This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers — each tailored to specific tensor modes — and develop an efficient alternating direction method of multipliers (ADMM)-based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework’s ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis. • NS-KTR: nonnegative structured Kruskal tensor regression with hybrid regularization. • Mode-specific regularization: LASSO, total variation, and ridge across tensor modes. • Unified framework supports linear and logistic regression for diverse responses. • ADMM-based optimization achieves superior accuracy with significant speedups.

Learning-based downlink power control in cell-free massive multiple-input multiple-output (CFmMIMO) systems offers a promising alternative to conventional iterative optimization algorithms, which are computationally intensive due to online iterative steps. Existing learning-based methods, however, often fail to exploit the intrinsic structure of channel data and neglect pilot allocation information, leading to suboptimal performance, especially in large-scale networks with many users. This paper introduces the pilot contamination-aware power control (PAPC) transformer neural network, a novel approach that integrates pilot allocation data into the network, effectively handling pilot contamination scenarios. PAPC employs the attention mechanism with a custom masking technique to utilize structural information and pilot data. The architecture includes tailored preprocessing and post-processing stages for efficient feature extraction and adherence to power constraints. Trained in an unsupervised learning framework, PAPC is evaluated against the accelerated proximal gradient (APG) algorithm, showing comparable spectral efficiency fairness performance, while significantly improving computational efficiency. Simulations demonstrate PAPC’s superior performance over fully connected networks (FCNs) that lack pilot information, its scalability to large-scale CFmMIMO networks, and its computational efficiency improvement over APG. PAPC is further validated through ablation studies and evaluated across several representative CFmMIMO scenarios, demonstrating robustness to pilot contamination, scalability, and adaptability to varying user counts without retraining.

Publisher Copyright: © 2026 The Authors.

A novel multibeam time-division (TD) multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) approach is proposed to achieve a balanced tradeoff between sensing and communication functionalities and accurate sensing parameter estimation with a wide field-of-view. Firstly, the TD strategy is introduced to address the simultaneous high demands for sensing performance and communication rate. By allocating time resources between sensing and communications, this approach can reach a desired balance between them while avoiding spectrum and spatial interference, as well as competition in power allocation. Next, a new multibeam method is developed to achieve wide-area sensing for TD MIMO ISAC. Conventional multibeam methods typically rely on beam scanning for direction estimation, suffering from limited accuracy. Inspired by Doppler division multiple access (DDMA) approach, the proposed method divides the Doppler spectrum into more subbands, generating more beams than the number of transmit antenna elements using only phase modulation. Beyond enabling flexible control over the sensing coverage location through beam selection, the proposed method also improves parameter estimation accuracy by fully leveraging the inter-beam relationships, particularly for targets located at null directions. Specifically, for such targets, the proposed method achieves a significantly higher maximum unambiguous velocity, mitigating the velocity ambiguity inherent in conventional DDMA. Simulation results validate the effectiveness of the proposed approach in enhancing both the performance tradeoff between sensing and communication, and the accuracy of sensing parameter estimation.

Leveraging one-bit analog-to-digital converter (ADC) instead of high resolution ADC has been introduced as a promising solution for reducing the power consumption and hardware cost of massive millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. However, performance loss caused by discarding the amplitude information by one-bit quantizers is a significant impairment which calls for the development of more accurate channel estimators. To address this problem, a one-bit mmWave MIMO channel estimation method based on adaptive boosting (AdaBoost) which employs two-stage weak classifiers is developed. In the first stage of each weak classifier, an approximate Gaussian discriminant analysis (GDA) binary classifier is used. To capture the sparsity of mmWave channels in the angular domain, a hard thresholding operator is employed in the second stage of each weak classifier. Numerical simulations are included to demonstrate the efficiency and accuracy of the proposed channel estimator.

Earth Observation (EO) data is captured with different instruments and available in multiple formats. The complementation of two passive remote sensing approaches in local small areas is performed here to produce a single, large-area coverage, volumetric soil moisture (VSM) solution. The sensing approaches under consideration are GNSS Interferometric Reflectometry (GNSS-IR), which is a local land-based microwave remote sensing approach that exploits ground-reflected navigation signals; and also multispectral satellite imagery, which is a space-based optical remote sensing approach that allows to analyze the spectral response of surface materials. The focus is on the processing of GNSS-IR outputs aiding a multispectral model using Landsat-8 data. The aim is to provide an accurate, cost-effective solution with wide-area coverage. Landsat-8 spectral indexes highly correlated with soil moisture are fused with GNSS-IR VSM on multiple terrain types. The proposed solution is demonstrated and verified against data from the Soil Moisture Active Passive (SMAP) satellite mission over large-areas.

We propose a robust activity detection for grant free random access using greedy covariance-learning-based matching pursuit (RCL-MP) algorithm. The method incorporates a robust loss function into the Gaussian negative log-likelihood function, and uses matching pursuit framework for greedily selecting the indices of active users. This algorithm employs a flexible loss function effectively recovering sparse support under non-Gaussian noise conditions. Furthermore, we numerically demonstrate the robustness of RCL-MP across various conditions in massive access scenarios.

Robust hybrid beamforming for integrated sensing and communications (ISAC) system under bounded uncertainties in sensing reception is developed using algorithm unrolling technique. First, the robust hybrid beamforming design problem is formulated as an optimization problem that jointly maximizes the communication sum-rate and the worst-case sensing mutual information under the uncertainty of receive steering vector. Then, a benchmark method using projected gradient descent and ascent (PGDA) algorithm is designed to solve this optimization problem. Finally, we propose to unroll the developed PGDA algorithm using the algorithm unrolling technique. Numerical results demonstrate the advantages of the unrolled PGDA algorithm over the PGDA benchmark for addressing the newly introduced problem of robust hybrid beamforming design for ISAC.

We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The new method exploits additional information about the objective function and is built by embedding a heavy-ball type of momentum into the Fast Gradient Method (FGM). We devise a generalization of the estimating sequences, which allows for encoding any form of information about the objective function that can aid in further accelerating the minimization process. In the black box framework, we propose a construction for the generalized estimating sequences, which is obtained by exploiting the history of the previously constructed estimating functions. Moreover, we prove that the proposed method requires at most κ 2 ln 1 ϵ + O ( 1 ) iterations to find a point x with f ( x ) − f ∗ ≤ ϵ , where ϵ is the desired tolerance and κ is the condition number of the problem. Our theoretical results are corroborated by numerical experiments on various types of optimization problems, often dealt with in different areas of the information processing sciences. Both synthetic and real-world datasets are utilized to demonstrate the efficiency of our proposed method in terms of decreasing the distance to the optimal solution, the norm of the gradient and the function value.

A noise covariance matrix estimation approach in unknown noise field for direction finding applicable for the practically important cases of nonuniform and block-diagonal sensor noise is proposed. It is based on an alternating procedure that can be adjusted for a specific noise type. Numerical simulations are conducted in order to establish the generality and superiority of the proposed approach over the existing state-of-the-art methods, especially in challenging scenarios.

In the integrated sensing and communication system, sensing functionalities are expected to benefit the communication instead of compromising its performance. In this paper, a sensing-aided communication channel estimation method is proposed, where the non-cooperative moving targets are localized and the associated propagation paths are excluded from the channel. Specifically, the received signal is formulated as a high-order tensor and then decomposed for channel parameter estimation. The parameters including velocity and angles of each path are automatically paired in the decomposed tensor factors, which enables identification of the high-velocity paths of moving targets. Then, by excluding the parameters of moving targets, a stable communication channel can be constructed. According to simulation, the proposed method contributes to enhanced data transmission performance while accurately localizing the moving targets.

The integration of communication and radar systems could enhance the robustness of future communication systems to support advanced application demands, e.g., target sensing, data exchange, and parallel computation. In this article, we investigate the beamforming design for integrated sensing, computing, and communication (ISCC) in the Internet of Robotic Things (IoRT) scenario. Specifically, we assume that each robot uploads its preprocessed sensing information to the access point (AP). Meanwhile, leveraging the additive features of the spatial wireless channels between robots and AP, over-the-air computation (AirComp) through multirobot cooperation could bolster system performance, particularly in tasks like target localization through sensing. To get a full picture of the effects of antenna array structures and beampatterns on the ISCC system, we evaluate the performance by considering the shared and separated antenna structures, as well as the omnidirectional and directional beampatterns. Based on these setups, the nonconvex optimization problems for the performance tradeoff between sensing and AirComp are formulated to minimize the mean-squared error (MSE) of AirComp and sensing. To efficiently solve these optimization problems, we designed the gradient descent augmented Lagrangian (GDAL) algorithm, which involves dynamically adjusting the step sizes while updating the variables. Simulation results show that the separated antenna structure achieves a lower AirComp MSE than the shared antenna setup because it has greater beam steering Degrees of Freedom. Moreover, the beampattern types have almost no effect on the AirComp MSE for the given antenna structure setup. This comprehensive investigation provides useful guidelines for ISCC framework implementation in IoRT applications.

The use of one-bit analog-to-digital converter (ADC) has been considered as a viable alternative to high resolution counterparts in realizing and commercializing massive multiple-input multiple-output (MIMO) systems. However, the issue of discarding the amplitude information by one-bit quantizers has to be compensated. Thus, carefully tailored methods need to be developed for one-bit channel estimation and data detection as the conventional ones cannot be used. To address these issues, the problems of one-bit channel estimation and data detection for MIMO orthogonal frequency division multiplexing (OFDM) system that operates over uncorrelated frequency selective channels are investigated here. We first develop channel estimators that exploit Gaussian discriminant analysis (GDA) classifier and approximate versions of it as the so-called weak classifiers in an adaptive boosting (AdaBoost) approach. Particularly, the combination of the approximate GDA classifiers with AdaBoost offers the benefit of scalability with the linear order of computations, which is critical in massive MIMO-OFDM systems. We then take advantage of the same idea for proposing the data detectors. Numerical results validate the efficiency of the proposed channel estimators and data detectors compared to other methods. They show comparable/better performance to that of the state-of-the-art methods, but require dramatically lower computational complexities and run times.

Sensing function in integrated sensing and communication (ISAC) system concentrates on collecting and extracting information of the targets from noisy observations, which can assist positioning the users and enable a precise directional communication link. This paper deals with noise reduction via tensor ring (TR) decomposition and total variation (TV) for linear frequency modulated continuous-wave (FMCW) signals in the multiple-input multiple-output ISAC system. Specifically, TR decomposition is used to exploit the low-rankness and describe the global correlation among different dimensions of the high-order received signal. The noise suppression is addressed by the integration of a TV regularization and a Frobenius norm term to ensure sufficient signal-to-noise ratio (SNR). The corresponding optimization problem is solved using augmented Lagrange multiplier (ALM) and proximal alternating minimization. Simulation results illustrate that the proposed method improves denoising performance, leading to a higher output SNR of the target and a better detection probability.

Most available convolutional dictionary learning (CDL) methods use a batch-learning strategy, which consists of alternating optimization of the dictionary and the sparse representations using a training dataset. The computational efficiency of CDL can be improved using an online-learning approach, where the dictionary is optimized incrementally following a sparse approximation of each training sample. However, the existing online CDL (OCDL) methods are still computationally costly when learning large dictionaries. In this paper, we propose an OCDL approach that incorporates decomposed sparse approximations instead of the training samples and substantially improves the computational costs of the existing CDL methods. The resulting optimization problem is addressed using the alternating direction method of multipliers (ADMM).

Recently, Parallel Factor-Direct (PARAFAC-Direct) method has been proposed for parameter estimation including velocity disambiguation for Doppler Division Multiple Access (DDMA) Multiple-Input Multiple-Output (MIMO) radar. However, DDMA MIMO radar spreads the overall transmit energy into the entire spatial region, and therefore, suffers from beam-shape loss that can limit the performance of PARAFAC-Direct method. To solve this problem, a Transmit Beamspace (TB) Slow-Time MIMO (ST-MIMO) approach is proposed that focuses the transmit energy within a desired spatial region. Unlike traditional DDMA MIMO radars, the Doppler spectrum is divided into more subbands than the number of transmit elements to reduce the mainlobe intervals between adjacent beams formed by DDMA modulation vectors. Then, the TB ST-MIMO beam set can be directed to the spatial region of interest via a proper selection of DDMA modulation vectors. Parameter estimation performance of TB ST-MIMO is improved as compared to conventional DDMA MIMO techniques. Simulations are conducted to validate the proposed method.

Existing matrix-based neural network for direction-of-arrival (DOA) estimation has to train a large amount of parameters proportional to the length of vectorized signal statistics, resulting in a heavy system overload. To address the problem, a tensorized neural layer decomposition-based neural network is proposed for 2-D DOA estimation. In particular, the covariance tensor of tensor signals is propagated to hidden state tensors. The feedforward propagation is formulated as an inverse Tucker decomposition, such that parameters in the tensorized neural layers are compressed into inverse Tucker factors. Accordingly, the tensorized backpropagation procedure is designed for network training. It is proved that the number of parameters is significantly reduced, which leads to a faster training process. Simulation results demonstrate that the proposed method reduces the number of trained parameters by more than 122,000 times compared to the matrix-based neural network while maintaining a moderate accuracy.

Low-power millimeter wave (mmWave) multi-input multi-output communication systems can be enabled with the use of one-bit analog-to-digital converters. Owing to the extreme quantization, conventional signal processing tasks such as channel estimation are challenging, making uplink (UL) multiuser receivers difficult to implement. To address this issue, we first reformulate the UL channel estimation problem, and then combine the idea of$\ell_{1}$regularized logistic regression classification and Toeplitz matrix reconstruction in a properly designed optimization problem. Our new method is referred to as$\ell_{1}$regularized logistic regression with Toeplitz matrix reconstruction (L1-RLR-TMR). In addition, we develop a computationally efficient alternating direction method of multi-pliers (ADMM)-based implementation for the L1-RLR-TMR method. Numerical results demonstrate the performance of the L1-RLR-TMR method in comparison with other existing methods.

A plethora of problems arising in signal processing, machine learning and statistics can be cast as large-scale optimization problems with a composite objective structure. Such problems are typically solved by utilizing iterative first-order algorithms. In this work, we devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite objective structure. Specifically, we introduce a new class of estimating functions, which are obtained by utilizing both a tight lower bound on the objective function, as well as the gradient mapping technique. Then, using the proposed estimating functions, we construct a class of Composite Objective Multi-step Estimating-sequence Techniques (COMET), which are endowed with an efficient line-search procedure. We prove that our proposed COMET enjoys the accelerated convergence rate, and our newly established convergence results allow for step-size adaptation. Our theoretical findings are supported by extensive computational experiments on various problem types and real-world datasets. Moreover, our numerical results show evidence of the robustness of the proposed method to the imperfect knowledge of the smoothness and strong convexity parameters.

Direction-of-arrival (DOA) estimation using sub-Nyquist tensor signals benefits from enhanced performance by extracting structural angular information with multi-dimensional sparse arrays. Although convolutional neural network (CNN) has been employed to achieve efficient DOA estimation in challenging conditions, conventional methods demand excessive memory storage and computation power to process sub-Nyquist tensor statistics. In this letter, we propose a decomposed CNN for sub-Nyquist tensor-based 2-D DOA estimation, where an augmented coarray tensor is derived and used as the network input. To compress convolution kernels for efficient coarray tensor propagation, we develop a convolution kernel decomposition approach. This enables the acquisition of canonical polyadic (CP) factors containing compressed parameters. Performing decomposable convolution between the coarray tensor and the CP factors leads to resource-efficient DOA estimation. Our simulation results indicate that the proposed method conserves system resources while maintaining competitive performance.

A novel algorithm for direction-of-arrival (DOA) estimation in nonuniform sensor noise is developed. The diagonal nonuniform sensor noise covariance matrix is estimated by an iterative procedure, which only requires a few iterations. Using the generalized eigendecomposition of two matrices and the least squares, the noise subspace is refined and the noise covariance matrix is estimated iteratively. Since there is no need for knowledge of true DOAs when estimating the noise covariance matrix, our method is superior to most existing approaches. For the proposed noise covariance estimator, we also derive the asymptotic variance of one iteration. Numerical simulations are carried out to demonstrate the advantages of the proposed algorithm over existing state-of-the-art methods.

The robust adaptive beamforming (RAB) problem is considered via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization over distributional uncertainty sets for the random interference-plus-noise covariance (INC) matrix and desired signal steering vector. The distributional uncertainty set of the INC matrix accounts for the support and the positive semidefinite (PSD) mean of the distribution, and a similarity constraint on the mean. The distributional uncertainty set for the steering vector consists of the constraints on the known first- and second-order moments. The RAB problem is formulated as a minimization of the worst-case expected value of the SINR denominator achieved by any distribution, subject to the expected value of the numerator being greater than or equal to one for each distribution. Resorting to the strong duality of linear conic programming, such a RAB problem is rewritten as a quadratic matrix inequality problem. It is then tackled by iteratively solving a sequence of linear matrix inequality relaxation problems with the penalty term on the rank-one PSD matrix constraint. To validate the results, simulation examples are presented, and they demonstrate the improved performance of the proposed robust beamformer in terms of the array output SINR.

A novel method for learning correlated features in multimodal images based on convolutional sparse coding with applications to image fusion is presented. In particular, the correlated features are captured as coupled filters in convolutional dictionaries. At the same time, the shared and independent features are approximated using separate convolutional sparse codes and a common dictionary. The resulting optimization problem is addressed using alternating direction method of multipliers. The coupled filters are fused based on a maximum-variance rule, and a maximum-absolute-value rule is used to fuse the sparse codes. The proposed method does not entail any prelearning stage. The experimental evaluations using medical and infrared-visible image datasets demonstrate the superiority of our method compared to state-of-the-art algorithms in terms of preserving the details and local intensities as well as improving objective metrics.

We present a new type of heavy-ball momentum term, which is used to construct a class of generalized estimating sequences. These allow for accelerating the minimization process by exploiting the information accumulated in the previous iterates. Combining a newly introduced momentum term with the estimating sequences framework, we devise, as an example, a new black-box accelerated first-order method for solving smooth unconstrained optimization problems. We prove that the proposed method exhibits an improvement over the rate of the celebrated fast gradient method by at least a factor of $\frac{1}{{\sqrt 2 }}$, and establish that lower bound on the number of iterations carried through until convergence is $\mathcal{O}\left( {\sqrt {\frac{\kappa }{2}} } \right)$. Finally, the practical performance benefits of the proposed method are demonstrated by numerical experiments.

This paper presents a multimodal image fusion method using a novel decomposition model based on coupled dictionary learning. The proposed method is general and can be used for a variety of imaging modalities. In particular, the images to be fused are decomposed into correlated and uncorrelated components using sparse representations with identical supports and a Pearson correlation constraint, respectively. The resulting optimization problem is solved by an alternating minimization algorithm. Contrary to other learning-based fusion methods, the proposed approach does not require any training data, and the correlated features are extracted online from the data itself. By preserving the uncorrelated components in the fused images, the proposed fusion method significantly improves on current fusion approaches in terms of maintaining the texture details and modality-specific information. The maximum-absolute-value rule is used for the fusion of correlated components only. This leads to an enhanced contrast-resolution without causing intensity attenuation or loss of important information. Experimental results show that the proposed method achieves superior performance in terms of both visual and objective evaluations compared to state-of-the-art image fusion methods.

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. In this letter, we present a novel solution for this subproblem, which improves the computational efficiency of the existing algorithms. The same approach is also used to develop an efficient dictionary learning method. In addition, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error. Source codes for the proposed algorithms are available online.

Direction-of-arrival (DOA) estimation problem is a challenging one in the presence of coherent sources, when the sample size is small, and the signal-to-noise ratio is low. We address this problem by developing a new method called enhanced standard ESPRIT (ES ESPRIT), and also its unitary extension called enhanced unitary ESPRIT (EU ESPRIT). The proposed methods use statistics of the subspace perturbation. First, they generate 2K DOA candidates for K sources, and then discreetly select K of them. Numerical results show the superiority of EU ESPRIT over other existing methods especially in improving threshold performance and separating closely located sources with a small sample size.

In this paper, a general sparse array (SA) design principle, called uniform linear array (ULA) fitting, is proposed. It uses concatenation of sub-ULAs to design SAs with feasible difference coarrays (DCAs). Motivation for the ULA fitting is that the nested array and coprime array are in fact the examples of concatenations of two sub-ULAs which provide good properties. The polynomial model is utilized to investigate the case when an SA is composed of multiple sub-ULAs. An example of SA designed via ULA fitting is presented, and it attests that the ULA fitting enables to design SAs with closedform expressions, low coupling leakage and long consecutive DCA.

In this paper, a constrained tensor decomposition method that enables two dimensional (2D) direction of arrival (DOA) estimation for transmit beamspace (TB) Multiple-Input Multiple-Output (MIMO) radar with subarrays is proposed. Specifically, a higher-order tensor model is designed to collect the received signal for TB MIMO radar with multiple subarrays. By exploiting the inner structure of the factor matrix, the constrained tensor decomposition is conducted, and subsequently the target DOA is estimated. In addition, the angular information can also be computed by solving the minimization problem that originates from the second factor matrix to improve the robustness of the 2D DOA estimation. Simulation results validate the proposed approach.

The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little attention has been paid to modelling such errors in the adjacency matrix, and studying their effects on GSP methods. However, modelling errors in the adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically when possible and numerically, the graph error effect on the performance of GSP methods in different types of problems such as filtering of graph signals and independent component analysis of graph signals (graph decorrelation).

This paper studies the impact of additional pilot overhead for covariance matrix estimation in a time-division duplexed (TDD) massive multiple-input multiple-output (MIMO) system. We choose average uplink (UL) and downlink (DL) spectral efficiencies (SEs) as performance metrics for the massive MIMO system, and derive closed form expressions for them in terms of the additional pilot overhead. The expressions are derived by considering linear minimum mean squared error (LMMSE)-type and element-wise LMMSE-type channel estimates that represent LMMSE and element-wise LMMSE with estimated covariance matrices, respectively. Using these expressions, a detailed theoretical analysis of SE behavior as a function of pilot overhead for both LMMSE-type and element-wise LMMSE-type channel estimation are presented, followed by simulations, which also demonstrate and validate theoretical results.

With a change of signal notion to graph signal, new means of performing blind source separation (BSS) appear. Particularly, existing independent component analysis (ICA) methods exploit the non-Gaussianity of the signals or other types of prior information. For graph signals, such prior information is present in a graph of dependencies in the signals. We propose BSS of graph signals which uses the prior information presented by the signal graph together with non-Gaussianity. We derive the identifiability conditions for the proposed method and compare them to the conditions when only graph or non-Gaussianity approach is used. In simulation studies, we verify that the new method can separate a broader range of graph signals and show that it is also more efficient when both approaches are useful.

We present a diversity multiplexing tradeoff (DMT) optimal tree pruning sphere decoding algorithm which visits merely a single branch of the search tree of the sphere decoding (SD) algorithm, while maintaining the DMT optimality at high signal to noise ratio (SNR) regime. The search tree of the sphere decoding algorithm is pruned via intersecting one dimensional spheres with the hypersphere of the SD algorithm, and the radii are chosen to guarantee the DMT optimality. In contrast to the conventional DMT optimal SD algorithm, which is known to have a polynomial complexity at high SNR regime, we show that the proposed method achieves the DMT optimality by solely visiting a single branch of the search tree at high SNR regime. The simulation results are corroborated with the claimed characteristics of the algorithm in two different scenarios.

The image fusion problem consists in combining complementary parts of multiple images captured, for example, with different focal settings into one image of higher quality. This requires the identification of the sharpest areas in sets of input images. Recently, it was shown that coupled dictionary learning can successfully capture the relationships between high- and low-resolution patches in the context of single image super-resolution. In this work, to identify the sharp image patches, we propose an improved discriminative coupled dictionary learning approach using joint sparse representations in blurred and focused dictionaries. In addition, a pixel-wise processing of the boundaries (i.e., patches containing blurred and focused pixels) is proposed. The experimental results using two natural image datasets, as well as a sequence of in vivo microscopy images, show the competitiveness of the proposed method compared to state-of-the-art algorithms in terms of accuracy and computational time.

We develop a new tensor model for slow-time multiple-input multiple-output (MIMO) radar, and apply it for joint direction-of-departure (DOD), and direction-of-arrival (DOA) estimation. This tensor model aims to exploit the independence of phase modulation matrix, and receive array in the received signal for slow-time MIMO radar. Such tensor can be decomposed into two tensors of different ranks, one of which has identical structure to that of the conventional tensor model for MIMO radar, and the other contains all phase modulation values used in the transmit array. We then develop a modification of the alternating least squares algorithm to enable parallel factor decomposition of tensors with extra constants. The Vandermonde structure of the transmit, and receive steering matrices (if both arrays are uniform, and linear) is then utilized to obtain angle estimates from factor matrices. The multi-linear structure of the received signal is maintained to take advantage of tensor-based angle estimation algorithms, while the shortage of samples in Doppler domain for slow-time MIMO radar is mitigated. As a result, the joint DOD, and DOA estimation performance is improved as compared to existing angle estimation techniques for slow-time MIMO radar. Simulation results verify the effectiveness of the proposed method.

The worst-case robust adaptive beamforming problem for generalrank signal model is considered. This is a nonconvex problem, and an approximate version of it (by introducing a matrix decomposition on the presumed covariance matrix of the desired signal) has been studied in the literature. Herein the original robust adaptive beamforming problem is tackled. Resorting to the strong duality of a linear conic program, the robust beamforming problem is reformulated into a quadratic matrix inequality (QMI) problem. There is no general method for solving a QMI problem in the literature. Here- in, employing a linear matrix inequality (LMI) relaxation technique, the QMI problem is turned into a convex semidefinite programming problem. Due to the fact that there often is a positive gap between the QMI problem and its LMI relaxation, a deterministic approximate algorithm is proposed to solve the robust adaptive beamforming in the QMI form. Last but not the least, a sufficient optimality condition for the existence of an optimal solution for the QMI problem is derived. To validate our theoretical results, simulation examples are presented, which also demonstrate the improved performance of the new robust beamformer in terms of the output signal-to-interference- plus-noise ratio.

The MVDR robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the SOI steering vector. In order to find the optimal steering vector estimate of the SOI, a new beamformer output power maximization problem is formulated subject to a double-sided norm perturbation constraint, a generalized similarity constraint, and a direction-of-arrival (DOA) constraint that guarantees that the DOA of the SOI is away from the DOA region of all linear combinations of the interference steering vectors. It turns out that the power maximization problem is a nonconvex quadratically constrained quadratic program (QCQP) with two homogenous and one inhomogeneous constraints. In general, a globally optimal solution for the QCQP is not guaranteed; however, we herein derive sufficient optimality conditions to ensure the existence of an optimal solution, and develop an efficient algorithm to find the solution. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust adaptive beamformer in terms of the output SINR.

An analytical lower bound on uplink channel capacity of a user in a massive multiple-input multiple-output system where the channel vector and the covariance matrices of the users in that cell are unknown is derived in this paper. This analytical bound enables us to choose appropriate sample size for covariance matrix estimation to meet the spectral efficiency requirements. The accurate agreement between the derived bound and the simulated bound based on random samples of channel vectors and covariance matrices is shown.

Recovering a graph signal from samples is a central problem in graph signal processing. Least mean squares (LMS) method for graph signal estimation is computationally efficient adaptive method. In this paper, we introduce a technique to robustify LMS with respect to mismatches in the presumed graph topology. It builds on the fact that graph LMS converges faster when the graph topology is specified correctly. We consider two measures of convergence speed, based on which we develop randomized greedy algorithms for robust interpolation of graph signals. In simulation studies, we show that the randomized greedy robust least mean squares (RGRLMS) outperforms the regular LMS and has even more potential given a robust sampling design.

The uniform white noise assumption is one of the basic assumptions in most of the existing direction-of-arrival (DOA) estimation methods. In many applications, however, the nonuniform white noise model is more adequate. Then, the noise variances at different sensors have to be also estimated as nuisance parameters while estimating DOAs. In this letter, different from the existing iterative methods that address the problem of nonuniform noise, a non-iterative two-phase subspace-based DOA estimation method is proposed. The first phase of the method is based on estimating the noise subspace via eigendecomposition (ED) of some properly designed matrix and it avoids estimating the noise covariance matrix. In the second phase, the results achieved in the first phase are used to estimate the noise covariance matrix, followed by estimating the noise subspace via generalized ED. Since the proposed method estimates DOAs in a non-iterative manner, it is computationally more efficient and has no convergence issues as compared to the existing methods. Simulation results demonstrate better performance of the proposed method as compared to other existing state-of-the-art methods.

In this letter, we present a generic and computationally efficient method for coupled dictionary learning (CDL). The proposed method enforces relations between the corresponding atoms of dictionaries learned to represent two related (but not necessarily of the same dimensionality) feature spaces, aiming that each pair of related signals from the two feature spaces has the same sparse representation with respect to their corresponding learned dictionaries. Coupled learned dictionaries have various applications in many sparse representation-based recognition and reconstruction problems, where the two related feature spaces are representing the same signal of different modalities or different qualities. The presented experimental comparisons show that the results obtained using our proposed CDL method are competitive to those of the state-of-the-art CDL methods in performance, while the proposed method has a significantly lower computational cost. Furthermore, the proposed method can be straightforwardly used for learning coupled dictionaries from more than two related feature spaces.

Most of the existing ultrasound image restoration methods consider a spatially-invariant point-spread function (PSF) model and circulant boundary conditions. While computationally efficient, this model is not realistic and severely limits the quality of reconstructed images. In this work, we address ultrasound image restoration under the hypothesis of piece-wise linear vertical variation of the PSF based on a small number of prototypes. No assumption is made on the structure of the prototype PSFs. To regularize the solution, we use the classical elastic net constraint. Existing methodologies are rendered impractical either due to their reliance on matrix inversion or due to their inability to exploit the strong convexity of the objective. Therefore, we propose an optimization algorithm based on the Accelerated Composite Gradient Method, adapted and optimized for this task. Our method is guaranteed to converge at a linear rate and is able to adaptively estimate unknown problem parameters. We support our theoretical results with simulation examples.

The millimeter wave WLAN standard can be used for joint communication-radar by exploiting the waveform preamble as a radar pulse. The velocity estimation accuracy with this approach, however, is limited due to the short integration time. A physical increase in the radar pulse integration duration, however, leads to a decrease in the communication data rate. In this paper, a coprime-based pulse design approach for IEEE 802.11ad-based radar is proposed that uses only a few non-uniformly placed preambles to construct several virtual pulses for enhancing the velocity estimation accuracy/resolution as compared to the conventional approach without sacrificing the communication data rate. The simulation results demonstrate that the coprime-based virtual pulse design improves the velocity estimation resolution by a factor of about 60x at a vehicle separation distance of 10m and by a factor of about 20× at a distance of 100 m, while simultaneously achieving 7 Gbps data rate.

A novel computationally efficient method for jointly designing the space-(slow) time (SST) transmission with unimodular waveforms and receive adaptive filter is developed for different radar configurations. The range sidelobe effect and Doppler characteristics are considered. In particular, we develop a novel approach for jointly synthesizing unimodular SST waveforms and minimum variance distortionless response receive adaptive filter for two cases of known Doppler information and presence of uncertainties on clutter bins. Corresponding non-convex optimization problems are formulated and efficient algorithms are derived. The main ideas of the algorithm developments are to decouple composite objective function of the formulated problems, generate minorizing surrogates, and then solve the joint design problem iteratively, but in closed-form for each iteration by means of minorization - maximization technique. The proposed algorithms demonstrate good performance and have fast convergence speed and low complexity.

The first step in any graph signal processing (GSP) task is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little, if any, attention has been paid to modeling such errors in the adjacency matrix, and studying their effects on GSP tasks. Modeling errors in adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically and in terms of simulations, the graph error effect on the performance of GSP based on the example of independent component analysis of graph signals (graph decorrelation).

Millimeter wave (mmWave) multiple-input multiple-output (MIMO) transceivers employ narrow beams to obtain a large array-gain, rendering them sensitive to changes in the angles of arrival and departure of the paths. Since the singular vectors that span the channel subspace are used to design the precoder and combiner, we propose a method to track the receiver-side channel subspace during data transmission using a separate radio frequency (RF) chain dedicated for channel tracking. Under certain conditions on the transmit precoder, we show that the receiver-side channel subspace can be estimated during data transmission without knowing the structure of the precoder or the transmitted data. The performance of the proposed method is evaluated through simulations.

Existing ultrasound deconvolution approaches unrealistically assume, primarily for computational reasons, that the convolution model relies on a spatially invariant kernel and circulant boundary conditions. We discard both restrictions and introduce an image formation model applicable to ultrasound imaging and deconvolution based on an axially varying kernel, which accounts for arbitrary boundary conditions. Our model has the same computational complexity as the one employing spatially invariant convolution and has negligible memory requirements. To accommodate the state-of-the-art deconvolution approaches when applied to a variety of inverse problem formulations, we also provide an equally efficient adjoint expression for our model. Simulation results confirm the tractability of our model for the deconvolution of large images. Moreover, in terms of accuracy metrics, the quality of reconstruction using our model is superior to that obtained using spatially invariant convolution.

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio, incorporating a positive semidefinite constraint on the actual covariance matrix of the desired signal. In the literature, semidefinite program (SDP) techniques, together with others, have been applied to approximately solve this problem. Herein, an inner second-order cone program (SOCP) approximate algorithm is proposed to solve it. In particular, a sequence of SOCPs are constructed and solved, while the SOCPs have the nonincreasing optimal values and converge to a locally optimal value (it is in fact a globally optimal value through our extensive simulations). As a result, our algorithm does not use computationally heavy SDP relaxation technique. To validate our inner approximation results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformer in terms of the averaged cpu-time (indicating how fast the algorithms converge) in a high signal-to-noise region.

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

In this paper, we investigate the downlink throughput performance of a massive multiple-input multiple-output system that employs superimposed pilots for channel estimation. The component of downlink (DL) interference that results from transmitting data alongside pilots in the uplink (UL) is shown to decrease at a rate proportional to the square root of the number of antennas at the BS when the least-squares channel estimate is employed in a matched-filter precoder. The normalized mean-squared error (NMSE) of the channel estimate is compared with the Bayesian Cramér-Rao lower bound that is derived for the system, and the former is also shown to diminish with increasing number of antennas at the base station. Furthermore, we show that staggered pilots are a particular case of superimposed pilots and offer the downlink throughput of superimposed pilots while retaining the UL spectral and energy efficiency of regular pilots. We also extend the framework for designing a hybrid system, consisting of users that transmit either regular or superimposed pilots, to minimize both the UL and DL interference. The improved NMSE and DL rates of the channel estimator based on superimposed pilots are demonstrated by means of simulations.

The Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is regarded as the state-of-the-art among a number of proximal gradient-based methods used for addressing large-scale optimization problems with simple but non-differentiable objective functions. However, the efficiency of FISTA in a wide range of applications is hampered by a simple drawback in the line search scheme. The local estimate of the Lipschitz constant, the inverse of which gives the step size, can only increase while the algorithm is running. As a result, FISTA can slow down significantly if the initial estimate of the Lipschitz constant is excessively large or if the local Lipschitz constant decreases in the vicinity of the optimal point. We propose a new FISTA-like method endowed with a robust step size search procedure and demonstrate its effectiveness by means of a rigorous theoretical convergence analysis and simulations.

A new method for designing single/multiple unimodular waveforms with good weighted correlation properties, which is based on minimizing the weighted integrated sidelobe levels of waveforms, is developed. The main contributions of the paper lie in formulating the objective as a quartic form where Hadamard product of matrices is involved, converting the non-convex quartic optimization problem into a quadratic form and then solving it by means of majorization-minimization technique which seeks to find the solution iteratively. Corresponding algorithm enables good weighted correlations of the designed waveforms and shows fast convergence compared with existing methods.

In massive multiple-input multiple-output (MIMO) systems, superimposed (SP) and time-multiplexed (TM) pilots exhibit a complementary behavior, with the former and latter schemes offering a higher throughput in high and low inter-cell interference scenarios, respectively. Based on this observation, in this paper, we propose an algorithm for partitioning users into two disjoint sets comprising users that transmit TM and SP pilots. This selection of user sets is accomplished by minimizing the total inter-cell and intra-cell interference, and since this problem is found to be non-convex, a greedy approach is proposed to perform the partitioning. Based on simulations, it is shown that the proposed method is versatile and offers an improved performance in both high and low-interference scenarios.

Waveform separation based on matched filtering leads to autocorrelation sidelobe and cross correlation, which deteriorate the performance of multiple-input multiple-output synthetic aperture radar (MIMO-SAR). This letter investigates the performance of a waveform-separation approach employing an extended space-time coding (STC) scheme for MIMO-SAR. Using the autocorrelation property of multiphase complementary codes, we propose a novel STC scheme to effectively cancel out both the autocorrelation sidelobe and cross correlation. Using theoretical analysis also confirmed by simulations, we show that the proposed scheme decreases the sidelobe ratio while increasing the signal-to-noise ratio, leading to high-quality.

The letter addresses the image fusion problem, where multiple images captured with different focus distances are to be combined into a higher quality all-in-focus image. Most current approaches for image fusion strongly rely on the unrealistic noise-free assumption used during the image acquisition, and then yield limited fusion robustness. In our approach, we formulate the multifocus image fusion problem in terms of an analysis sparse model, and simultaneously perform the restoration and fusion of multifocus images. Based on this model, we propose an analysis operator learning, and define a novel fusion function to generate an all-in-focus image. Experimental evaluations confirm the effectiveness of the proposed fusion approach both visually and quantitatively, and show that our approach outperforms the state-of-the-art fusion methods.

Optimal relay selection is investigated for secure cooperative communications against an adaptive eavesdropper that can perform eavesdropping if the eavesdropping link has good channel quality or perform jamming otherwise. A number of decode-and-forward relays are available for legitimate communications, among which one relay can be selected to help. For legitimate communications, three cases for availability of the eavesdropping channel information are considered: full channel knowledge, partial channel knowledge, and statistical channel knowledge. An optimal relay selection scheme is proposed for each case. For the first and third cases, exact secrecy outage probability expressions in closed form are derived, and for the second case, an approximate secrecy outage probability is derived, which is tight in the high main-to-eavesdropper ratio regime. Moreover, secrecy diversity order for the proposed relay selection scheme in each case is also derived, which is shown to be a full secrecy diversity. Finally, numerical results are given to verify the theoretical analysis derived in this paper.

A novel multi-focus image fusion approach using coupled dictionary training is proposed. It exploits the facts that (i) the patches in example data can be sparsely represented by a couple of over-complete dictionaries related to the focused and blurred categories of images and (ii) merging such representations is better than just selecting the sparsest one in the estimate of the original image. Inspired by these observations, we enforce the similarity of sparse representations between the focused and blurred image patches by jointly training the coupled dictionary, and then fuse these representations to generate an all-in-focus image by a fusion rule. The key characteristics of our approach are bridging the gap between coupled dictionaries, combining plain averaging and "choose-max" as an appropriate fusion rule, and forming a more accurate representation, compared to existing approaches which simply admit sparse representation over one dictionary. Extensive experimental comparisons with state-of-the-art multi-focus image fusion algorithms validate the effectiveness of the proposed approach.

We address the problem of terrain-scattered jammer suppression in multiple-input multiple-output (MIMO) radar using space-(fast) time adaptive processing (SFTAP). The correlation function of jamming components after matched filtering at the receiving end of MIMO radar is derived, and its relationship to the correlation matrix of the transmitted waveforms is established. This correlation function serves as a theoretical measure of evaluating the matched filtering effect on the received jamming signals. We propose a minimum variance distortionless response (MVDR) type SFTAP design by taking into account the factors of waveform-introduced range sidelobes and cold clutter stationarity over different pulse intervals. A closed-form solution to this design is derived by means of the method of Lagrange multipliers. We also propose a relaxed SFTAP design by modifying the constraints of the MVDR type design. Both proposed SFTAP designs can support further slow-time Doppler processing procedure. Simulation results show the validity of our SFTAP designs.

Superimposed pilots are proposed as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output systems. Provided that the uplink duration is larger than the total number of users in the system, superimposed pilots enable each user to be assigned a unique pilot sequence, thereby allowing for a significant reduction in pilot contamination. Channel estimation performance in the uplink is further improved using an iterative data-aided algorithm. Based on approximate expressions for the uplink signal-to-interference-plus-noise ratio, it is shown that superimposed pilots provide a better performance when compared with methods that use time-multiplexed data and pilots. Numerical simulations are used to validate the approximations and the improved performance of the proposed method.

In this letter, a joint robust transmit/receive adaptive beamforming for multiple-input multiple-output (MIMO) radar based on probability-constrained optimization approach is developed in the case of Gaussian and arbitrary distributed mismatches present in both the transmit and receive signal steering vectors. A tight lower bound of the probability constraint is also derived by using duality theory. The formulated probability-constrained robust beamforming problem is nonconvex and NP-hard. However, we reformulate its cost function into a bi-quadratic function while the probability constraint splits into transmit and receive parts. Then, a block coordinate descent method based on second-order cone programming is developed to address the biconvex problem. Simulation results show an improved robustness of the proposed beamforming method as compared to the worst-case and other existing state-of-the-art joint transmit/receive robust adaptive beamforming methods for MIMO radar.

In this paper, the problem of joint hot and cold clutter mitigation in the context of transmit beamspace (TB)-based multipleinput multiple-output (MIMO) radar is studied. The TB-based MIMO radar enables special spatio-temporal structure and low rank of clutter covariance matrices. To efficiently mitigate the hot clutter such as terrain scattered multipath jamming concentrated in the sector-of-interest and the enhanced cold clutter due to transmit energy focusing, we resort to three-dimensional (3D) space-time adaptive processing (STAP) technique. A new 3D STAP method is proposed, which significantly reduces the computational complexity. We show from interference mitigation perspective that the TB-based MIMO radar enables superior output signal-to-interference-plus-noise ratio to that of its traditional MIMO radar counterpart.

Subspace based methods provide a good compromise between performance and complexity. However, these methods are exposed to performance breakdown at the low SNR and/or small sample size region. It has been known for a long time that a major reason for such performance breakdown is the subspace swap phenomenon. However, in some scenarios such as the case of closely spaced sources, the breakdown happens before the subspace swap occurs. The reason is identified to be the intersubspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, we formally define the notion of subspace leakage which can be used as a measure for performance analysis and comparison of different methods used for estimating the signal and noise subspaces. We further study the statistical properties of the subspace leakage for the case of sample data covariance matrix.

The desired property of having the same beampattern for different columns of a beamspace transformation matrix (beamforming vectors) often plays a key importance in practical applications. At most 2M - 1- 1 beamforming vectors with the same beampattern can be generated from any given beamforming vector, where M is the size of the beamforming vector. Thus, one can start with a single (mother) beamforming vector, which gives a desired beampattern, but may not satisfy some other desired properties, and generate all other beamforming vectors, which give the same beampattern, in a computationally efficient way. Then the beamforming vectors, which in addition satisfy other desired properties that the mother beamforming vector may not satisfy, can be selected. Such procedure is developed in this letter in the application to the transmit beamspace design that ensures practically important properties for multiple-input multiple-output radar. A computationally efficient sub-optimal method for selecting best beamforming vectors from a population of vectors that give the same beampattern is also developed.

In this letter, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramér-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.

An equivalent model for a multiple-input-multiple-output communication system with space-time block codes (STBCs) is proposed based on a revealed connection between STBCs and Euclidean codes. Examples of distance spectra, signal constellations, and signal coordinate diagrams of Euclidean codes equivalent to simplest orthogonal STBCs are given. A new asymptotic upper bound for the symbol error rate (SER) of STBCs, based on the distance spectra of the equivalent Euclidean codes, is derived, and new general design criteria for signal constellations of the optimal code are proposed. Some bounds relating distance properties, dimensionality, and cardinality of STBCs with constituent signals of equal energy are given, and new signal constellations with cardinalities of 8 and 16 for Alamouti's code are designed. A general methodology for performance analysis of STBCs is revisited. As an example of the application of this methodology, an exact evaluation of the SER of an orthogonal STBC is given. Namely, a new expression for the SER of Alamouti's code with binary phase shift keying signals is derived.

The problem of jamming on a multiple-input multiple-output (MIMO) Gaussian channel is investigated. We show that the existing result based on the simplification of the system model by neglecting the jamming channel leads to losing important insights regarding the effect of jamming power and jamming channel on the jamming strategy. We find a closed-form optimal solution for the problem under some positive semidefinite condition without considering simplifications in the model. If the condition is not satisfied and the optimal solution may not exist in closed-form, we find a suboptimal solution in closed-form as a close approximation of the optimal solution. Simulation results verify the effectiveness of the proposed solutions.

In this paper, we introduce and solve a particular generalization of the quadratically constrained quadratic programming (QCQP) problem which is frequently encountered in different fields of signal processing and communications. Specifically, we consider such generalization of the QCQP problem that comprises compositions of one-dimensional convex and quadratic functions in the constraint and the objective functions. We show that this class of problems can be precisely or approximately recast as the difference-of-convex functions (DC) programming problem. Although the DC programming problem can be solved through the branch-and-bound methods, these methods do not have any worst-case polynomial-time complexity guarantees. Therefore, we develop a new approach with worst-case polynomial-time complexity that can solve the corresponding DC problem of a generalized QCQP problem. It is analytically guaranteed that the point obtained by this method satisfies the Karsuh-Kuhn-Tucker (KKT) optimality conditions. Furthermore, the global optimality can be proved analytically under certain conditions. The new proposed method can be interpreted in terms of the Newton's method as applied to a non-constrained optimization problem.

The problem of jammers suppression in colocated multiple-input multiple-output (MIMO) radar is considered. We resort to reduced dimension (RD) beamspace designs with robust-ness/adaptiveness to achieve the goal of efficient jammers suppression. Specifically, our RD beamspace techniques aim at designing optimal beamspace matrices based on reasonable tradeoffs between the desired in-sector source distortion and the powerful jammer (possibly in-sector) attenuation when conducting the jammers suppression. These designs are cast as convex optimization problems which are derived using second-order cone programming. Meanwhile, we study the MUSIC-based direction-of-arrival estimation performance of the proposed beamspace designs by comparing to the conventional algorithms. Moreover, we demonstrate that the capability of efficient powerful in-sector jammers suppression using these designs is unique in MIMO radar.

An ambiguity function (AF) for the multiple-input multiple-output (MIMO) radar with correlated waveforms is derived. It serves as a generalized AF for which the phased-array and the traditional MIMO radar AFs are important special cases. A simplified expression for the AF for the case of far-field targets and narrow-band waveforms is also derived. We establish relationships between the generalized MIMO radar AF metric and the previous works on AF including the Woodward's AF and the AF defined for the traditional colocated MIMO radar. Moreover, we compare the AF of the MIMO radar with correlated waveforms with the squared-summation-form AF definition. Simulation results show that the generalized MIMO radar AF achieves lower relative sidelobe level with proper design of the waveform correlation matrix or, equivalently, the transmit beamspace matrix.

In this paper, we consider the problem of optimizing the transmit co-variance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convex difference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the co-variance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.

We consider a MIMO radar with arbitrary multi-dimensional array, and propose a method for transmit array interpolation that maps an arbitrary transmit array into an array with a certain desired structure. A properly designed interpolation matrix is used to jointly achieve transmit array interpolation and design transmit beamforming. The transmit array interpolation problem is cast as a convex optimization problem based on minmax criterion. Our designs enable to control the side-lobe levels of the transmit beampattern and enforce different transmit beams to have rotational invariance with respect to each other, a property that enables the use of computationally efficient direction finding techniques. It is shown that the rotational invariance can be achieved independently in both the elevation and the azimuth spatial domains, allowing for independent elevation and azimuth direction finding.

The challenge in designing relay beamforming in two-way relaying systems is the non-convex nature of the corresponding optimization problem. In this work, we concentrate on the mathematical issues of such design for the cases when the max-min rate and proportional fairness are used as the design criteria. We show that the corresponding optimization problems belong to the class of difference-of-convex functions (DC) programming problems. Due to the specific structure of the corresponding DC problems, they can be efficiently addressed by using the polynomial-time DC (POTDC) algorithm which guarantees to find the Karush-Kuhn-Tucker (KKT) optimal point in polynomial-time. We have also shown earlier that the question of global optimality of the POTDC algorithm boils down to a simple numerical convexity check for a certain one-dimensional optimal value function.

The problem of sum-rate maximization with minimum power consumption is studied for a decode-and-forward (DF) multiple-input multiple-output (MIMO) two-way relaying system consisting of two sources and one relay. Two scenarios are investigated. In the first scenario, the relay optimizes its own power allocation/beamforming strategy given that the strategies of the sources maximize the sum-rate of the multiple-access channel (MAC) phase. In the second scenario, the relay and the sources jointly optimize their power allocation/beamforming strategies over both the MAC and broadcasting (BC) phases. The considered problem of sum-rate maximization with minimum power consumption is shown to be nonconvex in both scenarios. For the first scenario, an algorithm is proposed to find the optimal strategy of the relay. For the second scenario, the sources and the relay find their strategies either through transferring the original nonconvex problem into corresponding convex problems or using a proposed low-complexity algorithm. Simulation results demonstrate the performance of proposed algorithms.

We consider the problem of separating simultaneous source blended data in applied seismology. Cross-source interference that masks the desired signal in the common source domain can be translated into incoherent noise by rearranging the data in the common receiver domain. We show that applying a virtual blending/deblending process to the data in the common receiver domain enables obtaining an additional noisy version of the data. By measuring the local similarities and dissimilarities between the two noisy versions of the data, it is possible to discriminate between corrupt and non-corrupt data points. Corrupt data points can be replaced by a weighted sum (e.g., averaging) of neighboring non-corrupt data points. The proposed method is applied directly in the time-space domain, i.e., no computationally expensive data transformation is needed. Moreover, it can be straightforwardly extended to higher-dimensional data scenarios. Simulation results are given to validate the effectiveness of the proposed method.

The problem of sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying is considered. Mathematically, this problem is equivalent to the constrained maximization of the product of quadratic ratios that is a non-convex problem. Such problems appear also in many other applications. This problem can be further relaxed into a difference-of-convex functions (DC) programming problem, which is typically solved using the branch-and-bound method without polynomial-time complexity guarantees. We, however, develop a polynomial-time convex optimization-based algorithm for solving the corresponding DC programming problem named polynomial-time DC (POTDC). POTDC is based on a specific parameterization of the problem, semi-definite programming (SDP) relaxation, linearization, and iterations over a single parameter. The complexity of the problem solved at each iteration of the algorithm is equivalent to that of the SDP problem. The effectiveness of the proposed POTDC method for the sum-rate maximization in two-way AF MIMO relay systems is shown.

This paper studies the correlogram spectrum estimation method for the case that only a subset of the Nyquist samples is available. The method is able to estimate the spectrum from undersampled data. The bias and variance of the estimator are derived. We also show that there is a tradeoff between the accuracy of the estimation and the frequency resolution. The asymptotic behavior of the estimator is also investigated, and it is proved that this method is a consistent estimator.

The standard least mean squares (LMS) parameter estimation method does not assume any special structure for the parameters being estimated. However, when additional knowledge about the system is available, the performance of LMS can be improved by appropriate modification of the algorithm. We develop such modifications for the case of estimating frequency sparse channels. Such modifications provide either better performance or less complexity when compared to the standard LMS algorithm. Decimated LMS and zero attracting decimated LMS are the two methods proposed in this paper. Simulation results are also provided to compare the performance of the proposed algorithms to the standard LMS and other sparsity aware modifications of LMS.

We consider a multi-pair two-way relay network with multiple single antenna amplify-and-forward relays. The sum rate maximization problem subject to a total transmit power constraint is studied for such network. The optimization problem is non-convex. First, we show that the problem is a monotonic optimization problem and propose a polyblock approximation algorithm for obtaining the global optimum. However, this algorithm is only suitable for benchmarking because of its high computational complexity. After observing that the necessary optimality condition for our problem is similar to that of the generalized eigenvalue problem, we propose to use the generalized power iterative algorithm which can approach the global optimum recursively. Finally, we propose the total signal-to-interference-plus-noise ratio (SINR) eigen-beamformer which is a closed-form suboptimal solution that reduces the computational complexity significantly. Simulation results show that the proposed algorithms outperform the existing scheme. Moreover, the total SINR eigen-beamformer almost achieves the performance of the optimal solution.

In this paper, we present interference models for cognitive radio (CR) networks employing various interference management mechanisms including power control, contention control or hybrid power/contention control schemes. For the first case, a power control scheme is proposed to govern the transmission power of a CR node. For the second one, a contention control scheme at the media access control (MAC) layer, based on carrier sense multiple access with collision avoidance (CSMA/CA), is proposed to coordinate the operation of CR nodes with transmission requests. The probability density functions (PDFs) of the interference received at a primary receiver from a CR network are first derived numerically for these two cases. For the hybrid case, where power and contention controls are jointly adopted by a CR node to govern its transmission, the interference is analyzed and compared with that of the first two schemes by simulations. Then, the interference PDFs under the first two control schemes are fitted by log-normal PDFs to reduce computation complexity. Moreover, the effect of a hidden primary receiver on the interference experienced at the receiver is investigated. It is demonstrated that both power and contention controls are effective approaches to alleviate the interference caused by CR networks. Some in-depth analysis of the impact of key parameters on the interference of CR networks is given as well.

A wireless relay network with one source, one relay and one destination is considered, where nodes communicate via N orthogonal channels. We develop optimal power allocation strategies at both the source and relay for maximizing the overall source-destination capacity under individual power constraints at the source and relay. Some properties of the optimal solution are studied.

A problem of joint optimal bandwidth and power allocation in cognitive networks under fading channels is considered. It is assumed that multiple secondary users (SUs) share the spectrum of a primary user (PU) using frequency division multiple access. The bandwidth and power are allocated so as to maximize the sum ergodic capacity of all SUs under the total bandwidth constraint of the licensed spectrum as well as different combinations of the peak/average transmit power constraints at the SUs and the peak/average interference power constraint imposed by the PU. Although the optimization problem is convex, its dimension and, thus, complexity may be high. Therefore, computationally efficient ways of solving the problem are of importance and are investigated here by finding structures of the optimal solutions to the problem under different combinations of the constraints.

In this paper, we consider the problem of direction finding in multiple-input multiple-output (MIMO) radar based on focusing the transmitted pulse energy within certain spatial sector(s). We propose a method for designing the transmit weight matrix based on maximizing the energy transmitted within the desired spatial sector and minimizing the energy disseminated in the out-of-sector area. The proposed transmit energy focusing results in the signal-to-noise ratio increase at the receive array which in turn leads to lower Cramer-Rao bound and improved direction of arrival estimation performance. Simulation results show the substantial improvements offered by the proposed transmit energy focusing based MIMO radar as compared to the traditional MIMO radar and the MIMO radar with receive beamspace post-processing.

The transmit beamspace design problem for colocated multiple-input multiple-output (MIMO) radar is considered. We show that the MIMO radar transmit beampattern can be designed so that it is as close as possible to the desired one, the power is uniformly distributed across the transmit antennas, and most significantly, the rotational invariance property at the receive array with arbitrary geometry is satisfied. The latter enables a straightforward application of search-free direction of arrival estimation techniques such as ESPRIT in the unconventional case with the receive array of arbitrary geometry. The transmit beamspace design problem is cast as an optimization problem which is non-convex in general, but can be solved efficiently using the semi-definite programming relaxation technique.

This paper introduces a new algorithm for reconstructing signals with sparse spectrums from noisy compressive measurements. The proposed model-based algorithm takes the signal structure into account for estimating the unknown parameters which are the frequencies and amplitudes of linearly combined sinusoids. A high-resolution spectral estimation method is used to recover the frequencies of the signal elements, while the amplitudes of the signal components are estimated by minimizing the squared norm of the compressed estimation error using the least squares (LS) technique. The Cramer-Rao bound (CRB) for the given system model is also derived. It is shown that the proposed algorithm with properly selected step size of the LS algorithm achieves the CRB at high signal to noise ratio values.

The least mean squares (LMS) algorithm is one of the most popular recursive parameter estimation methods. In its standard form it does not take into account any special characteristics that the parameterized model may have. Assuming that such model is sparse in some domain (for example, it has sparse impulse or frequency response), we aim at developing such LMS algorithms that can adapt to the underlying sparsity and achieve better parameter estimates. Particularly, the example of channel estimation with sparse channel impulse response is considered. The proposed modifications of LMS are the lp-norm and reweighted l1-norm penalized LMS algorithms. Our simulation results confirm the superiority of the proposed algorithms over the standard LMS as well as other sparsity-aware modifications of LMS available in the literature.

In this paper, we investigate the interference mitigation from a cross-layer perspective for a cognitive radio (CR) multiple-input multiple-output (MIMO) network coexisting with a primary time-division-duplexing (TDD) system. The channel allocation in the media access control (MAC) layer and a subspace-based precoding scheme in the physical layer of the CR network are jointly considered to minimise the interference to the primary user and maximise the CR throughput. Two distributed cross-layer algorithms, namely, joint iterative channel allocation and precoding (JICAP) and non-iterative channel allocation and precoding (NICAP), are proposed for the cases with and without channel information among CR nodes, respectively. Moreover, a channel estimation scheme is also proposed to enable the NICAP. The effectiveness of the proposed algorithms over non-cross-layer counterpart is demonstrated via simulations.

The problem of power allocation/channel selection in two-user games is considered. Unlike most of the game theoretic studies on resource allocation problems which consider pure strategies, this work investigates mixed strategies and mixed strategy Nash equilibrium (MSNE) that enables users to adopt more subtle strategies to improve their utilities. The necessary and sufficient conditions for the existence/uniqueness of MSNE are derived, first in a two-channel case and then in a more practical N channel case. In the two-channel game, the MSNE which maximizes the utilities of both users is found. In the N-channel game, a channel selection algorithm for the users, the outputs of which can be used to check the existence/uniqueness of MSNE, is proposed.

The problem of resource allocation among multiple users with total power and spectral mask constraints is studied based on cooperative game-theoretic approach. The problem is non-convex, and finding the optimal solution requires joint power and bandwidth allocation that renders high-complexity algorithms. Therefore, we first categorize the systems to bandwidth-dominant and power-dominant according to their bottleneck resources. Then, different manners of cooperation are adopted for each type of systems, and a two-user algorithm is developed for each case. Such categorization guarantees that the solution obtained in each case is Pareto-optimal, while the complexity is significantly reduced.

The resource allocation problem in wireless multi-user decode-and-forward (DF) relay networks is considered. The conventional resource allocation schemes based on the equal distribution of bandwidth and/or power may not be efficient for the networks with constrained/limited power and bandwidth resources at both sources and relays. Therefore, joint bandwidth and power allocation schemes are proposed based on (i) the maximization of the sum capacity of all users (source-destination pairs); (ii) the maximization of the worst user capacity; (iii) the minimization of the total power consumptions for all users. It is shown that the proposed problem formulations can be transformed to equivalent convex optimization problems. Therefore, the joint bandwidth and power allocation problems can be efficiently solved. The performance improvements offered by the proposed schemes are demonstrated by simulations.

In this paper, we present an interference model for cognitive radio (CR) networks employing power control or contention control scheme. The probability density functions (PDFs) of the interference received at a primary receiver from a CR network are derived for two cases. For the first case, a power control scheme is proposed to govern the transmission power of a CR node. For the second one, a cognitive media access control (MAC) employs carrier sense multiple access with collision avoidance (CSMA/CA) based contention control to coordinate the operation of CR nodes with transmission requests. These two control schemes are compared in terms of their resulting interference distributions. It is demonstrated that both power and contention controls are effective approaches to alleviate the interference caused by CR networks. Some in-depth analysis for the impact of key parameters on the interference of CR networks is given via numerical studies as well.

A precoding strategy for multi-user spectrum sharing over an interference channel is proposed and analyzed from a game-theoretic perspective. The proposed strategy is based on finding the Nash bargaining solution for precoding matrices in a cooperative scenario over frequency selective channels under a spectrum mask constraint. An in-time update of the precoding matrices is enabled by using time slots to guarantee the effectiveness of the bargaining solution when the number of users varies. A dual decomposition approach is exploited to construct a distributed structure for solving the bargaining problem. The proposed distributed algorithm realizes the physical process of bargaining, which is not present in the Nash bargaining theory.

We propose a new technique for multiple-input multiple-output (MIMO) radar with colocated antennas. The essence of the proposed technique is to partition the transmitting array into a number of subarrays that are allowed to overlap. Each subarray is used to coherently transmit a waveform which is orthogonal to the waveforms transmitted by other subarrays. Coherent processing gain can be achieved by designing a weight vector for each subarray to form a beam towards a certain direction in space. Moreover, the subarrays are combined jointly to form a MIMO radar resulting in higher resolution capabilities. Simulation results show the substantial improvements offered by the proposed technique as compared to previous techniques that validate its effectiveness.

In this paper, the source covariance matrices of multiple-input multiple-output (MIMO) interference channels (IFCs) are investigated from a game-theoretic perspective. It is proved that the requirement of sufficiently small interference-to- noise ratio (INR) is the sufficient condition for the uniqueness of the Nash bargaining (NB) solution. The structure of the source covariance matrices, which constitute the feasible set of NB solution, is analyzed by comparing them with the covariance matrices leading to the Nash equilibrium (NE). The existence of the NB solution and concavity of the rate product for MIMO IFCs are also studied.

In multiuser diversity systems, the impact of large-scale fading on the total system performance such as link quality and system power has not been widely addressed. Considering large-scale fading, we propose an adaptive multiuser scheduling to minimize the total system power while reducing the effect of large-scale fading on the system bit error rate. The number of active users is adapted to every shadow variation, which varies slower than small-scale fading. We consider the two widely used multiuser systems (i.e., delay-tolerant, and delay-sensitive multiuser systems). Closed-form expressions for the bit error rate are derived. The selection procedure for the minimum number of users is introduced for guaranteed performance of the above multiuser systems. The impact of adaptive multiuser diversity gain on the system power and bit error rate is illustrated over large-scale fading channels by numerical results.

Optimal power allocation for multi-user amplify- and-forward wireless relay networks in which multiple source-destination pairs are assisted by a set of relays is investigated. Two relay power allocation strategies based on maximization of either i) the minimum rate among all users or ii) the weighted sum of rates are developed. A distributed implementation of the maximum weighted-sum-rate power allocation strategy is also studied. Numerical results demonstrate the efficiency of the proposed strategies and reveal their interesting throughput-fairness tradeoff in resource allocation.

We develop a data-adaptive dimension reduction algorithm that is robust against out-of-sector sources in application to array processing. The dimension reduction is done as a linear transformation (matrix filter). The matrix filter is designed adaptively such that the signal power within a certain sector is preserved while the out-of-sector power is maximally rejected. The columns of the beamspace matrix are designed sequentially, one column at a time. This sequential implementation is carried out by imposing orthogonality constraints between beamspace matrix columns. Hence, the white noise property at the output of the beamspace preprocessor is preserved. The latter is important for subsequent data processing. The proposed algorithm is computationally less expensive as compared to the existing data-adaptive beamspace design techniques. Simulation results validate the robustness of the developed algorithm, and they show its effectiveness and superiority to the existing algorithms.

Collaborative beamforming has been recently introduced in the context of wireless sensor networks (WSNs) to increase the transmission range of individual sensor nodes. The challenge in using collaborative beamforming in WSNs is the uncertainty regarding the sensor node locations. However, the actual sensor node spatial distribution can be modeled by a properly selected probability density function (pdf). In this paper, we model the spatial distribution of sensor nodes in a cluster of WSN using Gaussian pdf. Gaussian pdf is more suitable in many WSN applications than, for example, uniform pdf which is commonly used for flat ad hoc networks. The average beampattern and its characteristics, the distribution of the beampattern level in the sidelobe region, and the distribution of the maximum sidelobe peak are derived using the theory of random arrays. We show that both the uniform and Gaussian sensor node deployments behave qualitatively in a similar way with respect to the beamwidths and sidelobe levels, while the Gaussian deployment gives wider mainlobe and has lower chance of large sidelobes.

The performance of multiple-antenna communication systems is known to critically depend on the amount of channel state information (CSI) available at the transmitter. In the low-rate CSI feedback case, an important problem is what kind of information should be submitted to the transmitter in each feedback cycle and what is the optimal transmission strategy in this case. In this paper, we address this problem in the multiple-input single-output (MISO) case by analytically comparing the bit error rate (BER) performance of different low-rate feedback based transmitter strategies involving various combinations of transmit antenna selection, Alamouti's spacetime coding, and adaptive power allocation.

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

In this paper, preceding strategies over interference channels are analyzed from a game-theoretic perspective. The Nash equilibrium and Nash bargaining solutions of preceding matrices, as the optimal precoding strategies in non-cooperative and cooperative cases, respectively, are derived for a two-player game over both flat fading and frequency selective channels. It is shown that the non-cooperative and cooperative solutions of precoding matrices are the same over multiple-input single- output(MISO) flat fading interference channels under a total power constraint. The solution in flat fading channel case is also extended to an M-player case.

In this paper, we consider an amplify-and-forward (AF) wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. While each user is assisted by one relay, one relay can assist many users. Conventionally, each relay node is assumed to equally distribute the available bandwidth and power resources to all sources for which it helps to relay information. Realizing the sub-optimality of this approach, in this paper, we present efficient power allocation schemes to i) maximize the minimum end-to-end signal-to-noise ratio among all users; ii) minimize the total transmit power over all sources; iii) maximize the system throughput. Our approach is based on geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal power allocation can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

Collaborative beamforming has been recently introduced in the context of wireless sensor networks (WSNs) to increase the transmission range of individual sensor nodes. In this paper, it is proposed to model the spatial distribution of sensor nodes in a cluster using Gaussian probability density function (pdf). Gaussian pdf is more appropriate for many WSN applications than the previously considered uniform pdf which is more suitable when sensor nodes are deployed one at a time. The average beampattern and its characteristics, the distribution function of the beampattern level in the sidelobe region, and the upper bound on the outage probability of sidelobes are derived using the theory of random arrays.

In this paper, a new algorithm for robust adaptive beamforming is developed. The basic idea of the proposed algorithm is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Unlike other robust beamforming techniques, our algorithm does not assume that the norm of the mismatch vector is upper bounded, and hence it does not suffer from the negative effects of over/under estimation of the upper bound. Simulation results show the effectiveness of the proposed algorithm.

The performance of multiuser detection (MUD) algorithms for code- division multiple-access (CDMA) systems depends on the accuracy of channel estimates. Such estimates are typically affected by errors, which can lead to significant degradation of the performance. In this paper, we develop a MUD technique which is based on probability constrained optimization of the minimum mean-square error (MMSE) multiuser receiver, and is robust against channel estimation errors. Its relationship to the recently proposed robust worst case optimization based MUD technique is established. The uncertainty parameter of the worst case based design is quantified in terms of the outage probability used in the probability constrained design and second-order statistics of the channel estimation errors. Simulation results demonstrate the potential of the proposed technique to outperform the existing robust techniques.

A new approach to the design of robust adaptive beamforming is introduced. The essence of the new approach is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Contrary to the worst-case performance-based and the probability-constrained-based approaches, our approach does not make any assumptions on either the norm of the mismatch vector or its probability distribution. Hence, it avoids the need for estimating their values.

In this letter, a robust code-division multiple-access (CDMA) multiuser detection technique which is based on the probability-constrained optimization approach is developed, and its relationship to the popular worst-case-based robust CDMA multiuser detection technique is established. The important advantage of the proposed probability-constrained optimization-based approach with respect to the worst-case-based design is that in the former approach, the parameter of the uncertainty region of the worst-case-based design is quantified in terms of the outage probability and second-order statistics of the user signature estimation error. A simulation example demonstrates the advantages of such statistically motivated choice of the parameter of the uncertainty region.

It is a challenging task for multi-hop wireless networks to support multimedia applications with quality-ofservice (QoS) requirements. This letter presents a joint crosslayer optimization approach, i.e., joint medium access control, routing, and energy distribution. User satisfaction represented by user utility is maximized within the required network lifetime, given the constraints on the total available energy in the network and the minimum user rates. Although the resulting optimization problem is nonlinear and nonconvex, we prove that it is approximately equivalent to a two-step convex problem. Furthermore, we prove that the problem of maximizing network utility within achievable network lifetime is quasiconvex

In this paper, an interesting relationship between the worst-case optimization-based and probability-constrained approaches to the robust adaptive beamformer design is found both in the cases of Gaussian and non-Gaussian steering vector mismatch. The established relationship demonstrates that the probabilistic beamformer design may be approximately interpreted in terms of the worst-case design, and quantifies the parameters of the latter design in terms of the beamformer outage probability.

Two related problems of the design of robust adaptive beamformers and multiuser multiple-input multiple-output (MIMO) receivers are considered. A popular recent solution to these problems is based on the worst-case performance optimization. Unfortunately, in practical applications the actual worst case occurs with a very low probability and, as a result, the worst-case based designs may be overly conservative. As a less conservative alternative to the worst-case designs, the so-called probabilistically constrained designs are introduced. The latter approach guarantees that the distortionless response constraint is satisfied for a mismatched array response with a certain selected probability. Improved flexibility and performance of the robust probabilistically constrained designs with respect to the worst-case designs are illustrated via simulations.

Traditional multiuser receiver algorithms developed for multiple-input-multiple-output (MIMO) wireless systems are based on the assumption that the channel state information (CSI) is precisely known at the receiver. However, in practical situations, the exact CSI may be unavailable because of channel estimation errors and/or outdated training. In this paper, we address the problem of robustness of multiuser MIMO receivers against imperfect CSI and propose a new linear technique that guarantees the robustness against CSI errors with a certain selected probability. The proposed receivers are formulated as probabilistically constrained stochastic optimization problems. Provided that the CSI mismatch is Gaussian, each of these problems is shown to be convex and to have a unique solution. The fact that the CSI mismatch is Gaussian also enables to convert the original stochastic problems to a more tractable deterministic form and to solve them using the second-order cone programming approach. Numerical simulations illustrate an improved robustness of the proposed receivers against CSI errors and validate their better flexibility as compared with the robust multiuser MIMO receivers based on the worst case designs.

In the orthogonal frequency-division multiplexing (OFDM) scheme, some subcarriers may be subject to a deep fading. Adaptive techniques can be applied to mitigate this effect if the channel-state information (CSI) is available at the transmitter. In this paper, we study the performance of an OFDM-based communication system whose transmitter has only one bit of CSI per subcarrier, obtained through a low-rate feedback. Three adaptive approaches are considered to exploit such a CSI feedback: adaptive subcarrier selection; adaptive power allocation (APA); and adaptive modulation selection (AMS). Under the conditions of a constant raw data rate and perfect feedback channel, the performance of these approaches are analyzed and compared in terms of raw bit-error rate. It is shown that one-bit CSI feedback can greatly enhance the system performance. Moreover, imperfections of the feedback channel are considered, and their impact on the performance of these techniques is studied. It is shown that by exploiting the knowledge that the feedback channel is imperfect, the performance of the APA and AMS techniques can be substantially improved

In the orthogonal frequency division multiplexing (OFDM) scheme, some subcarriers may be subject to a deep fading. Adaptive techniques can be applied to mitigate this effect if the channel state information (CSI) is available at the transmitter. In this paper, we study the performance of an OFDM-based communication system whose transmitter has only one bit (of CSI per subcarrier that is obtained through a low rate feedback. Three adaptive approaches are considered to exploit such a CSI feedback: adaptive subcarrier selection, adaptive power allocation and adaptive modulation selection. Under the condition of constant raw data rate, the performance of these approaches is analyzed and compared in terms of raw bit error rate (BER). We have found that one-bit CSI feedback can greatly enhance the system performance. Among the three approaches, the adaptive subcarrier selection approach is found to have the lowest BER when the feedback is perfect.

Parallel factor (PARAFAC) analysis is an extension of low-rank matrix decomposition to higher-way arrays. It decomposes a given array in a sum of multilinear terms. PARAFAC analysis generalizes and unifies common array processing models (like joint diagonalization and ESPRIT); it has found numerous applications from blind multiuser detection and multi-dimensional harmonic retrieval to clustering and nuclear magnetic resonance. The prevailing fitting algorithm in all these applications is based on alternating least squares (ALS) optimization, which is matched to Gaussian noise. In many cases, however, measurement errors are far from being Gaussian. We develop an iterative algorithm for least absolute error fitting of general multilinear models, based on efficient interior point methods for linear programming (LP). We also benchmark its performance in Laplacian, Cauchy, and Gaussian noise environments, versus the respective CRBs and the commonly used ALS algorithm.

Adaptive beamforming methods degrade in the presence of both signal steering vector errors and interference nonstationarity. We develop a new approach to adaptive beamforming that is jointly robust against these two phenomena. Our beamformer is based on the optimization of the worst case performance. A computationally efficient convex optimization-based algorithm is proposed to compute the beamformer weights. Computer simulations demonstrate that our beamformer has an improved robustness as compared to other popular robust beamforming algorithms.

Adaptive beamforming methods are known to degrade in the presence of both signal steering vector errors and interference nonstationarity. In this paper, we develop a new approach to adaptive beamforming which is jointly robust against these two phenomena. Our approach is based on the optimization of the worst-case beamforming performance. A computationally efficient convex optimization based algorithm is proposed to compute the beamformer weights. Computer simulations compare the performance of our algorithm with other robust adaptive beamforming techniques.

If the desired signal is present in training snapshots, the adaptive array performance is known to be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors. Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration or distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance using Second-Order Cone (SOC) programming. The adaptive beamformer proposed is shown to have a substantially improved robustness as compared to existing algorithms and enjoy simple implementation.