reduce the energy spread over symbol time. The resulting problem is a large-scale convex problem, and we develop an efficient alternating direction method of multipliers (ADMM) algorithm for the problem. Simulation results demonstrate that our proposed algorithm significantly outperforms some conventional linear beamforming schemes.

This paper considers multiuser massive MIMO downlink transmission, where the base station (BS) employs a massive number of transmit antennas, each equipped with a low-resolution phase shifter, to simultaneously shape desired symbols at user side, after passing through the channels and receive beamforming. This channel-aided shaping technique, known as symbol-level nonlinear precoding, has recently gained considerable attention owing to its high power efficiency and low implementation cost. However, the design of the transmit signal itself is challenging because the restriction of the transmit signals to a discrete constant envelope (DCE) set leads to a discrete optimization problem. In this paper, we adopt a minimum symbol-error probability design criterion for joint optimization of the transmit DCE signal at the BS and the receive beamformers at the users. An alternating minimization method is built for the problem. The design of the transmit DCE signal leverages on a negative square penalty (NSP) method developed in our recent work. The design of receive beamformers can be decoupled among users and updated by non-convex gradient projection independently. Our simulation results show that the bit-error rate performance markedly improves as the number of receive antennas increases.

Simplex-structured matrix factorization (SSMF) is a problem of recovering a basis matrix and the corresponding coefficient vectors from data, where the coefficient vectors are constrained to lie in the unit simplex. SSMF has attracted growing attention in recent years, with numerous applications such as hyperspectral unmixing and document clustering. In this work, we develop a maximum-likelihood (ML) approach for SSMF. Specifically, by modeling the coefficient vectors as random variables following a Dirichlet mixture distribution-which allows us to model more complex data distributions in real-life data, a probabilistic model for SSMF is employed. We consider a marginalized likelihood with respect to the coefficient vectors, and use ML estimation to learn the basis matrix and unknown Dirichlet mixture parameters. The marginalized likelihood does not admit a closed form and is non-concave, and this makes the problem challenging to solve. To handle this challenge, an effective algorithm using sample average approximation and block successive upper-bound minimization is proposed. We consider the aforementioned two real-world applications by simulations. Numerical results show that the proposed algorithm delivers appealing performance in both applications.

This work focuses on the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image that admits high spatial and spectral resolutions. Existing algorithms are mostly based on joint low-rank factorization of the ma-tricized HSI and MSI. This framework is effective to some extent, but several challenges remain. First, it is unclear whether or not the super-resolution image is identifiable in theory under this framework, while identifiability usually plays an essential role in such estimation problems. Second, most algorithms assume that the degradation operators from the super-resolution image to the HSI and MSI are known or can be easily estimated - which is hardly true in practice. In this work, we propose a novel coupled tensor decomposition method that can effectively circumvent these issues. The proposed approach guarantees the identifiability of the super-resolution image under realistic conditions. The method can work even without knowing the spatial degradation operator, which could be hard to accurately estimate in practice. Simulations using AVIRIS Cuprite data are employed to demonstrate the effectiveness of the proposed approach.

This paper considers symbol-level precoding (SLP) for multiuser multiple-input single-output (MISO) downlink. SLP is a nonlinear precoding scheme that utilizes symbol constellation structures. It has been shown that SLP can outperform the popular linear beamforming scheme. In this work we reveal a hidden connection between SLP and linear beamforming. We show that under an energy minimization design, SLP is equivalent to a zero-forcing (ZF) beamforming scheme with perturbations on symbols. This identity gives new insights and they are discussed in the paper. As a side contribution, this work also develops a symbol error probability (SEP)-constrained SLP design formulation under quadrature amplitude modulation (QAM) constellations.

Massive multiple-input multiple-output (MIMO) has the potential to substantially improve the spectral efficiency, robustness and coverage of mobile networks. However, such potential is limited by hardware cost and power consumption associated with a large number of RF chains. Recently, one-bit quantization is proposed to address this issue by replacing high-resolution digital-to-analog converters (DACs) with one-bit DACs, thereby simplifying the RF chains. Despite low system cost, advanced signal processing techniques are needed to compensate for quantization distortions caused by low-resolution DACs. In this paper, a symbol-error-rate (SER)-based one-bit precoding scheme is proposed to minimize the detection error probability of all users under one-bit constraints. The problem is recast as a continuous optimization problem with a biconvex objective. By applying the block coordinate descent (BCD) method and the FISTA method, we develop an efficient iterative algorithm to obtain a one-bit precoding solution. Simulation results demonstrate its superiority over state-of-the-art algorithms in terms of bit error rate performance in high-order modulation cases.

Hyperspectral super-resolution (HSR) is a problem of recovering a high-spectral-spatial-resolution image from a multispectral measurement and a hyperspectral measurement, which have low spectral and spatial resolutions, respectively. We consider a low-rank structured matrix factorization formulation for HSR, which is a non-convex large-scale optimization problem. Our contributions contain both computational and theoretical aspects. On the computational side, we develop three inexact block coordinate descent (BCD) schemes that are empirically found to run many times faster than a state-of-the-art method, which uses exact BCD. We achieve this by applying concepts in the proximal gradient (PG) and Frank-Wolfe (FW) methods and by exploiting the HSR problem structures. On the theoretical side, we show that these inexact BCD schemes guarantee convergence to a stationary point. In particular, the convergence result for a hybrid PG- FW inexact BCD scheme is new.

Hyperspectral super-resolution refers to the task of fusing a hyperspectral image (HSI) and a multispectral image (MSI) in order to produce a super-resolution image (SRI) that has high spatial and spectral resolution. Popular methods leverage matrix factorization that models each spectral pixel as a convex combination of spectral signatures belonging to a few endmembers. These methods are considered state-of-the-art, but several challenges remain. First, multiband images are naturally three dimensional (3-d) signals, while matrix methods usually ignore the 3-d structure, which is prone to information losses. Second, these methods do not provide identifiability guarantees under which the reconstruction task is feasible. Third, a tacit assumption is that the degradation operators from SRI to MSI and HSI are known - which is hardly the case in practice. Recently [1], [2] proposed a coupled tensor factorization approach to handle these issues. In this work we propose a hybrid model that combines the benefits of tensor and matrix factorization approaches. We also develop a new algorithm that is mathematically simple, enjoys identifiability under relaxed conditions and is completely agnostic of the spatial degradation operator. Experimental results with real hyperspectral data showcase the effectiveness of the proposed approach.

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.

This paper focuses on an average robust transmit beamforming optimization problem for the multiuser multiple-input-single-output (MISO) downlink scenario. In this problem, the channels are modeled as Gaussian variables with mean zero and with known covariance at the transmitter. The design criterion is to maximize the sum of the users' average rates with respect to the channels, subject to the total transmission power constraint. The challenge of this problem is that the average rate function generally admits a complex expression. Such an issue can be tackled by stochastic approximation (SA) approaches, but SA may require a large number of samples, or iterations, to provide reasonable performance. In this work, a simple deterministic approximation scheme is proposed. First, we propose a closed-form surrogate of the per-user average rate function. The proposed surrogate function is shown to have an approximation accuracy within 0.8314 bits from the true average rate. Then, we utilize the proposed surrogate function to establish an algebraically simple alternating optimization algorithm for the beamforming problem. Simulation results show that the proposed algorithm is computationally much more efficient than an SA-based state-of-the-art algorithm when they are compared under similar sum rate performance levels.

This paper considers practical deployment issues of a multi-user MIMO system with full-duplex (FD) base station and half-duplex (HD) user equipment. The aim is to select a set of uplink (UL) and downlink (DL) users at any instant that will provide a satisfactory performance in system resource allocation. Furthermore, it is also necessary to deal with the interference created by the UL users to the DL users, which limits communication quality. In this work, we consider implementing a joint processing beamforming algorithm that can provide effective UL/DL selection and achieve system utility maximization. Our results show that with 20 dB self-interference cancellation, FD system significantly outperforms HD system under proportional fairness utility.

Consider a structured matrix factorizaton (SMF) whose coefficient vectors are constrained to lie in the unit simplex. This kind of simplex SMF (SSMF) has received growing attention and has found many applications such as hyperspectral unmixing in remote sensing, text mining in machine learning, and blind source separation in signal processing. The aim of this paper is to establish a maximum-likelihood (ML) estimation framework for SSMF in the presence of Gaussian noise and outliers, and to demonstrate its potential. Our ML formulation has the coefficient vectors marginalized in accordance with a prescribed probabilistic model, and this leads to a likelihood function that contains multi-dimensional integrals. Unfortunately these integrals do not appear to have analytically tractable solutions, and this makes the ML problem challenging. We tackle the problem by using sample average approximation in stochastic optimization and majorization-minimization. Simulation results show that the resulting ML algorithm significantly outperforms several existing methods when noise and outliers are present.

In this work, we consider the robust beamforming design for secondary downlink multicasting channels, where primary users are present with norm-bounded channel errors. In particular, the max-min-fair formulation is considered and the resulting design problem is a quadratically constrained quadratic program (QCQP) with a set of semi-infinite constraints, which is NP-hard in general. As a remedy, we apply the semidefinite relaxation (SDR) technique and S-lemma to approximate the problem into a tractable form. The key contribution of this paper is to study the approximation quality. Our analytical results show that, the SDR solution achieves an objective value that is at least Ω(1/MN log J) times the optimal objective value, where M is the number of secondary users, J is the number of primary users, and N is the number of antennas at the secondary base station. This is a fundamentally new result for SDR applied to robust QCQPs. Practically, it provides a performance guarantee for the robust beamforming design. All these results are verified by our numerical simulations.

This paper focuses on volume minimization (VolMin)-based structured matrix factorization (SMF), which factors a data matrix into a full-column rank basis and a coefficient matrix whose columns reside in the unit simplex. The VolMin criterion achieves this goal via finding a minimum-volume enclosing convex hull of the data. Recent works showed that VolMin guarantees the identifiability of the factor matrices under mild and realistic conditions, which suit many applications in signal processing and machine learning. However, the existing VolMin algorithms are sensitive to outliers or lack efficiency in dealing with volume-associated cost functions. In this work, we propose a new VolMin-based matrix factorization criterion and algorithm that take outliers into consideration. The proposed algorithm detects outliers and suppress them automatically, and it does so in an algorithmically very simple way. Simulations are used to showcase the effectiveness of the proposed algorithm.

This paper considers a special subclass of separable semidefinite programs (SDPs), with the goal of identifying certain conditions under which the SDP has a low-rank solution. We prove that when the data matrices of the SDP satisfy certain matrix inequalities, the SDP has a low-rank solution. Moreover, the rank of this solution is related to parts of the data matrices only, irrespective of any other factors such as the number of constraints. This is quite different from the well-known Shapiro-Barvinok-Pataki rank reduction result, where the rank of the SDP solution relies on the number of constraints. The usefulness of our result is demonstrated through advanced beamforming applications in simultaneous wireless information and power transfer (SWIPT) and physical-layer security, for which rank-one optimal solutions can be easily identified by checking our derived matrix inequality conditions.

We are interested in a low-rank matrix factorization problem where one of the matrix factors has a special structure; specifically, its columns live in the unit simplex. This problem finds applications in diverse areas such as hyperspectral unmixing, video summarization, spectrum sensing, and blind speech separation. Prior works showed that such a factorization problem can be formulated as a self-dictionary sparse optimization problem under some assumptions that are considered realistic in many applications, and convex mixed norms were employed as optimization surrogates to realize the factorization in practice. Numerical results have shown that the mixed-norm approach demonstrates promising performance. In this letter, we conduct performance analysis of the mixed-norm approach under noise perturbations. Our result shows that using a convex mixed norm can indeed yield provably good solutions. More importantly, we also show that using nonconvex mixed (quasi) norms is more advantageous in terms of robustness against noise.

The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the underlying materials in a given hyperspectral image by selecting a small subset of spectral samples in the dictionary to represent the whole image. A drawback with the current SR developments is that an actual spectral signature in the scene is often assumed to have zero mismatch with its corresponding dictionary sample, and such an assumption is considered too ideal in practice. In this paper, we tackle the spectral signature mismatch problem by proposing a dictionary-adjusted nonconvex sparsity-encouraging regression (DANSER) framework. The main idea is to incorporate dictionary correcting variables in an SR formulation. A simple and low per-iteration complexity algorithm is tailor-designed for practical realization of DANSER. Using the same dictionary correcting idea, we also propose a robust subspace solution for dictionary pruning. Extensive simulations and real-data experiments show that the proposed method is effective in mitigating the undesirable spectral signature mismatch effects.

In this paper, we consider a two-hop one-way relay network for multigroup multicast transmission between long-distance users, in which the relay is equipped with multiple antennas, while the transmitters and receivers are all with a single antenna. Assuming that the perfect channel state information is available, we study amplify-and-forward (AF) schemes that aim at optimizing the max-min-fair (MMF) rate. We begin by considering the classic beamformed AF (BF-AF) scheme, whose corresponding MMF design problem can be formulated as a rank-constrained fractional semidefinite program (SDP). We show that the gap between the BF-AF rate and the SDR rate associated with an optimal SDP solution is sensitive to the number of users as well as the number of power constraints in the relay system. This reveals that the BF-AF scheme may not be well suited for large-scale systems. We, therefore, propose the stochastic beamformed AF (SBF-AF) schemes, which differ from the BF-AF scheme in that time-varying AF weights are used. We prove that the MMF rates of the proposed SBF-AF schemes are at most 0.8317 bits/s/Hz less than the SDR rate, irrespective of the number of users or power constraints. Thus, SBF-AF can outperform BF-AF especially in large-scale systems. Finally, we present numerical results to demonstrate the viability of our proposed schemes.

We consider the design of the linear precoder for a multiple-input single-output (MISO) downlink in a system that employs limited feedback using Grassmannian quantization. The goal is to minimize the outage probability of a target signal-to-interference-and noise ratio (SINR) under a transmitted power constraint. By approximating the outage constraint by a zero-outage region, employing a semidefinite relaxation, and applying an extension of the S-Lemma, the problem is converted into a quasi-convex problem. Insights into the structure of the solution of that problem generate an alternate design formulation that provides greater robustness in the presence of significant uncertainties and has a quasi-closed form solution.

In this paper, we consider a cloud relay network (C-RN) which provides reliable communication between long-distance users. Specifically, we study the amplify-and-forward (AF) schemes in C-RNs. In our scenario setting, with the cloud processor units fully coordinating in the network, the C-RN can be treated as an MIMO relay system. We therefore propose the beamformed (BF) Alamouti AF scheme to provide multigroup multicast information delivery in this network. By applying an Alamouti space-time code structure, the relays adopt two rank-one weights to AF the received signals in two time slots. Then, one more degree of freedom is available compared to the traditional BF AF scheme, and a new fractional semidefinite relaxation (SDR) is obtained from a max-min-fair quality-of-service (QoS) perspective. We prove that the Gaussian randomization algorithm based on the new fractional SDR has the same approximation quality-i.e., on the order of √M-as the traditional rank-two SDR approximation in multigroup multicast networks without relays, where M is the number of users served in the network. This result is verified by our numerical experiments.

In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization algorithms. Our analysis focuses on the successive projection algorithm (SPA), a simple, efficient, and provably robust algorithm. Recently, a provably robust preconditioning was proposed by Gillis and Vavasis [SIAM J. Optim., 25 (2015), pp. 677--698] which requires the resolution of a semidefinite program (SDP). Since solving the SDP in high precisions can be time consuming, we generalize the robustness analysis to approximate solutions of the SDP showing that a high accuracy solution is not crucial for robustness, paving the way for faster preconditionings. This first contribution also allows us to provide a robustness analysis for two other preconditionings. The first one is prewhitening, which can be interpreted as an optimal solution of the same SDP with additional constraints. We analyze the robustness of prewhitening, which allows us to characterize situations in which it performs competitively with the SDP-based preconditioning. The second one is based on SPA itself and can be interpreted as an optimal solution of a relaxation of the SDP. It is extremely fast when competing with the SDP-based preconditioning on several synthetic data sets.

This letter considers multi-input single-output (MISO) downlink multicasting with finite-alphabet inputs when perfect channel state information is known at the transmitter. Two advanced transmit schemes, namely the beamformed (BF) Alamouti scheme and the stochastic beamforming (SBF) scheme, for maximizing the finite-alphabet-constrained multicast rate are studied. We show that the transmit optimization for these two schemes can be formulated as an SNR-based max-min-fair (MMF) problem with Gaussian inputs, which can be handled via the semidefinite relaxation (SDR) technique. Apart from transmit optimization, we analyzed the rate performance of the two schemes. Our analytical results show that for BF Alamouti, the multicast rate degrades with the number of users M at a rate of √M, which is better than the traditional transmit beamforming scheme. For SBF, the multicast rate degradation is less sensitive to the increase in the number of users and outperforms BF Alamouti for large M. All the results were verified by numerical simulations.

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.

Unraveling power spectra mixtures and finding the directions of the constituent sources can enable effective spatial occupancy prediction by location-dependent combining of the recovered source power spectra; and it is also useful for primary interference avoidance. Such unmixing and direction-finding is a challenging leap beyond ordinary `aggregate' spectrum sensing. This paper presents a promising new method for blind (power) spectra separation and emitter direction finding using a network of cognitive radios. Each radio has a pair of antennas, and the baselines of different radios are aligned (e.g., using a compass), in a configuration reminiscent of classical spatial correlation-based ESPRIT. Unlike classical ESPRIT, array geometry is exploited here in the temporal correlation domain to come up with a simple and effective blind spectra separation and direction finding solution with guaranteed identifiability and robustness to noise. A notable feature is that the different radios need not be synchronized, as they do in spatial ESPRIT.

Consider a wireless scenario in which a multi-antenna transmitter wants to send a confidential message to a single-antenna information receiver (IR) while transferring wireless energy to a number of multi-antenna energy receivers (ERs). In order to keep the ERs from retrieving the confidential message, an artificial noise (AN)-aided physical-layer secrecy approach is employed at the transmitter. The AN has dual purpose: First, it can interfere with the ERs' information receptions and thus help improve security. Secondly, it provides wireless energy for the ERs to harvest. Assuming imperfect channel state information at the transmitter, we jointly optimize the co-variances of confidential information and AN such that the secrecy rate at the IR is maximized, while each ER receives a prescribed amount of wireless energy. Although this secrecy-rate maximization problem is non-convex, we show that it can be handled by solving a sequence of convex optimization problems. Numerical results are provided to demonstrate the efficacy of the proposed design.

This paper considers robust transmit beamforming for multiuser multi-input single-output (MISO) downlink transmission, where imperfect channel state information (CSI) is assumed at the base station (BS). The imperfect CSI is captured by a moment-based random error model, in which the BS knows only the mean and covariance of each CSI error, but not the exact distribution. Under this error model, we formulate a distributionally robust beamforming (DRB) problem, in which the total transmit power at the BS is to be minimized, while each user's SINR outage probability, evaluated w.r.t. any distribution with the given mean and covariance, is kept below a given threshold. The DRB problem is a semi-infinite chance-constrained problem. By employing recent results in distributionally robust optimization, we show that the DRB problem admits an explicit conic reformulation, which can be conveniently turned into a convex optimization problem after semidefinite relaxation (SDR). We also consider the case where the mean and covariance are not perfectly known. We show that the resulting DRB problem still admits a conic reformulation and can be approximately solved using SDR. The robustness of the proposed designs are demonstrated by numerical simulations.

This paper considers robust constant envelope (CE) precoding with antenna-subset selection (AS) in a large-scale MISO downlink scenario where only imperfect channel state information at the transmitter (CSIT) is available. CE precoding is a recently proposed transmission scheme that enables the use of cheap but highly power-efficient power amplifiers, while AS is a well-known approach for reducing the number of power amplifiers. The combination of these two techniques can significantly cut down costs in hardware implementations. We formulate a power minimization problem for AS CE precoding where the worst-case symbol error rate is constrained to be less than a given threshold. The formulation utilizes our recent results on signal characterization of CE precoding. The formulated power minimization optimization problem turns out to be a zero-one linear program. We show that this problem is NP-hard in general. Then, we propose an efficient approximation by Lagrangian dual relaxation and greedy knapsack approximation. Simulation results show that the proposed algorithm can achieve near-optimal performance, and the average number of active antennas accounts for only 19-53% of the total transmit antennas.

Recently, simultaneous wireless information and power transfer (SWIPT) has received considerable attention. In this paper, we consider a multicast SWIPT system, where a multi-antenna transmitter broadcasts common information to a group of single-antenna information receivers (IRs) and at the same time provides certain amount of energy transfer to a group of single-antenna energy receivers (ERs). Assuming imperfect channel state information (CSI) at the transmitter, two transmit schemes are proposed to maximize the IRs' outage-constrained multicast rate subject to a minimum provision of average energy transfer to ERs. In the first transmit scheme, we consider transmit beamforming and develop a safe approximation approach to obtain a conservative beamforming solution for maximizing the outage-constrained multicast rate. To further improve the performance of transmit beamforming, in the second transmit scheme, we consider a stochastic beamforming (SBF) approach, which allows the beamformer to randomly change over time according to some prescribed distribution. By doing so, the SBF scheme is able to fully exploit the temporal degree of freedom to achieve more balanced outage-constrained achievable rates among IRs. Simulation results demonstrated that the SBF scheme is generally better than the transmit beamforming scheme.

Consider a multi-input multi-output (MIMO) channel wiretapped by multiple multi-antenna eavesdroppers. Assuming imperfect eavesdroppers' channel state information (CSI) at the transmitter, an outage-constrained secrecy rate maximization (OC-SRM) problem is considered. Specifically, we aim to design the transmit covariance matrix such that the outage secrecy rate is maximized for a given outage probability. The OC-SRM problem is challenging, and as a compromise, we resort to a recently developed Bernstein-type inequality approach to obtain a safe (conservative) approximate solution for OC-SRM. The merit of the proposed safe design lies in its tractability. In particular, a safe solution can be efficiently computed by alternately solving two convex conic optimization problems. The efficacy of the proposed design is demonstrated by simulations.

This paper presents an efficient method for blind source separation of convolutively mixed speech signals. The method follows the popular frequency-domain approach, wherein researchers are faced with two main problems, namely, per-frequency mixing system estimation, and permutation alignment of source components at all frequencies. We adopt a novel concept, where we utilize local sparsity of speech sources in transformed domain, together with non-stationarity, to address the two problems. Such exploitation leads to a closed-form solution for per-frequency mixing system estimation and a numerically simple method for permutation alignment, both of which are efficient to implement. Simulations show that the proposed method yields comparable source recovery performance to that of a state-of-the-art method, while requires much less computation time.

In this paper, we consider transmit design in multiple-input single-output (MISO) multi-group multicast (MM) cognitive radio (CR) systems. Previously, semidefinite relaxation (SDR)-based transmit beamforming has been very successful in transmit design. However, recent research shows that further performance gain is possible by suitably modifying the transmit structure. Here, we propose a transmit beamformed Alamouti space-time code scheme for MM-CR systems, whose corresponding transmit design problem can be reformulated as a rank-2 constrained fractional semidefinite program. We then develop an SDR framework for this scheme and study its signal-to-interference-and-noise ratio (SINR) performance via both theoretical analysis and simulations. Specifically, we show that the worst-case approximation accuracy of the proposed scheme scales on the order of √MSlog MP, where MP(resp. MS) is the number of primary (resp. secondary) users in the CR network. This unifies and generalizes a number of results in the literature and is, to the best of our knowledge, the first provable bound on the performance of a beamforming scheme in a general MM-CR system. Finally, simulation results show that our proposed scheme indeed has a better performance in both MM and MM-CR scenarios than the traditional beamforming scheme.

This paper considers transmit covariance optimization for a multi-input multi-output (MIMO) Gaussian wiretap channel. Specifically, we aim to maximize the MIMO secrecy capacity by judiciously designing the transmit covariance under the sum power and per-antenna power constraints. The MIMO secrecy capacity maximization (SCM) problem is nonconvex, and so far there is no tractable solution available. We propose an alternating optimization (AO) approach to handle the SCM problem. In particular, our development consists of two steps: First, we show that the SCM problem can be reexpressed to a form that can be conveniently processed by AO. Second, we develop a custom-designed fast algorithm for each AO iteration. Interestingly, with this fast implementation, the overall AO algorithm can be viewed as performing iterative reweighting and water-filling. Finally, the convergence of the proposed algorithm to a stationary solution of SCM is shown, and numerical results are provided to demonstrate its efficacy.

This paper considers constant envelope (CE) precoding in single-user MISO downlink systems. CE precoding is a transmission scheme recently proposed for very large antenna arrays, in which the use of highly power-efficient RF amplifiers is a requirement. There are two important issues in CE precoding, namely the characterization of the region of all possible noise-free receive signals, and the recovery of the phases of the transmitting signal. An existing result by Mohammed and Larsson showed that the noise-free receive signal region can be geometrically interpreted as a region between two circles centered at the origin of the complex plane. However, this result did not prove the expression of the radius of the inner circle. We provide a new analysis approach to characterize the noise-free receive signal region. Our result shows that the radius of the inner circle has a simple closed-form expression, there by completing the result by Mohammed and Larsson. In addition, we propose an algorithm that can recover the phases of the transmitting signal exactly with a complexity linear in the number of antennas. Simulation results show that the proposed method can be significantly faster than an existing phase recovery algorithm.

Semi-definite relaxation (SDR) is a popular technique for Multi-Input Multi-Output (MIMO) detection. For Binary Phase-Shift Keying (BPSK) and Quadratic Phase-Shift Keying (QPSK), it has been found that SDR can provide a near-optimal Bit Error rate (BER) performance in a Gaussian channel. However if the noise in the channel deviates from the Gaussian model, as it does in many real wireless channels, BER performance drops considerably. In this paper we show that SDR can be applied for detection in a non-Gaussian channel using Huber's M-estimation method for robust regression.

This paper considers a discrete sum rate maximization (DSRM) problem for transmit optimization in multiuser MISO downlink. Unlike many existing sum rate maximization designs, DSRM focuses on a scenario where each user's achievable rate can only be chosen from a given discrete rate set. This discrete rate-based design is motivated by the fact that practical communication systems can support only a finite number of combinations of modulation and coding schemes. We tackle the DSRM problem first by deriving a novel reformulation of DSRM, in which the discrete rate variables are absorbed by the objective function. Then, from this reformulation, an approximation algorithm based on convex optimization and iterative solution refinement is developed. Simulations results are provided to demonstrate the performance of the proposed algorithm compared with some state-of-the-art algorithms.

Promoting the spatial resolution of off-the-shelf hyperspectral sensors is expected to improve typical computer vision tasks, such as target tracking and image classification. In this paper, we investigate the scenario in which two cameras, one with a conventional RGB sensor and the other with a hyperspectral sensor, capture the same scene, attempting to extract redundant and complementary information. We propose a non-negative sparse promoting framework to integrate the hyperspectral and RGB data into a high resolution hyperspectral set of data. The formulated problem is in the form of a sparse non-negative matrix factorization with prior knowledge on the spectral and spatial transform responses, and it can be handled by alternating optimization where each subproblem is solved by efficient convex optimization solvers; e.g., the alternating direction method of multipliers. Experiments on a public database show that our method achieves much lower average reconstruction errors than other state-of-the-art methods.

This paper investigates channel coded transmission schemes for two-way relay networks (TWRNs) where two terminal nodes exchange information through a set of amplify-and-forward (AF) relays over frequency-selective fading channels. Specifically, we assume that the two terminal nodes employ bit-interleaved coded modulation (BICM) and orthogonal frequency division multiplexing (OFDM) for coded data transmission, while the relays employ distributed space-time coding (DSTC) for forwarding the received signals. Our main contribution lies in analyzing the achievable diversity order of such channel coded AF-TWRNs. We show that the two terminal nodes, by using a maximum-likelihood (ML) BICM-OFDM decoder, can harvest the full cooperative and frequency diversity. Simulation results are presented to verify our analytical results.

The main goal of this special issue is to gather state-of-the art-contributions that address such challenges as they pertain to the design, analysis, and optimization of physical layer security in next-generation networks.

This paper considers transmit optimization in multi-input multi-output (MIMO) wiretap channels, wherein we aim at maximizing the secrecy capacity or rate of an MIMO channel overheard by one or multiple eavesdroppers. Such optimization problems are nonconvex, and appear to be difficult especially in the multi-eavesdropper scenario. In this paper, we propose an alternating optimization (AO) approach to tackle these secrecy optimization problems. We first consider the secrecy capacity maximization (SCM) problem in the single eavesdropper scenario. An AO algorithm is derived through a judicious SCM reformulation. The algorithm conducts some kind of reweighting and water-filling in an alternating fashion, and thus is computationally efficient to implement. We also prove that the AO algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point of the SCM problem. Then, we turn our attention to the multiple eavesdropper scenario, where the artificial noise (AN)-aided secrecy rate maximization (SRM) problem is considered. Although the AN-aided SRM problem has a more complex problem structure than the previous SCM, we show that AO can be extended to deal with the former, wherein the problem is handled by solving convex problems in an alternating fashion. Again, the resulting AO method is proven to have KKT point convergence guarantee. For fast implementation, a custom-designed AO algorithm based on smoothing and projected gradient is also derived. The secrecy rate performance and computational efficiency of the proposed algorithms are demonstrated by simulations.

This letter studies cooperative secure beamforming for amplify-and-forward (AF) relay networks in the presence of multiple eavesdroppers. Under both total and individual relay power constraints, we propose two schemes, namely secrecy rate maximization (SRM) beamforming and null-space beamforming. In the first scheme, our design problem is based on SRM. Using a suboptimal, but convex, technique-semidefinite relaxation (SDR), we show that this problem can be handled by performing a one-dimensional search which involves solving a sequence of semidefinite programs (SDPs). To reduce the complexity, in the second scheme, we instead maximize the information rate at the destination while completely eliminating the information leakage to all eavesdroppers. We prove that this problem can be exactly solved by SDR with one SDP only. Simulation results demonstrate the performance gains of the two proposed designs.

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.

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.

We consider the scenario of an unknown overdetermined instantaneous mixture of quasi-stationary sources. Blind source separation (BSS) under this scenario has drawn much attention, motivated by applications such as speech and audio separation. The ideas in the existing BSS works often focus on exploiting the time-varying statistics characteristics of quasi-stationary sources, through various kinds of formulations and optimization methods. In this paper, we are interested in further assuming that the sources exhibit some form of local sparsity, which is generally satisfied in speech. By exploiting this additional assumption, we show that there is a simple closed-form solution for the BSS problem. Simulation results based on real speech show that the proposed closed-form algorithm is computationally much lower than some existing BSS algorithms, while delivering a promising mean-square-error performance.

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.

In physical-layer multicasting over a multiuser MISO downlink channel, transmit beamforming using semidefinite relaxation (SDR) has been a popular approach. In this paper, we propose a rank-2 transmit beamformed Alamouti space-time code scheme, which may be seen as a generalization of the previous SDR-based beamforming framework. The beamforming problem arising from the proposed scheme is a rank-2 constrained semidefinite program (SDP).We deal with it using the SDR technique, but this time using rank-2 approximation rather than rank-1 approximation in the previous transmit beamforming. An analysis on the worst-case approximation accuracy of the rank-2 SDR approximation is provided, which reveals that the approximation accuracy degrades at a rate of √M, where M is the number of users served. This improves upon the case of transmit beamforming, where the worst-case approximation accuracy degrades at the higher rate of M. Simulation results further show that the proposed scheme performs better than the transmit beamforming scheme.

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.

Consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple-input multiple-output (MIMO) spectrum sharing cognitive radio (CR) network. The minimization problem of transmit power is formulated subject to both the quality-of-service (QoS) constraints on the secondary receivers and the interference temperature constraints on the primary users, under the assumption of imperfect channel state information (CSI). The problem is non-convex quadratically constrained quadratic program (QCQP), and it is hard to achieve the global optimality. As a compromise, we present a randomized approximation algorithm for the problem via convex optimization techniques. In particular, we point out that the robust beamforming problem is efficiently solvable when the number of primary and secondary links in the CR network is not larger than three. Simulation results are presented to demonstrate the performance gains of the proposed algorithm over an existing robust design.

This paper considers an artificial noise (AN) aided secrecy rate maximization (SRM) problem for a multi-input single-output (MISO) channel overheard by multiple single-antenna eavesdroppers. We assume that the transmitter has perfect knowledge about the channel to the desired user but imperfect knowledge about the channels to the eavesdroppers. Therefore, the resultant SRM problem is formulated in the way that we maximize the worst-case secrecy rate by jointly designing the signal covariance W and the AN covariance Σ. However, such a worst-case SRM problem turns out to be hard to optimize, since it is nonconvex in W and Σ jointly. Moreover, it falls into the class of semi-infinite optimization problems. Through a careful reformulation, we show that the worst-case SRM problem can be handled by performing a one-dimensional line search in which a sequence of semidefinite programs (SDPs) are involved. Moreover, we also show that the optimal W admits a rank-one structure, implying that transmit beamforming is secrecy rate optimal under the considered scenario. Simulation results are provided to demonstrate the robustness and effectiveness of the proposed design compared to a non-robust AN design.

This paper describes a new approximate maximum-likelihood (ML) MIMO detection approach by studying a Lagrangian dual relaxation (LDR) of ML. Unlike many existing relaxed ML methods, the proposed LDR employs a discrete domain for the problem formulation. We find that the proposed LDR exhibits an intriguing relationship to the lattice decoders (LDs) and the lattice reduction aided (LRA) detectors, both of which have caught much attention recently. Specifically, regularization in LDs, which was proposed to mitigate out-of-bounds symbol effects, can alternatively be interpreted as a way to constrain the symbol decision within bounds in a Lagrangian sense. We handle the LDR problem by using a projected subgradient method. The resultant method may physically be viewed as an adaptive regularization control in which a sequence of LDs are involved. Based on this newly developed insight, we propose two additional iterative LDR-based detectors using LRA decision-feedback (DF) and "lazy" DF. By simulation results, we show that the LDR LRA-DF and lazy-DF detectors yield better symbol error rate performance than the MMSE-regularized LRA-DF and DF detectors, respectively, where the SNR gaps can be more than 3dB.

This paper considers the problem of low complexity implementation of high-performance semidefinite relaxation (SDR) MIMO detection methods. Currently, most SDR MIMO detectors are implemented using interior-point methods. Although such implementations have worst-case polynomial complexity (approximately cubic in the problem size), they can be quite computationally costly in practice. Here we depart from the interior-point method framework and investigate the use of other low per-iteration-complexity techniques for SDR MIMO detection. Specifically, we employ the row by-row (RBR) method, which is a particular version of block coordinate descent, to solve the semidefinite programs that arise in the SDR MIMO context with an emphasis on the QPSK scenario. In each iteration of the RBR method, only matrix-vector multiplications are needed, and hence it can be implemented in a very efficient manner. Our simulation results show that the RBR method can indeed offer a significant speedup in runtime, while providing bit error rate performance on par with the interior-point methods.

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 there has been much interest in using transmit beamforming to provide multi-antenna physical-layer multicasting. A state of the art in this context is the semidefinite relaxation (SDR) method for handling the design optimization. This paper proposes an alternative multicast transmit strategy where the transmit beams are random and time-varying. This proposed strategy consists of two key ingredients: i) the randomizations are guided by SDR, but without the need of rank-one approximation as in the existing fixed transmit beamformer; and ii) channel coding is employed to deal with the time randomizations. We adopt an achievable rate perspective, and show that the gaps between the rates of the proposed stochastic beamformers and the optimal multicast capacity are no greater than 0.8314 bps/Hz, irrespective of any factor such as the number of users served. Our simulation results demonstrate that under a rate-1/3 turbo code setting, the stochastic beamformers can yield an SNR gain of more than 4dB compared to the fixed beamformer, given that the bit error rate is 10e−5.

Recently, there has been growing interest in secure communication via multi-antenna physical-layer designs. In this paper, we consider a transmit covariance design for a secrecy rate maximization problem under a multicast scenario, where a multi-antenna transmitter delivers a common confidential message to multiple single-antenna receivers in the presence of multiple multi-antenna eavesdroppers. This multicast secrecy rate maximization (SRM) problem is nonconvex by nature. By resorting to a convex approximation, we provide an upper bound and lower bounds of the multicast secrecy rate by solving a semidefinite program. In particular, for the case of either i) no more than three legitimate receivers and one eavesdropper, or ii) one legitimate receiver and arbitrary number of eavesdroppers, these bounds are shown to be tight and transmit beamforming is an optimal transmit strategy. We also demonstrate by simulations that the multicast SRM problem can be accurately approximated by the proposed method.

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.

Two-path successive relaying has recently been proposed as a mechanism for recovering the multiplexing loss of conventional relay networks; however, the full diversity cannot be guaranteed with this method. In this paper, distributed space-time block coding (STBC) is proposed for a two-path successive decode-and-forward relay network that can achieve both full rate and full diversity when perfect decoding is enabled at the relays. For the case of imperfect decoding, selection relaying is proposed with the distributed STBC to recover the full diversity. For the practical scenario in which the inter-relay channel is subject to fading, the two-path successive relaying transmission may not always be successful; for such cases an adaptive relaying scheme is proposed that can select a proper transmission mode between two-phase relaying transmission and two-path successive relaying transmission based on the channel quality of the relay network. Analytical results show that the proposed distributed STBC can offer both full diversity and a large symbol rate gain.

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.

A distributed space-time block code (STBC) based on a decode-and-forward (DF) protocol is proposed for two-path successive relaying. By making the two relay nodes transmit and listen in turn, the proposed distributed STBC can achieve not only full rate but also full diversity when the relay nodes can correctly decode the information symbols from the source node and when the inter-relay channels are sufficiently strong. We also analyze the situation when there are decoding errors at the relay nodes. We notice in this case full diversity will not be achieved. We then propose the application of selection relaying to the proposed distributed STBC to ensure that full rate and full diversity can still be obtained with decoding errors at the relay nodes.

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.

The advances of multi-antenna techniques has recently led to renewed interest in physical-layer secrecy, a meaningful topic that enables us to prevent eavesdroppers from retrieving information intended for a legitimate user through physical layer designs. This paper address a secrecy-rate maximization problem for the scenario of a multi-input single-output channel listened by multiple multi-antenna eavesdroppers; e.g., in downlink. This problem is nonconvex and has no analytical solution. Through a careful analysis and reformulation, we show that the secrecy-rate maximization problem has a convex equivalent in form of a semidefinite program (SDP). We also prove that the respective optimal transmit covariance generally can yield a rank-one structure, implying that transmit beamforming is secrecy-rate optimal in the considered scenario. Simulation results are also provided to illustrate that the optimal transmit design solved by our SDP approach can yield significantly improved secrecy rates than an existing closed-form design.

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.

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.

The problem of node localization in a wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an an important yet challenging research topic. Most WSN localization studies at present have assumed that the anchor positions are perfectly known which is not valid in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for finding the localizations of unknown-position nodes in the presence of anchor position uncertainty. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and Cramer-Rao lower bound.

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.

As an enabling functionality of overlay cognitive radio networks, spectrum sensing needs to reliably detect licensed signal in the band of interest. To achieve reliable sensing, we propose a linear fusion scheme for distributed spectrum sensing to combine the sensing results from multiple spatially distributed cognitive radios. The optimal linear fusion design is formulated into a nonconvex optimization problem. We show that the optimal solution of such a nonconvex problem can be solved via semi-definite programming reformulation.

A cooperative system may have both timing errors and multiple carrier frequency offsets (CFOs). To combat timing errors, space-frequency (SF) coded OFDM systems have been recently proposed for cooperative communications to achieve both full cooperative and full multipath diversities without time synchronization requirement. In this paper, we study the effect of multiple CFOs from relay nodes on a family of rotation based SF codes. We find that they can still achieve full diversities under the condition that the absolute values of normalized CFOs are less than 0.5. We further show that this full diversity property still holds for a complexity-reduced two-stage zero forcing (ZF) aided maximum likelihood (ML) decoding method, for which a ZF method is used to equalize multiple CFOs before ML decoding.

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.

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.

Estimating the positions of sensor nodes is a fundamental and crucial problem in wireless sensor networks. In this paper, a novel subspace approach for range-based measurements node localization is devised. Computer simulations are included to contrast the performance of the proposed algorithm with the conventional subspace positioning method, namely, classical multidimensional scaling, as well as the Cramer-Rao lower bound.

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.

Recently there has been growing interest in employing the orthogonal space-time block codes (OSTBCs) for blind maximum-likelihood (ML) detection. Several independent works have suggested that OSTBCs are favorable space-time codes from a blind receiver implementation standpoint. In this work we turn our attention to blind ML identifiability, with an emphasis on a special class of codes called the nonintersecting subspace (NIS) OSTBCs. We show a powerful property that NIS-OSTBCs are uniquely identifiable up to a sign for any nonzero channel. However, many existing OSTBCs are not NIS. We propose a code construction procedure that can convert an existing OSTBC to an NIS-OSTBC. Simulation result are provided to support our theoretical findings.

In this letter, the problem of adaptive tracking the amplitude and phase of a noisy sinusoid with known frequency is addressed. Based on approximating the recursive Gauss-Newton approach, two computationally simple algorithms, which provide direct parameter estimates, are devised and analyzed. Simulation results show that the proposed methods can attain identical estimation performance as their original one.

In recent years there has been much interest in the probability hypothesis density (PHD) filtering approach, an attractive alternative to tracking unknown numbers of targets and their states in the presence of data association uncertainty, clutter, noise, and miss-detection. In particular, it has been discovered that the PHD filter has a closed form solution under linear Gaussian assumptions on the target dynamics and birth. This finding opens up a new direction where the PHD filter can be practically implemented in an effective and reliable fashion. However, the previous work is not general enough to handle jump Markov systems (JMS), a popular approach to modeling maneuvering targets. In this paper, a closed form solution for the PHD filter with linear JMS is derived. Our simulations demonstrate that the proposed PHD filtering algorithm provides promising performance. In particular, the algorithm is capable of tracking multiple maneuvering targets that cross each other

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.

Maximum likelihood (ML) detection of symbols transmitted over a MIMO channel is generally a difficult problem due to its NP-hard nature. However, not every instance of the detection problem is equally hard. Thus, the average complexity of an ML detector may be significantly smaller than its worst-case counterpart. This is typically true in the high SNR regime where the received signals are closer to the noise free transmitted signals. Herein, a method which may be used to lower the average complexity of any ML detector is proposed. The method is based on the ability to verify if a symbol estimate is ML, using an optimality condition provided by the near-ML semidefinite relaxation technique. The average complexity reduction advantage of the proposed method is confirmed by numerical results.

We consider the problem of blind maximum-likelihood (ML) detection for the orthogonal space-time block code (OSTBC) scheme. Our previous work has shown that the problem can be simplified to a Boolean quadratic program (BQP). This sequel focuses on effective optimization methods for that BQP, which, from an optimization viewpoint, is still a computationally hard problem. First, we consider semidefinite relaxation (SDR), a high-precision BQP approximation algorithm with a computational cost that is polynomial in the problem size. We also propose a simple method that can significantly reduce the average complexity of the SDR technique. Second, we consider sphere decoding, an exact BQP solver that can be computationally expensive in the worst case, but generally incurs a reasonable average complexity particularly at high SNRs. Simulation results indicate that these two blind ML algorithms provide very similar bit error rate performance. Moreover, numerical studies show that SDR provides better complexity performance than sphere decoding in the worst-case sense, while sphere decoding provides better complexity performance in the average sense.

Using time-difference-of-arrival (TDOA) measurements to perform speaker localization has received much interest recently. Motivated by the significant progress in TDOA single speaker localization, this paper presents a TDOA multi-speaker location tracking algorithm based on Bayesian particle filtering. The development is based on the random finite set framework, which provides an effective treatment to the problem of an unknown time-varying number of active speakers. The proposed method can be viewed as a generalization of the existing single-speaker particle filter. Using a simulated reverberant room, we demonstrate the tracking capability of the proposed particle filter.

Joint multi-target detection and tracking is a challenging problem due to several factors such as the number of targets being an unknown time-varying random parameter, and the target generated measurements being obscured by clutter. The theory of random finite sets permits an elegant formulation of the joint multi-target detection and tracking problem in a Bayesian framework, in particular, the random finite set formalism leads to the probability hypothesis density (PHD) filtering method, which realizes Bayesian joint detection and tracking in a suboptimal but numerically tractable manner. In this paper the PHD filter is applied to jointly detect and track multiple maneuvering targets. The tracking performance fidelity of the PHD filter is demonstrated by numerical results.

The orthogonal frequency division multiplexing (OFDM) system has been demonstrated to be effective in a frequency selective multipath fading environment. To compensate the deleterious effects of the fading channels, pilot symbol assisted modulation (PSAM) technique has been used to obtain the channel estimate. In order to have an accurate estimate, a high percentage of pilot symbols is usually needed and thus reducing the spectrum efficiency. Therefore, the number of pilot symbols is a tradeoff between channel estimation accuracy and bandwidth efficiency. In this paper, we propose a novel method of deciding the optimal number of pilots in OFDM transmission. The method is based on the derivation and analysis of bit error rate (BER) of a PSAM-OFDM system in multipath fading channel in terms of the pilot spacing for a given block size.

The techniques of using wireless cellular networks to locate mobile stations have recently received considerable interest. The paper addresses the problem of maximum likelihood (ML) location estimation using (uplink) time-of-arrival (TOA) measurements. Under the standard assumption of Gaussian TOA measurement errors, ML location estimation is a nonconvex optimization problem in which the presence of local minima makes the search of the globally optimal solution hard. To circumvent this difficulty, we propose to approximate the ML problem by relaxing it to a convex optimization problem, namely semidefinite programming. Simulation results indicate that this semidefinite relaxation location estimator provides mean square position error performance close to the Cramer-Rao lower bound for a wide range of TOA measurement error levels.

This paper addresses the blind symbol identifiability of the orthogonal space-time block code (OSTBC) scheme. That is, the conditions under which OSTBC symbols can be identified without ambiguity when channel state information is not available. In many space-time communication schemes, achieving unique blind symbol identification requires certain assumptions on the number of receiver antennas and the rank of the channel matrix. In this paper, we show that unique blind symbol identification of OSTBCs is possible for any number of receiver antennas and for any (nonzero) channel matrix. This attractive unique identifiability result is shown to be achieved by a class of OSTBCs that exhibit certain matrix non-rotational properties. Using these properties, we validate the identifiability of a number of commonly used OSTBCs.

Tracking multiple speakers in an acoustic environment involves jointly estimating the number of speakers and their states. This important problem in signal processing is challenging in theory as well as implementation. The paper presents a novel and fundamentally well-grounded framework for tracking multiple speakers using random finite sets. Simulations are also presented to demonstrate the performance in tracking a randomly varying number of speakers in a reverberant room.

This paper studies a reference-assisted approach for interference canceling (IC) in microphone array systems. Conventionally, reference-assisted IC is based on the zero crosstalk assumption; i.e., when the desired source signal is absent in the reference microphones. In applications where crosstalk is inevitable, the conventional IC approach usually exhibits degraded performance due to cancellation of the desired signal. In this paper, we develop a crosstalk resilient IC method based on the Capon beamforming technique. The proposed beamformer deals with the uncertainty of crosstalk by applying a constraint on the worst-case crosstalk magnitude. The proposed beamformer not only performs IC, it also provides blind beamforming of the desired signal. We show that a blind beamformer based on the traditional minimum-mean-square-error (MMSE) IC method is a special case of the proposed beamformer. One key step of implementing the proposed Capon beamformer lies in solving a difficult nonconvex optimization problem, and we illustrate how the Capon optimal solution can be effectively approximated using the so-called semidefinite relaxation algorithm. Simulation results demonstrate that the proposed beamformer is more robust against crosstalk-induced signal cancellation than beamformers based on the MMSE-IC methods.

Orthogonal space-time block codes (OSTBCs) have attracted much attention because they provide an effective and simple scheme for fully utilizing the diversity gain in multi-antenna systems. We address the problem of decoding OSTBCs without channel state information. We place our emphasis on the blind maximum-likelihood (ML) method with the BPSK constellation, and show that blind ML decoding requires the solution of a computationally hard optimization problem. To overcome this computational difficulty, we propose using a high-precision and efficient approximation algorithm, called semidefinite relaxation (SDR), to implement blind ML decoding suboptimally. The resultant SDR-ML blind decoder is efficient in that its complexity is approximately cubic in the number of symbols processed, and is promising for its appealing theoretical worst-case approximation accuracy. Simulation results show that the bit error performance of the SDR-ML blind decoder is substantially better than that of several other blind decoders including the cyclic ML method and the subspace method.

Location estimation of mobile telephones has received considerable interest in the field of wireless communications. In this paper, a simple and efficient positioning algorithm using received signal strength measurements obtained from at least three base stations are developed. Our proposed method is based on solving a nonconvex constrained weighted least squares problem. Simulation results show that the performance of the proposed method achieves the Cramer-Rao lower bound.

In a microphone array system where references of interference are additionally available, the unwanted signals in the received signals can be removed using Widrow's interference-cancelling (IC) approach. However, in the presence of crosstalk, IC can result in severe cancellation of the desired speech signal. In this paper, we propose a crosstalk-resistant method for joint interference suppression and blind speech signal beamforming. The proposed method is based on the Capon blind estimation principle, and is implemented using a powerful approximation tool, namely semidefinite relaxation. Simulation results show that the proposed method yields improved mean squared error performance compared with the IC-based method.

Maximum-likelihood (ML) multiuser detection provides attractive bit error rate performance, but it is computationally prohibitive to implement (except in certain restricted cases). Recently, it has been shown that ML detection for synchronous CDMA can be efficiently and accurately approximated using the semi-definite relaxation (SDR) method. In this work, we consider the application of SDR to the more general scenario of asynchronous CDMA. To make this application computationally feasible, we incorporate a block coordinate ascent (BCA) technique into our detector. Simulation studies show that the resulting BCA-SDR detector has significantly better BER performance than several typical suboptimal multiuser detectors.

In multiuser detection, maximum-likelihood detection (MLD) is optimum in the sense of minimum error probability. Unfortunately, MLD involves a computationally difficult optimization problem for which there is no known polynomial-time solution (with respect to the number of users). In this paper, we develop an approximate maximum-likelihood (ML) detector using semi-definite (SD) relaxation for the case of anti-podal data transmission, SD relaxation is an accurate and efficient approximation algorithm for certain difficult optimization problems. In MLD, SD relaxation is efficient in that its complexity is O(K/sup 3.5/), where K stands for the number of users. Simulation results indicate that the SD relaxation ML detector has its bit error performance close to the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.

The upper bound derived by Verdu (1986) is often used to evaluate the bit error performance of both the maximum-likelihood (ML) sequence detector for single-user systems and the ML multiuser detector for code-division multiple-access (CDMA) systems. This upper bound, which is based on the concept of indecomposable error vectors (IEVs), can be expensive to compute because in general the IEVs may only be obtained using an exhaustive search. We consider the identification of IEVs for a particular class of ML detection problems commonly encountered in communications. By exploiting the properties of the IEVs for this case, we develop an IEV generation algorithm which has a complexity substantially lower than that of the exhaustive search. We also show that for specific communication systems, such as duobinary signaling, the expressions of Verdu's upper bound can be considerably simplified.

Investigation of detection schemes for non-orthogonal multicarrier modulation (MCM) is motivated by two reasons. Firstly, non-orthogonal MCM offers a higher degree of freedom in pulse-shaping design. Secondly, the problem of detecting orthogonal MCM under channel distortion can be viewed as a problem of detecting non-orthogonal MCM. In this work, the maximum likelihood detector (MLD) is considered for non-orthogonal multicarrier systems. In the absence of inter-block interference, it is shown that the MLD can be efficiently achieved by a Viterbi algorithm (VA). In contrast to using the VA for channel equalization, the proposed VA has its survivor metrics running in the""frequency domain". Incorporating this VA with an interference-canceling approach, we also develop a decision feedback MLD for the case of non-zero inter-block interference. Superior bit error performance of the MLDs is demonstrated by simulations.