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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]

Fractional programming (FP) refers to a family of optimization problems that involve ratio term(s). This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave–convex FP problem—in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper. [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 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]

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]

Networked radar systems have been demonstrated to offer enhanced target tracking capabilities. An effective radar resource allocation strategy can efficiently optimize system parameters, leading to performance enhancements. In this paper, two critical but limited system resources are considered for optimization: the number of radar nodes and the transmitted power. In this scenario, a joint node selection and power allocation (JSPA) strategy is developed with the objective of tracking multiple targets. The proposed mechanism implements the optimal resource allocation based on the feedback information in the tracking recursion cycle in order to improve the worst-case tracking accuracy with multiple targets. The network architecture considered in this paper is decentralized so that communication requirements may be reduced while maintaining system robustness. Since the predicted conditional Cramér–Rao lower bound (PC-CRLB) provides a lower bound on the accuracy of the target state estimates conditional on the actual measurement realizations, it is more accurate than the standard posterior CRLB and is thus derived and used as an optimization criterion for the JSPA strategy. It is shown that the optimal JSPA is a two-variable nonconvex optimization problem. We propose an efficient two-step semidefinite programming based solution to solve this problem. Numerical results demonstrate the superior performance of the proposed strategy and the effectiveness of the proposed solution. [ABSTRACT FROM AUTHOR]

Existing work regarding the performance comparison between nonorthogonal multiple access (NOMA) and orthogonal multiple access (OMA) can be generally divided into two categories. The work in the first category aims to develop analytical results for the comparison, often with fixed system parameters. The work in the second category aims to propose efficient algorithms for optimizing these parameters, and compares NOMA with OMA by computer simulations. However, when these parameters are optimized, the theoretical superiority of NOMA over OMA is still not clear. Therefore, in this paper, the theoretical performance comparison between NOMA and conventional OMA systems is investigated, from an optimization point of view. First, sum rate maximizing problems considering user fairness in both NOMA and various OMA systems are formulated. Then, by using the method of power splitting, a closed-form expression for the optimum sum rate of NOMA systems is derived. Moreover, the fact that NOMA can always outperform any conventional OMA systems, when both are equipped with the optimum resource allocation policies, is validated with rigorous mathematical proofs. Finally, computer simulations are conducted to validate the correctness of the analytical results. [ABSTRACT FROM PUBLISHER]

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]

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]

This paper establishes the velocity orientation requirements for dual or multiple mobile sensors to achieve optimal localization of a stationary emitter, based on TDOA and FDOA measurements. In one approach, optimal velocities are obtained by maximizing the determinant of the Fisher Information Matrix (FIM). The other approach calls for minimizing the trace of the FIM inverse. The paper shows that for a given source-sensor position geometry, two opposite optimal sensor velocity configurations are possible. One way to apply the results of this paper is to deploy sensors onboard highly maneuvering platforms, which are able to rapidly align the platform velocities with those computed by one of the optimization approaches. This usually brings a significant increase in emitter localization accuracy even if the initial sensor-source position geometry is poor. A number of computer simulations are given in the paper, which confirms the paper's theoretical findings. [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]

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]

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]

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]

This paper introduces the stochastic Fejér-monotone hybrid steepest descent method (S-FM-HSDM) to solve affinely constrained and composite convex minimization tasks. The minimization task is not known exactly; noise contaminates the information about the composite loss function and the affine constraints. S-FM-HSDM generates sequences of random variables that, under certain conditions and with respect to a probability space, converge point-wise to solutions of the noiseless minimization task. S-FM-HSDM enjoys desirable attributes of optimization techniques such as splitting of variables and constant step size (learning rate). Furthermore, it provides a novel way of exploiting the information about the affine constraints via fixed-point sets of appropriate nonexpansive mappings. Among the offsprings of S-FM-HSDM, the hierarchical recursive least squares (HRLS) takes advantage of S-FM-HSDM's versatility toward affine constraints and offers a novel twist to LS by generating sequences of estimates that converge to solutions of a hierarchical optimization task: minimize a convex loss over the set of minimizers of the ensemble LS loss. Numerical tests on a sparsity-aware LS task show that HRLS compares favorably to several state-of-the-art convex, as well as non-convex, stochastic-approximation, and online-learning counterparts. [ABSTRACT FROM AUTHOR]

We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. This paper leverages recent results that provide an exact characterization of the performance of the spectral method in the high-dimensional limit. This characterization allows us to map the task of optimal design to a constrained optimization problem in a weighted $L^2$ function space. The latter has a closed-form solution. Interestingly, under a mild technical condition, our results show that there exists a fixed design that is uniformly optimal over all sampling ratios. Numerical simulations demonstrate the performance improvement brought by the proposed optimal design over existing constructions in the literature. In a recent work, Mondelli and Montanari have shown the existence of a weak recovery threshold below which the spectral method cannot provide useful estimates. Our results serve to complement that work by deriving the fundamental limit of the spectral method beyond the aforementioned threshold. [ABSTRACT FROM AUTHOR]

In this paper, the partial relaxation approach is introduced and applied to the direction-of-arrival estimation problem using spectral search. Unlike existing spectral-based methods such as conventional beamformer, Capon beamformer, or MUSIC that can be considered as single source approximation of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the “interference” parameters. Thanks to this relaxation, the conventional multi-source optimization problem reduces to a simple spectral search. Following this principle, we propose estimators based on the deterministic maximum likelihood, weighted subspace fitting, and covariance fitting methods. To calculate the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that, irrespective of any specific structure of the sensor array, the performance of the proposed estimators is superior to the conventional methods, especially in the case of low signal-to-noise-ratio and low number of snapshots, while maintaining a computational cost that is comparable to MUSIC. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the symbol-level precoding (SLP) design problem in the downlink of a multiuser multiple-input single-output channel. We consider generic two-dimensional constellations with any shape and size, and confine ourselves to one of the main categories of constructive interference regions (CIR), namely distance preserving CIR (DPCIR). We provide a comprehensive study of DPCIRs and derive several properties for these regions. Using these properties, we first show that any signal in a given DPCIR has a norm greater than or equal to the norm of the corresponding constellation point if and only if the convex hull of the constellation contains the origin. It is followed by proving that the power of the noise-free received signal in a DPCIR is a monotonic strictly increasing function of two parameters relating to the infinite Voronoi edges. Using the convex description of DPCIRs and their characteristics, we formulate two design problems, namely the SLP power minimization with signal-to-interference-plus-noise ratio (SINR) constraints, and the SLP SINR balancing problem under max–min fairness criterion. The SLP power minimization based on DPCIRs can straightforwardly be written as a quadratic programming. We derive a simplified reformulation of this problem, which is less computationally complex. The SLP max–min SINR, however, is non-convex in its original form, and hence difficult to tackle. We propose alternative optimization approaches, including semidefinite programming formulation and block coordinate descent optimization. We discuss and evaluate the loss due to the proposed alternative methods through extensive simulation results. [ABSTRACT FROM AUTHOR]

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics. [ABSTRACT FROM AUTHOR]

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs’ Green function to derive a novel parameterization of the acquired images. This parameterization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a nonnegative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology. [ABSTRACT FROM AUTHOR]

Bounded component analysis (BCA) is a recent approach that enables the separation of both dependent and independent signals from their mixtures. This paper introduces a novel deterministic instantaneous BCA framework for the separation of sparse bounded sources. The framework is based on a geometric maximization setting, where the objective function is defined as the volume ratio of two objects, namely, the principal hyperellipsoid and the bounding $\ell _1$ -norm ball, defined over the separator output samples. It is shown that all global maxima of this objective are perfect separators. This paper also provides the corresponding iterative algorithms for both real and complex sparse sources. The numerical experiments illustrate the potential benefits of the proposed approach, with applications on image separation and neuron identification. [ABSTRACT FROM AUTHOR]

Sets of sequences with good correlation properties are desired in many active sensing and communication systems, e.g., multiple-input-multiple-output (MIMO) radar systems and code-division multiple-access (CDMA) cellular systems. In this paper, we consider the problems of designing complementary sets of sequences (CSS) and also sequence sets with both good auto- and cross-correlation properties. Algorithms based on the general majorization-minimization method are developed to tackle the optimization problems arising from the sequence set design problems. All the proposed algorithms can be implemented by means of the fast Fourier transform (FFT) and thus are computationally efficient and capable of designing sets of very long sequences. A number of numerical examples are provided to demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Distributed optimization in multi-agent systems under sparsity constraints has recently received a lot of attention. In this paper, we consider the in-network minimization of a continuously differentiable nonlinear function which is a combination of local agent objective functions subject to sparsity constraints on the variables. A crucial issue of in-network optimization is the handling of the communications, which may be expensive. This calls for efficient algorithms, that are able to reduce the number of required communication links and transmitted messages. To this end, we focus on asynchronous and randomized distributed techniques. Based on consensus techniques and iterative hard thresholding methods, we propose three methods that attempt to minimize the given function, promoting sparsity of the solution: asynchronous hard thresholding (AHT), broadcast hard thresholding (BHT), and gossip hard thresholding (GHT). Although similar in many aspects, it is difficult to obtain a unified analysis for the proposed algorithms. Specifically, we theoretically prove the convergence and characterize the limit points of AHT in regular networks under some proper assumptions on the functions to be minimized. For BHT and GHT, instead, we characterize the fixed points of the maps that rule their dynamics in terms of stationary points of original problem. Finally, we illustrate the implementation of our techniques in compressed sensing and present several numerical results on performance and number of transmissions required for convergence. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a tensor train neighborhood preserving embedding (TTNPE) to embed multidimensional tensor data into low-dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate a novel tradeoff gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior tradeoff in classification, computation, and dimensionality reduction in MNIST handwritten digits, Weizmann face datasets, and financial market datasets. [ABSTRACT FROM AUTHOR]

In this paper, we consider multiuser detection that copes with multiple access interference caused in low-rate wireless communication systems with a large number of nodes, such as machine-to-machine communications. We take account of discreteness of transmitted signals (e.g., binary signals taking values of $\pm 1$), which we utilize as prior information in detection. We first formulate the detection problem as a maximum a posteriori estimation problem. Since this problem is highly nonconvex and discontinuous, we propose convex relaxation based on the sum-of-absolute-values (SOAV) optimization, which can be efficiently solved by proximal splitting. We also derive an upper bound of the relaxation error by the SOAV optimization in noisy cases based on the restricted isometry property. Numerical simulations are shown to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases. A computationally efficient iterative algorithm for the continuous phase case (IA-CPC) is proposed to sequentially optimize the quadratic objective function. The quadratic optimization problem is turned into multiple one-dimensional optimization problems with closed-form solutions. For the discrete phase case, we present an iterative block optimization algorithm. Specifically, we partition the design variables into $K$ blocks, and then, we sequentially optimize each block via exhaustive search while fixing the remaining $K-1$ blocks. Finally, we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method-like and semidefinite relaxation related techniques. [ABSTRACT FROM PUBLISHER]

This paper investigates a new class of nonconvex optimization, which provides a unified framework for linear precoding in single/multiuser multiple-input multiple-output channels with arbitrary input distributions. The new optimization is called generalized quadratic matrix programming (GQMP). Due to the nondeterministic polynomial time hardness of GQMP problems, instead of seeking globally optimal solutions, we propose an efficient algorithm that is guaranteed to converge to a Karush-Kuhn-Tucker point. The idea behind this algorithm is to construct explicit concave lower bounds for nonconvex objective and constraint functions, and then solve a sequence of concave maximization problems until convergence. In terms of application, we consider a downlink underlay secure cognitive radio network, where each node has multiple antennas. We design linear precoders to maximize the average secrecy (sum) rate with finite-alphabet inputs and statistical channel state information at the transmitter. The precoding problems under secure multicast/broadcast scenarios are GQMP problems, and thus, they can be solved efficiently by our proposed algorithm. Several numerical examples are provided to show the efficacy of our algorithm. [ABSTRACT FROM PUBLISHER]

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems—as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity. [ABSTRACT FROM AUTHOR]

The emergence of big data has caused a dramatic shift in the operating regime for optimization algorithms. The performance bottleneck, which used to be computations, is now often communications. Several gradient compression techniques have been proposed to reduce the communication load at the price of a loss in solution accuracy. Recently, it has been shown how compression errors can be compensated for in the optimization algorithm to improve the solution accuracy. Even though convergence guarantees for error-compensated algorithms have been established, there is very limited theoretical support for quantifying the observed improvements in solution accuracy. In this paper, we show that Hessian-aided error compensation, unlike other existing schemes, avoids accumulation of compression errors on quadratic problems. We also present strong convergence guarantees of Hessian-based error compensation for stochastic gradient descent. Our numerical experiments highlight the benefits of Hessian-based error compensation, and demonstrate that similar convergence improvements are attained when only a diagonal Hessian approximation is used. [ABSTRACT FROM AUTHOR]

A sequential partial optimization method is presented in this paper for the minimax design of two-dimensional infinite impulse response filters with separable denominator. The method converts the minimax design problem into a sequence of smaller subproblems, each updating only one pair of second-order denominator factors. The necessary and sufficient stability triangles for one-dimensional filters are used as the stability constraints on the two-dimensional filters. The first-order Taylor expansion and a trust-region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm. By comparing with a corresponding joint optimization method, the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order. This is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method. Moreover, the limit solution of the sequential partial optimization algorithm has been proved to be a Karush–Kuhn–Tucker point of the design problem. Design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity. [ABSTRACT FROM PUBLISHER]

In heterogeneous wireless networks (HetNet), the multihomed user equipment (UE) utilizes multiple access options (AO) simultaneously and aggregate the offered resources from different AOs so as to support the same application, such as media streaming. Two important challenges of the resource optimization in this context are: 1) determining the connection results between UEs and AOs, and 2) determining the amount of radio resources that AOs should allocate to UEs. In this paper, we investigate the energy-efficient resource optimization for the HetNet with multihomed UEs. First, the energy-efficient resource optimization is formulated as an energy efficiency (EE) maximization problem. Second, the nonconcave objective function of EE maximization is converted by a fractional programming theory into a convex optimization problem. Considering that the connection results between UEs and AOs correspond to certain network topology configurations, the convex optimization problem is decomposed into a topology building problem and a resource allocation problem, which are proved as combination optimization and mixed integer nonlinear optimization, respectively. Then, the Markov approximation framework and continuity relaxation method are employed for solving the two problems, respectively. Finally, a joint topology building and resource allocation algorithm are proposed for optimizing the AOs radio resource energy efficiently. Simulation results validate the theoretical analysis of our proposed scheme. [ABSTRACT FROM PUBLISHER]

Conventional compressed sensing theory assumes signals have sparse representations in a known dictionary. Nevertheless, in many practical applications such as line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional compressed sensing technique to such applications, the continuous parameter space has to be discretized to a finite set of grid points, based on which a “nominal dictionary” is constructed for sparse signal recovery. Discretization, however, inevitably incurs errors since the true parameters do not necessarily lie on the discretized grid. This error, also referred to as grid mismatch, leads to deteriorated recovery performance. In this paper, we consider the line spectral estimation problem and propose an iterative reweighted method which jointly estimates the sparse signals and the unknown parameters associated with the true dictionary. The proposed algorithm is developed by iteratively decreasing a surrogate function majorizing a given log-sum objective function, leading to a gradual and interweaved iterative process to refine the unknown parameters and the sparse signal. A simple yet effective scheme is developed for adaptively updating the regularization parameter that controls the tradeoff between the sparsity of the solution and the data fitting error. Theoretical analysis is conducted to justify the proposed method. Simulation results show that the proposed algorithm achieves super resolution and outperforms other state-of-the-art methods in many cases of practical interest. [ABSTRACT FROM PUBLISHER]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

This paper studies distributed primal-dual strategies for adaptation and learning over networks from streaming data. Two first-order methods are considered based on the Arrow-Hurwicz (AH) and augmented Lagrangian (AL) techniques. Several revealing results are discovered in relation to the performance and stability of these strategies when employed over adaptive networks. The conclusions establish that the advantages that these methods exhibit for deterministic optimization problems do not necessarily carry over to stochastic optimization problems. It is found that they have narrower stability ranges and worse steady-state mean-square-error performance than primal methods of the consensus and diffusion type. It is also found that the AH technique can become unstable under a partial observation model, while the other techniques are able to recover the unknown under this scenario. A method to enhance the performance of AL strategies is proposed by tying the selection of the step-size to their regularization parameter. It is shown that this method allows the AL algorithm to approach the performance of consensus and diffusion strategies but that it remains less stable than these other strategies. [ABSTRACT FROM PUBLISHER]

Harmonic retrieval (HR) is a problem of significance with numerous applications. Many existing algorithms are explicitly or implicitly developed under Gaussian noise assumption, which, however, are not robust against non-Gaussian noise such as impulsive noise or outliers. In this paper, by employing the $\ell _p$ -fitting criterion and block successive upper-bound minimization (BSUM) technique, a variant of the classical RELAX algorithm named as BSUM-RELAX is devised for robust HR. It is revealed that the BSUM-RELAX successively performs alternating optimization along coordinate directions, i.e., it updates one harmonic by fixing the other $(K-1)$ components, such that the whole problem is split into $K$ single-tone HR problems, which are then solved by creating a surrogate function that majorizes the objective function of each subproblem. To further refine the frequency component, the Newton's method that takes linear complexity $\mathcal {O}(N)$ is derived for updating the frequency estimates. We prove that under the single-tone case, BSUM-RELAX converges to a Karush-Kuhn-Tucker point. Furthermore, the BSUM-RELAX is extended to the multidimensional HR case. Numerical results show that the proposed algorithm outperforms the state-of-the-art methods in heavy-tailed noise scenarios. [ABSTRACT FROM AUTHOR]

This paper studies joint spectrum allocation and user association in large heterogeneous cellular networks. The objective is to maximize some network utility function based on given traffic statistics collected over a slow timescale, conceived to be seconds to minutes. A key challenge is scalability: interference across cells creates dependencies across the entire network, making the optimization problem computationally challenging as the size of the network becomes large. A suboptimal solution is presented, which performs well in networks consisting of 100 access points (APs) serving several hundred user devices. This is achieved by optimizing over local overlapping neighborhoods, defined by interference conditions, and by exploiting the sparsity of a globally optimal solution. Specifically, with a total of $k$ user devices in the entire network, it suffices to divide the spectrum into $k$ segments, where each segment is mapped to a particular set, or pattern, of active APs within each local neighborhood. The problem is then to find a mapping of segments to patterns, and to optimize the widths of the segments. A convex relaxation is proposed for this, which relies on a reweighted $\ell _1$ approximation of an $\ell _0$ constraint, and is used to enforce the mapping of a unique pattern to each spectrum segment. A distributed implementation based on alternating direction method of multipliers is also proposed. Numerical comparisons with benchmark schemes show that the proposed method achieves a substantial increase in achievable throughput and/or reduction in the average packet delay. [ABSTRACT FROM AUTHOR]

Acquiring channel state information (CSI) at the base station (BS) is a critical requirement for successfully employing transmit beamforming in multiantenna systems. In practice, channel estimation/quantization errors, feedback delays, and fast fading can make it difficult to obtain accurate CSI at the BS. In this paper, we consider an outage-based approach for transmit beamforming in order to deal with the channel uncertainty at the BS. Our formulation is applicable to both point-to-point transmit beamforming as well as single-group multicasting scenarios. A key difference from prior works is that we do not assume knowledge of the underlying channel distribution; instead, stochastic approximation is used for computing approximate solutions of a nonconvex stochastic optimization problem via simple first-order methods (FOMs). We evaluate the performance of our FOMs in two settings: First) where we design a beamformer at the BS based on historical channel realizations collected over a relatively long time window before deployment, and second) in a post-deployment phase where we perform incremental updates of our beamformer based on intermittent, delayed, or peer feedback. Simulation results reveal the effectiveness of FOMs for our problem compared to other alternatives. [ABSTRACT FROM AUTHOR]

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms. [ABSTRACT FROM AUTHOR]

We read with great interest the recently published paper [1] (together with some additional technical details in [2]) dealing with an important topic for the radar signal processing Community.With regret, we noticed that the mentioned reference [1] provides some claims which do not agree with what we proved in paper [3]; contains some technical inconsistencies from the optimization theory point of view. Thus, respectfully, we feel obliged to provide the necessary clarifications and corrections. Specifically, this "comments on" paper has the following technical purposes: a) to rectify some untrue claims by the Authors of [1] about reference [3]; b) to show that the optimization problem arising in [1] (eq. (17)) is a special instance of the more general optimization problem addressed in [3] (eq. (13)); c) to prove that the solution of the waveform design problem in [1] (eq. (25)) given by eq. (36) is not generally correct. [1] P. Setlur and M. Rangaswamy, "Waveform Design for Radar STAP in Signal Dependent Interference," IEEE Transactions on Signal Processing, vol. 64, no. 1, pp. 19-34, Jan. 2016. [2] P. Setlur and M. Rangaswamy, Joint Filter and Waveform Design for Radar STAP in Signal Dependent Interference, Tech. Rep. DTIC, available at : https: // arxiv.org/abs/ 1510. 00055, US Air Force Res. Lab., Sensors Directorate, WPAFB, Dayton, OH, 2014. [3] A. Aubry, A. De Maio, A. Farina, and M. Wicks, "Knowledge-Aided (Potentially Cognitive) Transmit Signal and Receive Filter Design in Signal-Dependent Clutter," IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 1, pp. 93-117, Jan. 2013. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the spectrally compatible waveform design for multiple-input multiple-output (MIMO) radar in the presence of multiple targets and signal-dependent interference. Unlike the existing approaches to designing the waveform for a single target via output signal-to-interference-plus-noise ratio (SINR) maximization, a new method is proposed to deal with a more general problem, i.e., designing a spectrally compatible waveform for multiple targets, by minimizing the waveform energy of the overlayed space-frequency bands under constraints of waveform similarity and individual SINR requirements. Due to the existence of signal dependence, the formulated optimization problem is NP-hard. Toward this end, an iterative algorithm is developed. Concretely, at each iteration, the receive filter is first obtained with the aid of the minimum variance distortionless response method, then the transmit waveform is optimized by employing the dual ascent method. Both the convergence and asymptotic optimality of this algorithm are discussed. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the minimization of a general objective function $f(\boldsymbol{X})$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To reduce the computational burden, we factorize the variable $\boldsymbol{X}$ into a product of two smaller matrices and optimize over these two matrices instead of $\boldsymbol{X}$. Despite the resulting nonconvexity, recent studies in matrix completion and sensing have shown that the factored problem has no spurious local minima and obeys the so-called strict saddle property (the function has a directional negative curvature at all critical points but local minima). We analyze the global geometry for a general and yet well-conditioned objective function $f(\boldsymbol{X})$ whose restricted strong convexity and restricted strong smoothness constants are comparable. In particular, we show that the reformulated objective function has no spurious local minima and obeys the strict saddle property. These geometric properties imply that a number of iterative optimization algorithms (such as gradient descent) can provably solve the factored problem with global convergence. [ABSTRACT FROM AUTHOR]

In this paper, optimal deterministic encoding of a scalar parameter is investigated in the presence of an eavesdropper. The aim is to minimize the expectation of the conditional Cramér–Rao bound at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain threshold. First, optimal encoding functions are derived in the absence of secrecy constraints for any given prior distribution on the parameter. Next, an optimization problem is formulated under a secrecy constraint and various solution approaches are proposed. Also, theoretical results on the form of the optimal encoding function are provided under the assumption that the eavesdropper employs a linear minimum mean-squared error (MMSE) estimator. Numerical examples are presented to illustrate the theoretical results and to investigate the performance of the proposed solution approaches. [ABSTRACT FROM AUTHOR]

This paper considers the downlink transmission of cloud-radio access networks (C-RANs) with limited fronthaul capacity. We formulate a joint design of remote radio head (RRH) selection, RRH-user association, and transmit beamforming for simultaneously optimizing the achievable sum rate and total power consumption, using the multiobjective optimization concept. Due to the nonconvexity of perfronthaul capacity constraints and introduced binary selection variables, the formulated problem lends itself to a mixed-integer nonconvex program, which is generally non-deterministic polynomial-time hard. Motivated by powerful computing capability of C-RAN and for benchmarking purposes, we propose a branch and reduce and bound-based algorithm to attain a globally optimal solution. For more practically appealing approaches, we then propose three iterative low-complexity algorithms. In the first method, we iteratively approximate the continuous nonconvex constraints by convex conic ones using successive convex approximation framework. More explicitly, the problem obtained at each iteration is a mixed-integer second-order cone program (MI-SOCP) for which dedicated solvers are available. In the second method, we first relax the binary variables to be continuous to arrive at a sequence of SOCPs and then perform a postprocessing procedure on the relaxed variables to search for a high-performance solution. In the third method, we solve the considered problem in view of sparsity-inducing regularization. Numerical results show that our proposed algorithms converge rapidly and achieve near-optimal performance as well as outperform the known algorithms. [ABSTRACT FROM PUBLISHER]

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g., a sparsity promoting function), Majorize-Minimize (MM) methods have recently attracted much interest since they are fast, highly flexible, and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the data fidelity term corresponds to a least squares criterion and the cost function is replaced by a sequence of stochastic approximations of it. In this context, we propose an online version of an MM subspace algorithm and we study its convergence by using suitable probabilistic tools. Simulation results illustrate the good practical performance of the proposed algorithm associated with a memory gradient subspace, when applied to both nonadaptive and adaptive filter identification problems. [ABSTRACT FROM PUBLISHER]

The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria—or locally convergent when an equilibrium is only locally stable. To complement our convergence analysis, we also derive explicit bounds for the algorithm's convergence speed and we test it in realistic multicarrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between $100\%$ and $500\%$ in energy efficiency, even under very high uncertainty. [ABSTRACT FROM PUBLISHER]

In this paper, we conduct the joint design of transmitting sequence(s) and receiving filters subject to the Peak-to-Average Ratio (PAR) constraint in radar and communications applications. We consider optimizing the worst-case performance and the resulting optimization problem takes a maximin format. We propose two algorithms based on the MM (Majorization–Minimization or Minorization–Maximization) method as opposed to the traditional epigraph-based smooth reformulation. On top of that, both algorithms are guaranteed to converge to a B(oulingand)-stationary solution, and B-stationarity is the appropriate stationarity condition for problems with a nonconvex constraint set. The proposed algorithms successively solve a series of simple convex problems that enjoy low computational complexity. Numerical simulations have shown that the proposed algorithms empirically achieve slightly higher objective values and converge faster in terms of CPU time than the existing methods. [ABSTRACT FROM PUBLISHER]

Owing to the inherent sparsity of the target scene, compressed sensing (CS) has been successfully employed in radar applications. It is known that the performance of target scene recovery in CS scenarios depends highly on the coherence of the sensing matrix, which is determined by the radar transmit waveform. In this paper, we propose efficient transmit waveform optimization approaches for two different structures of the radar waveform, namely, the single-pulse and the more general pulse-train scenarios. By determining the identical coherence values associated with the sensing matrices of CS-based radars, the suggested methods provide a considerable reduction in the number of optimization variables. We show that, in the single-pulse scenario, fast Fourier transform operations can be used to improve the computation speed, whereas efficient power method-like iterations may be employed in the pulse-train scenarios. The effectiveness of the proposed algorithms is illustrated through several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) constraint, and similarity constraint, to name a few. The optimization technique we employ is the majorization–minimization (MM) method, which is iterative and enjoys guaranteed convergence to a stationary solution. We carry out the MM method in two stages: in the majorization stage, we propose three majorizing functions: two for the unified metric and one for the ISL metric; in the minimization stage, we give closed-form solutions for algorithmic updates under different constraints. The update step can be implemented with a few Fast Fourier Transformations (FFTs) and/or Inverse FFTs (IFFTs). We also show the connections between the MM and gradient projection method under our algorithmic scheme. Numerical simulations have shown that the proposed MM-based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, we aim to design the optimal sensor collaboration strategy for the estimation of time-varying parameters, where collaboration refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. We begin by addressing the sensor collaboration problem for the estimation of uncorrelated parameters. We show that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the nonconvexity. This specific problem structure enables the use of a convex–concave procedure to obtain a near-optimal solution. When the parameters of interest are temporally correlated, a penalized version of the convex–concave procedure becomes well suited for designing the optimal collaboration scheme. In order to improve computational efficiency, we further propose a fast algorithm that scales gracefully with problem size via the alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approach and the impact of parameter correlation and temporal dynamics of sensor networks on estimation performance. [ABSTRACT FROM PUBLISHER]