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Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes’ independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning. [ABSTRACT FROM AUTHOR]

This paper focuses on optimal time-of-arrival (TOA) sensor placement for multiple target localization simultaneously. In previous work, different solutions only using non-shared sensors to localize multiple targets have been developed. Those methods localize different targets one-by-one or use a large number of mobile sensors with many limitations, such as low effectiveness and high network complexity. In this paper, firstly, a novel optimization model for multi-target localization incorporating shared sensors is formulated. Secondly, the systematic theoretical results of the optimal sensor placement are derived and concluded using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), based on rigorous geometrical derivations. The reachable optimal trace of Cramér-Rao lower bound (CRLB) is also derived. It can provide optimal conditions for many cases and even closed form solutions for some special cases. Thirdly, a novel numerical optimization algorithm to quickly find and calculate the (sub-)optimal placement and achievable lower bound is explored, when the model becomes complicated with more practical constraints. Then, a hybrid method for solving the most general situation, integrating both the analytical and numerical solutions, is proposed. Finally, the correctness and effectiveness of the proposed theoretical and mathematical methods are demonstrated by several simulation examples. [ABSTRACT FROM AUTHOR]

This paper proposes a momentum algorithm based on Borges difference and an adaptive momentum (Adam) algorithm based on Borges difference to update parameters, which can adjust the momentum information more flexibly. The Borges difference is proposed from the definition of Borges derivative to be combined with the gradient algorithm in convolutional neural networks. The proposed momentum algorithm based on Borges difference and Adam algorithm based on Borges difference can be adjusted more flexibly in order to speed up the convergence. The parameter optimization algorithm with the Borges difference presents a better performance compared with the integer-order momentum algorithm and integer-order Adam algorithm, with the proposed nonlinear adjustment method for the parameter tuning of convolutional neural networks. By analyzing experimental results of Fashion-MNIST dataset and CIFAR-10 dataset, the optimization algorithms based on Borges difference proposed in this paper gain better effects on the optimization model compared with the corresponding ones based on the integer-order difference, and can speed up the convergence speed and recognition accuracy of the image recognition. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so degrades when the noise is heteroscedastic across samples, as occurs, e.g., when samples come from sources of heterogeneous quality. This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model. Unlike in the homoscedastic setting, the resulting nonconvex optimization problem is not seemingly solved by singular value decomposition. This paper develops a heteroscedastic probabilistic PCA technique (HePPCAT) that uses efficient alternating maximization algorithms to jointly estimate both the underlying factors and the unknown noise variances. Simulation experiments illustrate the comparative speed of the algorithms, the benefit of accounting for heteroscedasticity, and the seemingly favorable optimization landscape of this problem. Real data experiments on environmental air quality data show that HePPCAT can give a better PCA estimate than techniques that do not account for heteroscedasticity. [ABSTRACT FROM AUTHOR]

Signal classification problems arise in a wide variety of applications, and their demand is only expected to grow. In this paper, we focus on the wireless sensor network signal classification setting, where each sensor forwards quantized signals to a fusion center to be classified. Our primary goal is to train a decision function and quantizers across the sensors to maximize the classification performance in an online manner. Moreover, we are interested in sparse sensor selection using a marginalized weighted kernel approach to improve network resource efficiency by disabling less reliable sensors with minimal effect on classification performance. To achieve our goals, we develop a multi-sensor online kernel scalar quantization (MSOKSQ) learning strategy that operates on the sensor outputs at the fusion center. Our theoretical analysis reveals how the proposed algorithm affects the quantizers across the sensors. Additionally, we provide a convergence analysis of our online learning approach by studying its relationship to batch learning. We conduct numerical studies under different classification and sensor network settings which demonstrate the accuracy gains from optimizing different components of MSOKSQ and robustness to reduction in the number of sensors selected. [ABSTRACT FROM AUTHOR]

This paper considers the integrated waveform design to simultaneously achieve a desired radar beampattern and multi-users communication for a dual-function Multiple-Input Multiple-Output (MIMO) system. To this end, a spatio-spectral modulation strategy via shaping the spatial waveform Energy Spectral Density (ESD) in directions of communication is proposed for the communication function, while beampattern Integrated Sidelobe Level (ISL) is minimized to enhance radar detectability. Meanwhile, Peak-to-Average Ratio (PAR) and power restrictions to comply with the current hardware technique and the mainlobe width constraint to cohere the beampattern main energy on the spatial region of interest are forced, respectively. Exploiting an equivalent reformulation of the original non-convex optimization problem, a Sequential Block Enhancement (SBE) framework that alternately updates each waveform in each emitting antenna is developed to monotonically decrease ISL. Each block involves the Dinkelbach’s procedure, sequential convex approximation and Alternating Direction Method of Multipliers (ADMM) to obtain single waveform, while the analytic proof with the converged block being a Karush-Kuhn-Tucker (KKT) point is provided. Finally, numerical results highlight the effectiveness of both the proposed dual function scheme and the waveform synthesis technique in comparison with some counterparts. [ABSTRACT FROM AUTHOR]

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic constraints that admit efficient projection. Problems of this form arise frequently in the context of semidefinite programming as well as when various NP-hard problems are solved approximately via semidefinite relaxation. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms, such as the stochastic Frank-Wolfe (FW) algorithm. On the other hand, the second set of constraints cannot be handled in the same way, and must be incorporated as an indicator function within the objective function, thereby complicating the application of FW methods. Similar problems have been studied before; however, they suffer from slow convergence rates. This work, equipped with momentum based gradient tracking technique, guarantees fast convergence rates on par with the best-known rates for problems without the second set of constraints. Zeroth-order variants of the proposed algorithms are also developed and again improve upon the state-of-the-art rate results. We further propose the novel trimmed FW variants that enjoy the same convergence rates as their classical counterparts, but are empirically shown to require significantly fewer calls to the linear minimization oracle speeding up the overall algorithm. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem. [ABSTRACT FROM AUTHOR]

Hammerstein model with a static nonlinearity followed by a linear filter is commonly used in numerous applications. This paper focuses on adaptive filtering techniques for parameter identification of Hammerstein systems and output prediction of nonlinear systems. By formulating the underlying filtering problem as a recursive bilinear least-squares optimization with the non-convex feasible region constraint, we develop a recursive non-convex projected least-squares (RncPLS) algorithm based on alternating direction method of multipliers (ADMM). The RncPLS algorithm alternates between implementing ridge regression and projecting on the non-convex feasible set, which successively refines the system parameters. The convergence and accuracy properties of the proposed RncPLS algorithm are theoretically investigated. Moreover, extensive simulation results in the context of system identification, nonlinear predication, and acoustic echo cancellation, are also included to demonstrate the performance characteristics of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Many signal processing and machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons: noise, faults and attacks. Providing erroneous updates leads the optimization process in a wrong direction, and degrades the performance of distributed machine learning algorithms. This paper considers the problem of decentralized learning using ADMM in the presence of unreliable agents. First, we rigorously analyze the effect of erroneous updates (in ADMM learning iterations) on the convergence behavior of the multi-agent system. We show that the algorithm linearly converges to a neighborhood of the optimal solution under certain conditions and characterize the neighborhood size analytically. Next, we provide guidelines for network design to achieve a faster convergence to the neighborhood. We also provide conditions on the erroneous updates for exact convergence to the optimal solution. Finally, to mitigate the influence of unreliable agents, we propose ROAD, a robust variant of ADMM, and show its resilience to unreliable agents with an exact convergence to the optimum. [ABSTRACT FROM AUTHOR]

In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel structure parameters and the kernel weight vector updating. For structure parameters, the kernel dictionary is selected by sparsification techniques with selective online modeling criteria, and the symmetric kernel covariance matrix is intermittently optimized with the covariance matrix adaptation evolution strategy (CMA-ES). This intermittent optimization can not only improve the kernel structure’s flexibility by utilizing the cross relatedness of input variables, but also partly alleviate the prediction uncertainty arisen by the kernel dictionary selection for nonstationary time series. In order to sufficiently capture the underlying dynamic characteristics in prediction-error time series, a generalized optimization strategy is designed to sequentially construct the kernel dictionary selection and weight vector updating procedures in multiple kernel connection modes. The generalized optimization strategy is highly flexible and effective, and it is capable of enhancing the ability to adaptively track the changing dynamic characteristics due to nonstationarity. Finally, in the perspective of top-level design, we summarize the information interaction between the network topology in kernel regressors and the optimization of inner model parameters. Numerical simulations demonstrate that the proposed approach has superior prediction performance for nonstationary time series. [ABSTRACT FROM AUTHOR]

With the help of auxiliary data, tensor completion may better recover a low rank multidimensional array from limited observation entries. Most existing methods, including coupled matrix-tensor factorization and coupled tensor rank minimization, mainly focus on how to extract and incorporate subspace or directly use auxiliary data for tensor completion. They are either sensitive to a given rank or lack of physical interpretations of subspace information. In addition, the shared subspace information receives little attention in current tensor completion methods, especially there is no analysis of its impact on sample complexity. In this paper, we propose to separately explore and exploit shared subspaces for tensor completion. Specifically, dictionary learning takes the subspace from auxiliary data in the first step. Then a low rank optimization model for tensor completion is provided to incorporate the trained subspace by assuming that the recovered tensor is composed of two low rank components where one shares the subspace information with auxiliary data and the other is outside the shared space. Based on this optimization model, we make a quantitative analysis to illustrate the effect of subspace information on sample complexity, and provide theoretical insights into the usefulness of subspace information. Finally, experiments on simulated data are conducted to validate the theoretical analysis on the impact of subspace information. Experiments in two real-world applications including color image and multispectral image recovery show that the proposed method outperforms state-of-the-art ones in terms of prediction accuracy and CPU time. [ABSTRACT FROM AUTHOR]

Cost-optimization through the minimization of hardware and processing costs with minimal loss in performance is an interesting design paradigm in evolving and emerging Multiple-Input-Multiple-Output (MIMO) radar systems. This optimization is a challenging task due to the increasing Radio Frequency (RF) hardware complexity as well as the signal design algorithm complexity in applications requiring high angular resolution. Towards addressing these, the paper proposes a low-complexity signal design framework, which incorporates a generalized time multiplex scheme for reducing the RF hardware complexity with a subsequent discrete phase modulation. The scheme further aims at achieving simultaneous transmit beamforming and maximum virtual MIMO aperture to enable better target detection and discrimination performance. Furthermore, the paper proposes a low-complexity signal design scheme for beampattern matching in the aforementioned setting. The conducted performance evaluation indicates that the listed design objectives are met. [ABSTRACT FROM AUTHOR]

In this paper, we propose two communication-efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on the objective functions. B-CPP can be applied in an asynchronous broadcast setting and further reduce communication costs compared to CPP. Numerical experiments complement the theoretical analysis and confirm the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, wepropose a novel two-stage transmission framework for an intelligent reflecting surface (IRS) assisted millimeter wave (mmWave) system in the presence of phase error caused by hardware impairments. Specifically, in Stage I, we introduce a pilot-based phase calibration task and reformulate it as an alternating optimization program. Building on this formulation, an efficient iterative algorithm is developed to jointly estimate the phase error, which needs to be calibrated, and the channels corresponding to the first user. Stage II consists of two blocks, channel estimation and data transmission. During the channel estimation block, by leveraging on the sparsity of mmWave channels, we propose a fast Fourier transform based scheme to estimate the IRS-BS channel and user-IRS channels. During the data transmission block, based on the estimated channel state information, base station precoders and IRS phase shifts are jointly optimized to maximize the sum signal-to-leakage-plus-noise ratio of all users. To handle this non-convex problem, we further develop a low-complexity joint beamforming algorithm by exploiting fractional programming techniques. Moreover, to examine the performance of the proposed phase calibration scheme, we derive the Cramer-Rao lower bound for the intended phase error estimation. Simulation results validate the effectiveness of our proposed transmission framework and the necessity of IRS phase calibration. [ABSTRACT FROM AUTHOR]

Data representation techniques have made a substantial contribution to advancing data processing and machine learning (ML). Improving predictive power was the focus of previous representation techniques, which unfortunately perform rather poorly on the interpretability in terms of extracting underlying insights of the data. Recently, the Kolmogorov model (KM) was studied, which is an interpretable and predictable representation approach to learning the underlying probabilistic structure of a set of random variables. The existing KM learning algorithms using semi-definite relaxation with randomization (SDRwR) or discrete monotonic optimization (DMO) have, however, limited utility to big data applications because they do not scale well computationally.In this paper, we propose a computationally scalable KM learning algorithm, based on the regularized dual optimization combined with enhanced gradient descent (GD) method. To make our method more scalable to large-dimensional problems, we propose two acceleration schemes, namely, the eigenvalue decomposition (EVD) elimination strategy and an approximate EVD algorithm. Furthermore, a thresholding technique by exploiting the error bound analysis and leveraging the normalized Minkowski $\ell _1$ -norm, is provided for the selection of the number of iterations of the approximate EVD algorithm. When applied to big data applications, it is demonstrated that the proposed method can achieve compatible training/prediction performance with significantly reduced computational complexity; roughly two orders of magnitude improvement in terms of the time overhead, compared to the existing KM learning algorithms. Furthermore, it is shown that the accuracy of logical relation mining for interpretability by using the proposed KM learning algorithm exceeds 80%. [ABSTRACT FROM AUTHOR]

In this paper, we consider remote state estimation with simultaneous wireless information and power transfer (SWIPT). A remote estimator receives the state estimate transmitted by a sensor and sends an acknowledgment (ACK) signal to the sensor via a feedback wireless channel. The sensor has no other energy supply except that it can harvest wireless energy from the received ACK signal, which carries information and energy simultaneously. Since the symbol error rate of the state estimate transmitted by the sensor depends on the sensor’s transmission power allocation, there exists a tradeoff between the accuracy of the state estimate received by the remote estimator and the transmission power consumption of the sensor. Moreover, the sensor’s transmission power is restricted by the remaining energy level in its battery, which is decided by the amount of the harvested wireless energy. Therefore, we jointly optimize the transmission power allocation of the remote estimator and the sensor and formulate the optimization problem into an infinite time-horizon average cost Markov decision process (MDP). We first prove the existence of the optimal stationary power allocation policy, and then present the monotonic structures of the optimal policy. Simulation results are provided to verify and illustrate the main results. [ABSTRACT FROM AUTHOR]

The paper addresses the transient change detection (TCD) problem, assuming that the duration of change is finite. The TCD criterion minimizes the worst-case probability of missed detection among all tests with a prescribed worst-case probability of false alarm. We study the fixed sample size (FSS) test as a solution to the TCD problem. First, the operating characteristics of the FSS test have been established for arbitrary pre- and post-change distributions. Next, a numerical method of the sample (block) size optimization has been considered for three particular log-likelihood ratio distributions, i.e., Gaussian, $\chi ^{2}$ and exponential. Moreover, simple asymptotic equations for the optimal operating characteristics and block size have been proposed in the Gaussian case. Numerical results are provided to confirm the theoretical findings for the above-mentioned distributions. The accuracy and sharpness of the asymptotic analytical equation is analyzed in the Gaussian case. Finally, the FSS test is compared to the finite moving average (FMA) test obtained by optimizing the CUSUM-type test with respect to the TCD optimality criterion for the above-mentioned distributions. The application of the FSS and FMA tests to the radio-navigation integrity monitoring is also considered. [ABSTRACT FROM AUTHOR]

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed $\ell _{2}/\ell _{1}$ norm over all possible block partitions. Then, by exploiting a variational representation of the $\ell _{2}$ norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Constrained reinforcement learning (CRL), also termed as safe reinforcement learning, is a promising technique enabling the deployment of RL agent in real-world systems. In this paper, we propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general CRL problem, which is formulated as a constrained Markov decision process (CMDP) in context of the average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problem with convex surrogate functions. The proposed SCAOPO enables reuse of experiences from previous updates, thereby significantly reducing implementation cost when deployed in real-world engineering systems that need to online learn the environment. In spite of the time-varying state distribution and the stochastic bias incurred by off-policy learning, the SCAOPO with a feasible initial point can still provably converge to a Karush-Kuhn-Tucker (KKT) point of the original problem almost surely. [ABSTRACT FROM AUTHOR]

One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced $\tau$ -stationarity, based on which, a gradient projection subspace pursuit (GPSP) algorithm is developed. It is proven that GPSP can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a high computational speed. [ABSTRACT FROM AUTHOR]

This paper presents secrecy analyses of a full-duplex MIMOME network which consists of two full-duplex multi-antenna users (Alice and Bob) and an arbitrarily located multi-antenna eavesdropper (Eve). The paper assumes that Eve's channel state information (CSI) is completely unknown to Alice and Bob except for a small radius of secured zone. The first part of this paper aims to optimize the powers of jamming noises from both users. To handle Eve's CSI being unknown to users, the focus is placed on Eve at the most harmful location, and the large matrix theory is applied to yield a hardened secrecy rate to work on. The performance gain of the power optimization in terms of maximum tolerable number of antennas on Eve is shown to be significant. The second part of this paper shows two analyses of anti-eavesdropping channel estimation (ANECE) that can better handle Eve with any number of antennas. One analysis assumes that Eve has a prior statistical knowledge of its CSI, which yields lower and upper bounds on secure degrees of freedom of the system as functions of the number (N) of antennas on Eve and the size (K) of information packet. The second analysis assumes that Eve does not have any prior knowledge of its CSI but performs blind detection of information, which yields an approximate secrecy rate for the case of K being larger than N. [ABSTRACT FROM AUTHOR]

Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general set of convex programs known as semi-definite and second-order cone programs. However, these methods are excessively slow for high dimensions. On the other hand, optimization algorithms on manifolds have shown great abilities in finding solutions to non-convex problems in a reasonable time. This paper suggests using a Riemannian optimization approach to solve a subset of convex optimization problems wherein the optimization variable is a doubly stochastic matrix. Optimization over the set of doubly stochastic matrices is crucial for multiple communications and signal processing applications, especially graph-based clustering. The paper introduces and investigates the geometries of three convex manifolds, namely the doubly stochastic, the symmetric, and the definite multinomial manifolds which generalize the simplex, also known as the multinomial manifold. Theoretical complexity analysis and numerical simulation results testify the efficiency of the proposed method over state-of-the-art algorithms. In particular, they reveal that the proposed framework outperforms conventional generic and specialized approaches, especially in high dimensions. [ABSTRACT FROM AUTHOR]

In this paper, the interference mitigation for Frequency Modulated Continuous Wave (FMCW) radar system with a dechirping receiver is investigated. After dechirping operation, the scattered signals from targets result in beat signals, i.e., the sum of complex exponentials while the interferences lead to chirp-like short pulses. Taking advantage of these different time and frequency features between the useful signals and the interferences, the interference mitigation is formulated as an optimization problem: a sparse and low-rank decomposition of a Hankel matrix constructed by lifting the measurements. Then, an iterative optimization algorithm is proposed to tackle it by exploiting the Alternating Direction of Multipliers (ADMM) scheme. Compared to the existing methods, the proposed approach does not need to detect the interference and also improves the estimation accuracy of the separated useful signals. Both numerical simulations with point-like targets and experiment results with distributed targets (i.e., raindrops) are presented to demonstrate and verify its performance. The results show that the proposed approach is generally applicable for interference mitigation in both stationary and moving target scenarios. [ABSTRACT FROM AUTHOR]

Ultra high-throughput satellite systems are expected to play an essential role in future beyond 5G and 6G networks. These systems must remain as flexible as possible to adapt to heterogeneous traffic demands, while also delivering the highest possible rate for dedicated services. Satellites flexible payloads are increasingly employing wideband output multiplexers. In this context, it is now more important than ever to evaluate frequency-dependent degradations on multicarrier signals. In particular, it is critical to characterize the distortions entailed by the output multiplexers filters. In this paper, models are presented and novel formulas are derived to determine the carrier-to-interference ratio resulting from these distortions. Derivations are oriented towards the applicability of either high-accuracy (e.g., for link budget) or low-complexity calculations (e.g., for real-time carrier allocation). The influence of key parameters such as the optimal decision instant, symbol rate and roll-off factor is thoroughly analyzed. Furthermore, formulas are evaluated in a practical scenario: the dynamic carrier allocation optimization. They are combined with efficient optimization algorithms to obtain the best performance based on user fairness. Relevant metrics such as accuracy, complexity and allocation gain are also investigated. In the end, the application of the proposed formulas and algorithms leads to a significant allocation gain that is increasing with the number of carriers. The feasibility of real-time dynamic carrier allocation to further increase the capacity of the next generation of satellite systems is emphasized. [ABSTRACT FROM AUTHOR]

This paper introduces a general framework for solving constrained convex quaternion optimization problems in the quaternion domain. To soundly derive these new results, the proposed approach leverages the recently developed generalized $\mathbb {H}\mathbb {R}$ -calculus together with the equivalence between the original quaternion optimization problem and its augmented real-domain counterpart. This new framework simultaneously provides rigorous theoretical foundations as well as elegant, compact quaternion-domain formulations for optimization problems in quaternion variables. Our contributions are threefold: (i) we introduce the general form for convex constrained optimization problems in quaternion variables, (ii) we extend fundamental notions of convex optimization to the quaternion case, namely Lagrangian duality and optimality conditions, (iii) we develop the quaternion alternating direction method of multipliers (Q-ADMM) as a general purpose quaternion optimization algorithm. The relevance of the proposed methodology is demonstrated by solving two typical examples of constrained convex quaternion optimization problems arising in signal processing. Our results open new avenues in the design, analysis and efficient implementation of quaternion-domain optimization procedures. [ABSTRACT FROM AUTHOR]

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can be generally obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks. [ABSTRACT FROM AUTHOR]

This paper investigates a novel intelligent reflecting surface (IRS)-based symbiotic radio (SR) system architecture consisting of a transmitter, an IRS, and an information receiver (IR). The primary transmitter communicates with the IR and at the same time assists the IRS in forwarding information to the IR. Based on the IRS’s symbol period, we distinguish two scenarios, namely, commensal SR (CSR) and parasitic SR (PSR), where two different techniques for decoding the IRS signals at the IR are employed. We formulate bit error rate (BER) minimization problems for both scenarios by jointly optimizing the active beamformer at the base station and the phase shifts at the IRS, subject to a minimum primary rate requirement. Specifically, for the CSR scenario, a penalty-based algorithm is proposed to obtain a high-quality solution, where semi-closed-form solutions for the active beamformer and the IRS phase shifts are derived based on Lagrange duality and Majorization-Minimization methods, respectively. For the PSR scenario, we apply a bisection search-based method, successive convex approximation, and difference of convex programming to develop a computationally efficient algorithm, which converges to a locally optimal solution. Simulation results demonstrate the effectiveness of the proposed algorithms and show that the proposed SR techniques are able to achieve a lower BER than benchmark schemes. [ABSTRACT FROM AUTHOR]

Distributed primal-dual methods have been widely used for solving large-scale constrained optimization problems. The majority of existing results focus on the problems with decoupled constraints. Some recent works have studied the problems subject to separable globally coupled constraints. This paper considers the distributed optimization problems with globally coupled constraints over networks without requiring the separability of the globally coupled constraints. This is made possible by the local estimates of the constraint violations. For solving such a problem, we propose a primal-dual algorithm in the augmented Lagrangian framework, combining the average consensus technique. We first establish a non-ergodic convergence rate of $\mathcal {O}(1/k)$ in terms of the objective residual for solving a distributed constrained convex optimization problem, where $k$ is the iteration counter. Specifically, the global objective function is the aggregate of the local convex and possibly non-smooth costs, and the coupled constraint is the sum of the local linear equality constraints. The numerical results illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The use of a large-scale antenna array (LSAA) has become an important characteristic of multi-antenna communication systems to achieve beamforming gains such as in designing millimeter-wave (mmWave) systems to combat severe propagation losses. In such applications, each antenna element has to be driven by a radio frequency (RF) chain for the implementation of fully-digital beamformers, significantly increasing the hardware cost, complexity, and power consumption. Therefore, constant-modulus analog beamforming (CMAB) becomes a viable solution. In this paper, we consider the scaled analog beamforming (SAB) or constant-modulus analog beamforming (CMAB) architecture and design the system parameters by solving two variants of beampattern matching problem. In the first case, both the magnitude and phase of the beampattern are matched to the given desired beampattern whereas in the second case, only the magnitude of the beampattern is matched. Both the beampattern matching problems are cast as a variant of the constant-modulus least-squares (CLS) problem. We provide efficient algorithms based on the alternating majorization-minimization (AMM) framework that combines the alternating minimization and the MM frameworks and the conventional-cyclic coordinate descent (C-CCD) algorithms to solve the problem in each case. We also propose algorithms based on a new modified-CCD (M-CCD) based approach. For all the developed algorithms we prove convergence to a Karush-Kuhn-Tucker (KKT) point (or a stationary point). Numerical results demonstrate that the proposed algorithms converge faster than the state-of-the-art solutions. Among all the algorithms, the M-CCD-based algorithms have faster convergence when evaluated in terms of the number of iterations and the AMM-based algorithms offer lower complexity. [ABSTRACT FROM AUTHOR]

This paper studies a statistical model for heteroscedastic (i.e., power fluctuating) signals embedded in white Gaussian noise. Using the Riemannian geometry theory, we propose an unified approach to tackle several problems related to this model. The first axis of contribution concerns parameters (signal subspace and power factors) estimation, for which we derive intrinsic Cramér-Rao bounds and propose a flexible Riemannian optimization algorithmic framework in order to compute the maximum likelihood estimator (as well as other cost functions involving the parameters). Interestingly, the obtained bounds are in closed forms and interpretable in terms of problem’s dimensions and SNR. The second axis of contribution concerns the problem of clustering data assuming a mixture of heteroscedastic signals model, for which we generalize the Euclidean K-means++ to the considered Riemannian parameter space. We propose an application of the resulting clustering algorithm on the Indian Pines segmentation problem benchmark. [ABSTRACT FROM AUTHOR]

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that the proposed algorithm can achieve an $\epsilon$ -stationary solution under a constant step size with $\mathcal {O}(1/\epsilon ^2)$ computation complexity and $\mathcal {O}(1/\epsilon)$ communication complexity when the epigraph of the non-smooth term is a polyhedral set. When compared to the existing gradient tracking based methods, the proposed algorithm has the same order of computation complexity but lower order of communication complexity. To the best of our knowledge, the presented result is the first stochastic algorithm with the $\mathcal {O}(1/\epsilon)$ communication complexity for non-convex and non-smooth problems. Numerical experiments for a distributed non-convex regression problem and a deep neural network based classification problem are presented to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate. [ABSTRACT FROM AUTHOR]

Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in various signal processing tasks. However, classical methods learn the dictionary and the sparse code based on alternating optimizations, usually without theoretical guarantees for either optimality or convergence due to the non-convexity of the problem. Recent works on sparse coding with a complete dictionary provide strong theoretical guarantees thanks to the development of non-convex optimization. However, initial non-convex approaches learned the dictionary in the sparse coding problem sequentially in an atom-by-atom manner, which led to a long execution time. More recent works  have sought to directly learn the entire dictionary at once, which substantially reduces the execution time. However, the associated recovery performance is degraded with a finite number of data samples. In this paper, we propose an efficient sparse coding scheme with a two-stage optimization. The proposed scheme leverages the global and local Riemannian geometry of the two-stage optimization problem and facilitates fast implementation for superb dictionary recovery performance by a finite number of samples. We further prove that, with high probability, the proposed scheme can exactly recover any atom in the target dictionary with a finite number of samples. Experiments on both synthetic and real-world data verify the efficiency and robustness of the proposed scheme.1 [ABSTRACT FROM AUTHOR]

In this paper, we consider the policy evaluation problem in reinforcement learning with agents on a decentralized and directed network. In order to evaluate the quality of a fixed policy in this decentralized setting, one option is for agents to run decentralized temporal-difference (TD) collaboratively. To account for the practical scenarios where the state and action spaces are large and malicious attacks emerge, we focus on the decentralized TD learning with linear function approximation in the presence of malicious agents (often termed as Byzantine agents). We propose a trimmed mean-based Byzantine-resilient decentralized TD algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Tensor completion aims to recover missing entries given incomplete multi-dimensional data by making use of the prior low-rank information, and has various applications because many real-world data can be modeled as low-rank tensors. Most of the existing methods are designed for noiseless or Gaussian noise scenarios, and thus they are not robust to outliers. One popular approach to resist outliers is to employ $\ell _p$ -norm. Yet nonsmoothness and nonconvexity of $\ell _p$ -norm with $0< p\leq 1$ bring challenges to optimization. In this paper, a new norm, named $\ell _{p,\epsilon }$ -norm, is devised where $\epsilon >0$ can adjust the convexity of $\ell _{p,\epsilon }$ -norm. Compared with $\ell _p$ -norm, $\ell _{p,\epsilon }$ -norm is smooth and convex even for $0< p\leq 1$ , which converts an intractable nonsmooth and nonconvex optimization problem into a much simpler convex and smooth one. Then, combining tensor ring rank and $\ell _{p,\epsilon }$ -norm, a robust tensor completion formulation is proposed, which achieves outstanding robustness. The resultant robust tensor completion problem is decomposed into a number of robust linear regression (RLR) subproblems, and two algorithms are devised to tackle RLR. The first method adopts gradient descent, which has a low computational complexity. While the second one employs alternating direction method of multipliers to yield a fast convergence rate. Numerical simulations show that the two proposed methods have better performance than those based on the $\ell _p$ -norm in RLR. Experimental results from applications of image inpainting, video restoration and target estimation demonstrate that our robust tensor completion approach outperforms state-of-the-art methods in terms of recovery accuracy. [ABSTRACT FROM AUTHOR]

The trace ratio optimization (TRO) problem consists of finding an orthonormal basis for the discriminative subspace that maximizes the ratio of two trace operators on two covariance matrices corresponding to two distinctive classes or signal components. The TRO problem is encountered in various signal processing problems such as dimensionality reduction, signal enhancement, and discriminative analysis. In this paper, we propose a distributed and adaptive algorithm for solving the TRO problem in the context of wireless sensor networks (WSNs), where the two matrices involved in the trace ratio operators correspond to the (unknown) spatial correlation of the sensor signals across the nodes in the network. We first focus on fully-connected networks where every node can communicate with each other, but only compressed signals observations can be shared to reduce the communication cost. After showing convergence, we modify the algorithm to operate in WSNs with more general topologies. Simulation results are provided to validate and complement the theoretical results. [ABSTRACT FROM AUTHOR]

Extracting multiple unknown sources from a single observation of a single-channel is an ill-posed problem encountered in a variety of applications. This paper characterizes the ambiguity of solutions to the source separation problem, and then proposes a novel adaptive-operator-based approach to deriving solutions based on a combination of separation operators and domain-specific knowledge related to sources. The proposed scheme involves transforming the original problem into a new problem, in which data-dependent operators and the unknown sources are variables to be optimized. We demonstrate that a solution to the proposed optimization problem must reside in the null spaces of the operators, and any such solution also provides an optimal value to the original problem. We then demonstrate the applicability of the proposed method to the separation of sparse sources as well as AM-FM sources. Note that the proposed scheme outperformed corresponding state-of-the-art methods in noiseless as well as noisy environments. Finally, we demonstrate the efficacy of the proposed scheme in separation tasks based on real-world ECG data (i.e., extracting fetal ECG signals from noisy observations in which maternal and fetal ECGs recordings are superimposed) and electrical data (i.e.,separating singularities from harmonic components in an observation of noisy data related to surges in electrical current). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the robust beamforming for the magnetic-based wireless power transfer (WPT) with multiple transmitters and multiple receivers to improve the power efficiency and reliability. By taking into account the imperfection of the magnetic mutual inductances information (MII), we firstly formulate a beamforming optimization problem to minimize the total transmit power while guaranteeing the reliable power delivery for each receiver simultaneously. Then, observing that the optimization problem is highly nonconvex with infinite number of constraints, we utilize the norm-bounded MII error models to reformulate the original problem into two worst-case optimization problems for the cases of the single receiver and multiple receivers, respectively. Finally, the optimal beamforming is obtained for the case of single receiver by applying the semidefinite programming relaxation (SDR) and the approximately optimal solution is obtained for the case of multiple receivers by adopting the SDR with randomization. Extensive simulation results verify the power transfer reliability and efficiency of the proposed beamforming schemes for the magnetic-based WPT systems. [ABSTRACT FROM AUTHOR]

Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used real-valued transformation works for uniform linear arrays (ULAs) only. In this paper, we propose a new real-valued transformation for DOA estimation with arbitrary linear arrays by exploiting the virtual steering of linear arrays. Then, we introduce an alternating optimization algorithm based on the variational Bayesian inference (VBI) methodology to iteratively obtain a stationary solution to the real-valued sparse representation problem. Because of utilizing the additional real-valued structure, the VBI scheme can achieve a better performance in terms of both estimation accuracy and computational complexity. Moreover, we embed the generalized approximate message passing (GAMP) into the VBI-based method for further complexity reduction. Although there may be a performance loss for the GAMP variant, simulation results reveal its substantial performance improvement over existing methods. [ABSTRACT FROM AUTHOR]

Traditional networked radar systems for target tracking usually suffer from a heavy data processing burden, and do not consider the sensor location uncertainties (SLUs), by assuming that radar locations are known perfectly, which is applicable only for static platforms. In this paper, considering sensors mounted on moving platforms, we propose a joint power allocation and measurement selection (JPAMS) strategy for multitarget tracking and data reduction in radar networks with the SLUs. The mechanism is to optimize the transmitted power and select the propagation paths with informative measurements, simultaneously. First, we adopt a distributed fusion architecture to estimate both states of targets and radars in clutter. Based on the distributed fusion architecture, the predicted conditional Cramér-Rao lower bound (PC-CRLB) considering the SLU and the measurement origin uncertainty is derived. Second, the JPAMS strategy is formulated as a bi-objective optimization problem, where the sum of weighted PC-CRLBs and the number of selected propagation paths are used as the performance metrics with respect to tracking and data reduction. The corresponding optimization is a NP-hard problem containing both continuous and binary variables. Third, to solve this nonconvex problem, we propose a sparsity-enhancing sequential convex programming algorithm. Finally, numerical simulations demonstrate the superiority of the proposed JPAMS strategy over the traditional allocation strategies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate designs of linear precoders for vector Gaussian channels via stochastic optimizations and deep neural networks (DNNs). We assume that the channel inputs are drawn from practical finite alphabets, and we search for precoders maximizing the mutual information between channel inputs and outputs. Though the problem is generally non-convex, we prove that when the right singular matrix of precoder is fixed, any local optima of this problem is a global optima. Based on this fact, an efficient projected stochastic gradient descent (PSGD) algorithm is designed to search the optimal precoders. Moreover, to reduce the complexity of calculating a posterior means involved in gradients calculation, K-best algorithm is adopted to make approximations of a posterior means with negligible loss of accuracy. Furthermore, to avoid explicit calculation of mutual information and its gradients, DNN-based autoencoders (AEs) are constructed for this precoding task, and an efficient training algorithm is proposed. We also prove that the AEs, with ‘softmax’ activation function and ‘categorical cross entropy’ loss, maximize the mutual information under reasonable assumptions. Then, in order to extend the AE methods to large scale systems, ‘sigmoid’ activation function and ‘binary cross entropy’ loss are used such that the size of AEs will not grow prohibitively large. We prove that this maximizes a lower bound of the mutual information under reasonable assumptions. Finally, to make the precoders practical for high speed wireless scenarios, we propose an offline training paradigm which trains DNNs to infer optimal precoders given channel state information instead of training online for every different channel. Simulation results show that all the proposed methods work well in maximizing mutual information and improving bit error rate (BER) performance. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing the $\ell _1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms with provable guarantees for tackling this problem. Specifically, our contribution is fourfold. First, we present a manifold proximal point algorithm (ManPPA) for the problem and show that it converges at a global sublinear rate. Furthermore, we show that ManPPA can achieve a local quadratic convergence rate when applied to sharp instances of the problem. Second, we develop a semismooth Newton-based inexact augmented Lagrangian method for computing the search direction in each iteration of ManPPA and show that it has an asymptotic superlinear convergence rate. Third, we propose a stochastic variant of ManPPA called StManPPA, which is well suited for large-scale computation, and establish its sublinear convergence rate. Both ManPPA and StManPPA have provably faster convergence rates than existing subgradient-type methods. Fourth, using ManPPA as a building block, we propose a new heuristic method for solving a matrix analog of the problem, in which the sphere is replaced by the Stiefel manifold. The results from our extensive numerical experiments on the ODL and RSR problems demonstrate the efficiency and efficacy of our proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where the cost of communication and/or computation can be expensive. We extend and generalize the analysis for a class of nested gradient-based distributed algorithms [NEAR-DGD, (Berahas et al., 2019)] to account for multiple gradient steps at every iteration. We show the effect of performing multiple gradient steps on the rate of convergence and on the size of the neighborhood of convergence, and prove R-Linear convergence to the exact solution with a fixed number of gradient steps and increasing number of consensus steps. We test the performance of the generalized method on quadratic functions and show the effect of multiple consensus and gradient steps in terms of iterations, number of gradient evaluations, number of communications and cost. [ABSTRACT FROM AUTHOR]

Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new Stochastically Corrected Stochastic Compositional gradient method (SCSC). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate as the stochastic gradient descent (SGD) method for non-compositional stochastic optimization. This is achieved by making a careful improvement to a popular stochastic compositional gradient method. It is easy to apply SGD-improvement techniques to accelerate SCSC. This helps SCSC achieve state-of-the-art performance for stochastic compositional optimization. In particular, we apply Adam to SCSC, and the exhibited rate of convergence matches that of the original Adam on non-compositional stochastic optimization. We test SCSC using the model-agnostic meta-learning tasks. [ABSTRACT FROM AUTHOR]

Neural networks with non-linear rectified linear unit (ReLU) activation functions have demonstrated remarkable performance in many fields. It has been observed that a sufficiently wide and/or deep ReLU network can accurately fit the training data, with a small generalization error on the testing data. Nevertheless, existing analytical results on provably training ReLU networks are mostly limited to over-parameterized cases, or they require assumptions on the data distribution. In this paper, training a two-layer ReLU network for binary classification of linearly separable data is revisited. Adopting the hinge loss as classification criterion yields a non-convex objective function with infinite local minima and saddle points. Instead, a modified loss is proposed which enables (stochastic) gradient descent to attain a globally optimal solution. Enticingly, the solution found is globally optimal for the hinge loss too. In addition, an upper bound on the number of iterations required to find a global minimum is derived. To ensure generalization performance, a convex max-margin formulation for two-layer ReLU network classifiers is discussed. Connections between the sought max-margin ReLU network and the max-margin support vector machine are drawn. Finally, an algorithm-dependent theoretical quantification of the generalization performance is developed using classical compression bounds. Numerical tests using synthetic and real data validate the analytical results. [ABSTRACT FROM AUTHOR]

As for Generative Adversarial Networks (GANs), its interpretability may be closely related to optimization objective functions, that is, information metrics play important roles in networks training and data generation. In terms of original GAN, the objective function based on Kullback-Leibler (KL) divergence has limitations on the performance of data training and generation. Therefore, it is significant to investigate objective functions for the optimization in GANs to bring gains on the efficiency of network learning from the perspective of metrics. In this paper, the objective function with exponential form, referred from the Message Importance Measure (MIM), is adapted to replace that with logarithm form in the optimization for adversarial networks. This approach named MIM-based GAN, may provide more hidden information in terms of interpretability on training process and probability events generation. Specifically, we first analyze the intrinsic relationship between the proposed approach and other classical GANs. Moreover, compared with the original GAN, LSGAN and WGAN, we discuss its advantages on training performance in theory including sensitivity, convergence rate and so on. In addition, we do simulations on the datasets to confirm why the MIM-based GAN achieves state-of-the-art performance on training process and data generation. [ABSTRACT FROM AUTHOR]

Regularized zero-forcing beamforming (RZFB) is an interesting class of linear signal processing problems, which is very attractive for use in large-scale communication networks due its simple visualization as a straightforward extension of the well-accepted zero-forcing beamforming (ZFB). However, unlike ZFB, which is multi-user interference free, RZFB must manage multi-user interference to achieve its high throughput performance. Most existing works focus on the performance analysis of particular RZBF schemes such as the equip-power allocated RZBF under a fixed regularization parameter. This paper is the first work to consider the joint design of power allocation and regularization parameter for RZFB to maximize the worst users’ throughput or the quality-of-service awarded energy efficiency under a fixed transmit power constraint. Such designs pose very computationally challenging optimization problems, for which the paper proposes two-stage optimization algorithms of low computational complexity. Their computational and performance efficiencies are substantiated through numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies linear distributed estimation of an unknown random parameter vector in a bandwidth-constrained multisensor network. To meet the bandwidth limitations, each sensor converts its observation into a low-dimensional datum via a suitable linear transformation. Then, the fusion center estimates the parameter vector by linearly combining all the received low-dimensional data, aiming at minimizing the estimation mean square error. The main purpose of this paper is to jointly determine the compression dimension of each sensor (referred to as dimension assignment) and design the corresponding compression matrix when the total compression dimensions is limited. Such a joint design problem can be formulated as a rank-constrained optimization problem and it is shown to be NP-hard for the first time. In addition, successive quadratic upper-bound minimization (SQUM), SQUM-block coordinate descent (SQUM-BCD) and nuclear norm regularization (NNR) methods are developed to solve it approximately. Furthermore, we show that any accumulation point of the sequence generated by the SQUM method satisfies the Karush-Kuhn-Tucker conditions of the rank-constrained optimization problem, and the Phase II algorithm of the SQUM-BCD and NNR methods (both are two-phase algorithms and have the same Phase II algorithm) guarantees convergence at least to a stationary point. Numerical experiments illustrate the advantages of the proposed methods compared with the existing method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of network structure manipulation in the absence of a central coordinator that collects network information and makes decisions. The primary focus is on the spectral radius minimization problem by removing/rewiring links to control epidemic spreading over networks. The resulting optimizations are generally combinatorial and NP-hard. The lack of the central base prevents us from solving such problems in a centralized fashion, thus driving the need for distributed computation and collaborative decision-making to support effective topology modification. In this paper, a distributed estimation scheme involving event-based communication and parallel algorithms is developed to enhance network capability against epidemics. Based on this low-complexity estimation algorithm, fully distributed strategies are proposed to enable individuals to sequentially discern the critical in-network contact, and to implement the desired link operation solely. We further extend the acquisitions to a more flexible framework based on a “coevolutionary networks” picture and discuss the optimality of solutions from an algebraic and topological perspective. Extensive simulation examples are presented to demonstrate the effectiveness of the proposed strategies. [ABSTRACT FROM AUTHOR]

Numerical optimization has played a central role in addressing key signal processing (SP) problems. Highly effective methods have been developed for a large variety of SP applications such as communications, radar, filter design, and speech and image analytics, just to name a few. However, optimization algorithms often entail considerable complexity, which creates a serious gap between theoretical design/analysis and real-time processing. In this paper, we aim at providing a new learning-based perspective to address this challenging issue. The key idea is to treat the input and output of an SP algorithm as an unknown nonlinear mapping and use a deep neural network (DNN) to approximate it. If the nonlinear mapping can be learned accurately by a DNN of moderate size, then SP tasks can be performed effectively—since passing the input through a DNN only requires a small number of simple operations. In our paper, we first identify a class of optimization algorithms that can be accurately approximated by a fully connected DNN. Second, to demonstrate the effectiveness of the proposed approach, we apply it to approximate a popular interference management algorithm, namely, the WMMSE algorithm. Extensive experiments using both synthetically generated wireless channel data and real DSL channel data have been conducted. It is shown that, in practice, only a small network is sufficient to obtain high approximation accuracy, and DNNs can achieve orders of magnitude speedup in computational time compared to the state-of-the-art interference management algorithm. [ABSTRACT FROM AUTHOR]