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Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data. [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]

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 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]

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]

Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples. [ABSTRACT FROM AUTHOR]

We consider a hybrid active-passive radar system that employs a wireless source as a passive illuminator of opportunity (IO) and a co-channel active radar transmitter operating in the same frequency band to seek spectral efficiency. The hybrid system can take advantage of the strengths of passive radar (e.g., energy efficiency, bi-/multi-static configuration, and spatial diversity) as well as those of active radar (dedicated transmitter, flexible transmit beam steering, waveform optimized for sensing, etc.). To mitigate the mutual interference and location-induced timing uncertainty between the radar and communication signals, we propose two designs for the joint optimization of the radar waveform and receive filters. The first is a max-min (MM) criterion that optimizes a worst-case performance metric over a timing uncertainty interval, and the other a weighted-sum (WS) criterion that forms a weighted sum of the performance metric at each delay within the delay uncertainty interval. Both design criteria result in nonconvex constrained optimization problems that are solved by sequential convex programming methods. When timing uncertainty vanishes, the two designs become identical and admit a simpler solution. Numerical results are presented to demonstrate the performance of the proposed hybrid schemes in comparison with conventional active-only and passive-only radar systems. [ABSTRACT FROM AUTHOR]

This paper investigates the benefits of intentionally adding noise to a Bayesian estimator, which comprises a linear combination of a number of individual Bayesian estimators that are perturbed by mutually independent noise sources and multiplied by a set of adjustable weighting coefficients. We prove that the Bayes risk for the mean square error (MSE) criterion is minimized when the same optimum weighting coefficients are assigned to the identical estimators in the combiner. This property leads to a simplified analysis of the noise benefit to the MSE of the combined Bayesian estimator even when the number of individual estimators tends to infinity. It is shown that, for a sufficiently large number of individual estimators, the MSE of the designed Bayesian estimator approaches a plateau for a wide range of added noise levels. This robust feature facilitates the incorporation of the added noise into the design of Bayesian estimators without tuning the noise level. For an easily implementable Bayesian estimator composed of quantizers, the benefit of the symmetric scale-family noise is demonstrated, and the optimal noise probability density function is approximated by solving a constrained nonlinear optimization problem. We further extend this potential Bayesian estimator to the nonlinear filter design. Finally, examples of the noise benefits in random parameter estimation and nonlinear filtering support the theoretical analyses. [ABSTRACT FROM AUTHOR]

In this paper, optimal deterministic encoding of a vector parameter is investigated in the presence of an eavesdropper. The objective is to minimize the expectation of the conditional Cramér–Rao bound at the intended receiver, while satisfying an individual secrecy constraint on the mean-squared error of estimating each parameter at the eavesdropper. The eavesdropper is modeled to employ the linear minimum mean-squared error estimator based on the noisy observation of the encoded parameter without being aware of encoding. First, the problem is formulated as a constrained optimization problem in the space of vector-valued functions. Then, two practical solution strategies are developed based on nonlinear individual encoding and affine joint encoding of parameters. Theoretical results on the solutions of the proposed strategies are provided for various scenarios on channel conditions and parameter distributions. Finally, numerical examples are presented to illustrate the performance of the proposed solution approaches. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to a constraint on the maximum regret-error for any other signal in the entire signal space. This framework addresses the primary limitation of existing GSRPs (consistent, subspace, and minimax regret), namely, the assumption that the a priori subspace is either fully known or fully ignored. We formulate constrained GSRP as a constrained optimization problem, the solution to which turns out to be a convex combination of the subspace and the minimax regret samplings. Detailed theoretical analysis on the reconstruction error shows that constrained sampling achieves a reconstruction that is, 1) (sub)optimal for signals in the input subspace, 2) robust for signals around the input subspace, and 3) reasonably bounded for any other signals with a simple choice of the constraint parameter. Experimental results on sampling-reconstruction of a Gaussian signal and a speech signal demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are non-convex and involve expectations over random states. Most existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic majorization-minimization, only consider minimizing a stochastic non-convex objective over a deterministic convex set. The proposed CSSCA algorithm can also handle stochastic non-convex constraints in optimization problems, and it opens the way to solving more challenging optimization problems that occur in many applications. The algorithm is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective/constraint functions in the original problems with some convex surrogate functions. The CSSCA algorithm allows a wide class of surrogate functions and thus provides many freedoms to design good surrogate functions for specific applications. Moreover, it also facilitates parallel implementation for solving large-scale stochastic optimization problems, which arise naturally in today's signal processing such as machine learning and big data analysis. We establish the convergence of the CSSCA algorithm with a feasible initial point, and customize the algorithmic framework to solve several important application problems. Simulations show that the CSSCA algorithm can achieve superior performance over existing solutions. [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]

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition, which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed, which enables high-dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images. [ABSTRACT FROM AUTHOR]

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distributionfree estimators shares a shrinkage-type form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed-form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for spatial and Doppler processing scenarios assuming different data statistical characterizations. The results show that interesting SINR improvementswith respect to some counterparts available in the open literature can be achieved especially in training starved regimes. [ABSTRACT FROM AUTHOR]

Existing approaches to online convex optimization make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret that measures the difference of losses between the online solution and the best yet fixed overall solution in hindsight. The present paper deals with online convex optimization involving adversarial loss functions and adversarial constraints, where the constraints are revealed after making decisions, and can be tolerable to instantaneous violations but must be satisfied in the long term. Performance of an online algorithm in this setting is assessed by the difference of its losses relative to the best dynamic solution with one-slot-ahead information of the loss function and the constraint (that is here termed dynamic regret); and the accumulated amount of constraint violations (that is here termed dynamic fit ). In this context, a modified online saddle-point (MOSP) scheme is developed, and proved to simultaneously yield sublinear dynamic regret and fit, provided that the accumulated variations of per-slot minimizers and constraints are sublinearly growing with time. MOSP is also applied to the dynamic network resource allocation task, and it is compared with the well-known stochastic dual gradient method. Numerical experiments demonstrate the performance gain of MOSP relative to the state of the art. [ABSTRACT FROM AUTHOR]

This paper considers a convex optimization problem with a globally coupled linear equality constraint and local polyhedron constraints and develops efficient distributed optimization methods. The considered problem has many engineering applications. Due to the polyhedron constraints, agents in the existing methods have to deal with polyhedron constrained subproblems at each iteration. One of the key challenges is that projection onto a polyhedron set is not trivial, which prohibits the agents from solving these subproblems efficiently. In this paper, based on the alternating direction method of multipliers (ADMM), we propose a new distributed optimization method, called proximal dual consensus ADMM (PDC-ADMM). The PDC-ADMM transforms the polyhedron constraints as quadratic penalty terms in the subproblems, making the subproblems efficiently solvable and consequently reducing the overall computational overhead of the agents. In addition, we propose a randomized PDC-ADMM which can deal with time-varying networks with randomly on/off agents and communication errors, and an inexact (randomized) PDC-ADMM for low-complexity computations. We show that the proposed distributed methods converge to the optimal solution set almost surely and have a \mathcalO\left(1/k\right) ergodic convergence rate in the mean. Numerical results show that the proposed methods offer significantly lower computation time than the existing distributed ADMM method in solving a linearly constrained LASSO problem. [ABSTRACT FROM AUTHOR]

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure. [ABSTRACT FROM PUBLISHER]

Cooperative localization differs from conventional localizations in using the measurements between the unknown nodes, which provide the relative location information of the nodes. This paper investigates cooperative localization by adopting the concept of relative configuration that describes the “shape” of the node network, without considering its absolute location, orientation, and/or scaling. Since the relative configuration is a non-Euclidean object, we introduce the Procrustes coordinates as a coordinate representation, suggest using the relative error as a coordinate independent error metric, and then derive the Cramér-Rao lower bound (CRLB) and a CRLB-type bound for the Procrustes coordinates and the relative error respectively. Three applications of the relative configuration are demonstrated: the first one gives the CRLB analysis for anchor-free localization; the second one discusses the optimal minimally constrained system (MCS) for deriving the absolute locations; and the third one refers to the anchor selection with consideration of anchor location uncertainty. These applications show the advantages of using the relative configuration to investigate cooperative localization. [ABSTRACT FROM PUBLISHER]

The Empirical Mode Decomposition (EMD) is a relatively new adaptive method for multicomponent signal representation which allows for analyzing nonlinear and nonstationary signals. In spite of its lack of mathematical foundations, very few papers are dedicated to defining new decompositions that would preserve the interesting properties of the EMD while improving the mathematical setting. The new decomposition based on direct constrained optimization we introduce in this article is an attempt in that direction. [ABSTRACT FROM AUTHOR]

In this paper the problem of semisupervised hyperspectral unmixing is considered. More specifically, the unmixing process is formulated as a linear regression problem, where the abundance's physical constraints are taken into account. Based on this formulation, a novel hierarchical Bayesian model is proposed and suitable priors are selected for the model parameters such that, on the one hand, they ensure the nonnegativity of the abundances, while on the other hand they favor sparse solutions for the abundances' vector. Performing Bayesian inference based on the proposed hierarchical Bayesian model, a new low-complexity iterative method is derived, and its connection with Gibbs sampling and variational Bayesian inference is highlighted. Experimental results on both synthetic and real hyperspectral data illustrate that the proposed method converges fast, favors sparsity in the abundances' vector, and offers improved estimation accuracy compared to other related methods. [ABSTRACT FROM PUBLISHER]

Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth-limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in-network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in-network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the nonparametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk. [ABSTRACT FROM AUTHOR]

Target tracking is investigated using particle filtering of data collected by distributed sensors. In lieu of a fusion center, local measurements must be disseminated across the network for each sensor to implement a centralized particle filter (PF). However, disseminating raw measurements incurs formidable communication overhead as large volumes of data are collected by the sensors. To reduce this overhead and thus enable distributed PF implementation, the present paper develops a set-membership constrained (SMC) PF approach that i) exhibits performance comparable to the centralized PF; ii) requires only communication of particle weights among neighboring sensors; and iii) can afford both consensus-based and incremental averaging implementations. These attractive attributes are effected through a novel adaptation scheme, which is amenable to simple distributed implementation using min- and max-consensus iterations. The resultant SMC-PF exhibits high gain over the bootstrap PF when the likelihood is peaky, but not in the tail of the prior. Simulations corroborate that for a fixed number of particles, and subject to peaky likelihood conditions, SMC-PF outperforms the bootstrap PF, as well as recently developed distributed PF algorithms, by a wide margin. [ABSTRACT FROM AUTHOR]

The performance of distributed estimation in wireless sensor networks (WSNs) is affected by observation noise, communication errors and the noise caused by the inevitable quantization process. Reducing the number of transmitted bits per node can minimize the energy consumption and communication load, thereby prolonging the network lifetime. However, reducing the number of transmitted bits has a significant impact on the estimation performance. In this work, we propose cooperative information aggregation (CIA) approaches for distributed estimation that consider the above-mentioned issues jointly. Under the proposed schemes, a multi-bit quantizer is used to generate the local observation codeword at each node. Then, each node only transmits one predesigned bit of the derived codeword to the fusion center (FC). At the FC, the information bits transmitted cooperatively by all nodes are aggregated and fused to obtain the estimation result. We design two estimators: an aggregation hard decision estimator (AHDE) and an aggregation maximum-likelihood estimator (AMLE). Predetermining the transmitted bit at each node is formulated as a constrained optimization problem for resource allocation and the corresponding suboptimal resource allocation policies are proposed. The simulation results demonstrate that the proposed schemes can overcome the impact of observation noise and communication errors effectively. [ABSTRACT FROM PUBLISHER]

Multiple-input multiple-output (MIMO) radars have many advantages over their phased-array counterparts: improved spatial resolution; better parametric identifiably and greater flexibility to design the transmit beampattern. The design of the transmit beampatterns generally requires the waveforms to have arbitrary auto- and cross-correlation properties. The correlation/covariance matrix, \bf R, of the waveforms must be positive semidefinite, therefore synthesis of a desired beampattern is usually a constrained optimization problem. In this paper, to simplify the constrained optimization problem, two algorithms are proposed to synthesize the waveform covariance matrix for the desired beampattern. In the first proposed algorithm the elements of a square-root matrix of the covariance matrix \bf R are parameterized using the coordinates of a hypersphere that implicitly fulfil the constraints. This yields an iterative algorithm, whose convergence speed can be increased significantly by providing good initial values. In the second algorithm the constraints and redundant information in the covariance matrix \bf R are exploited to find a closed-form solution. The drawback of the second algorithm is that it may yield a pseudocovariance matrix (pseudo-CM) that is not guaranteed to be positive semidefinite. However, the pseudo-CM can be easily converted into a covariance matrix using eigenvalue decomposition and/or shrinkage methods. Moreover, a pseudo-CM can also be used to provide good initial values for the first algorithm to enable faster convergence. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel framework for delay-tolerant particle filtering that is computationally efficient and has limited memory requirements. Within this framework the informativeness of a delayed (out-of-sequence) measurement (OOSM) is estimated using a lightweight procedure and uninformative measurements are immediately discarded. The framework requires the identification of a threshold that separates informative from uninformative; this threshold selection task is formulated as a constrained optimization problem, where the goal is to minimize state estimation error whilst controlling the computational requirements. We develop an algorithm that provides an approximate solution for the optimization problem. Simulation experiments provide an example where the proposed framework processes less than 40% of all OOSMs with only a small reduction in state estimation accuracy. [ABSTRACT FROM PUBLISHER]

This paper investigates the optimal design issue of general two-hop amplify-and-forward (AF) MIMO relay networks with one source, one destination and multiple relays, each having multiple antennas. Beginning with the study of the mean-square error (MSE) matrix of the system and the use of Wiener filter for the destination processing, a constrained optimization problem with respect to the unknown relay precoder matrix is formulated with a goal of minimizing the total relay transmit power subject to the MSE-based quality of service (QoS) requirement on each data stream. As the original optimization problem is very difficult to solve, a lower bound of the cost function is pursued to achieve an approximate optimization problem. The modified problem is then solved under the perfect channel state information (CSI) condition using the diagonalization method along with the majorization theory to obtain optimal relay precoder with either nonoptimal or optimal source precoding. It is shown that a convex relay precoding solution is available in the case of nonoptimal source precoding whereas a joint optimal source and relay precoder can be obtained through a multilevel waterfilling algorithm. The optimal design of the relay network under imperfect CSI condition is also considered by modifying the optimization problem with the channel mean and covariance matrix, leading to a robust optimization design of the relay precoder. The proposed technique is validated by Monto Carlo simulations and is also compared with one existing method. [ABSTRACT FROM AUTHOR]

We consider transmission scheduling using an ARQ protocol with retransmissions given channel state information (CSI) and a correlated fading channel. The problem is formulated as a countable state, infinite horizon, average cost Markov decision process (MDP) with an average delay constraint. Our main result is to give sufficient conditions on the channel memory, and transmission cost so that the optimal transmission scheduling policy is a monotonically increasing function of the buffer occupancy. In proving this result, we first prove positive recurrence (stability) of the buffer. The monotone structure proof consists of two steps. First, the constrained MDP (CMDP) is transformed into an unconstrained MDP using a Lagrangian dynamic programming formulation. It is proved that the unconstrained optimal policy is pure and monotonically increasing in the buffer occupancy. It is then shown that the constrained optimal policy is a randomized mixture of two pure transmission policies that are monotone in the buffer state. Finally, the monotone structure of the optimal transmission policy is exploited to derive a monotone-policy Q-learning algorithm and a stochastic approximation based monotone policy search algorithm for estimating the optimal policy in real time. [ABSTRACT FROM AUTHOR]

In order to find sparse approximations of signals, an appropriate generative model for the signal class has to be known. If the model is unknown, it can be adapted using a set of training samples. This paper presents a novel method for dictionary learning and extends the learning problem by introducing different constraints on the dictionary. The convergence of the proposed method to a fixed point is guaranteed, unless the accumulation points form a continuum. This holds for different sparsity measures. The majorization method is an optimization method that substitutes the original objective function with a surrogate function that is updated in each optimization step. This method has been used successfully in sparse approximation and statistical estimation [e.g., expectation-maximization (EM)] problems. This paper shows that the majorization method can be used for the dictionary learning problem too. The proposed method is compared with other methods on both synthetic and real data and different constraints on the dictionary are compared. Simulations show the advantages of the proposed method over other currently available dictionary learning methods not only in terms of average performance but also in terms of computation time. [ABSTRACT FROM AUTHOR]

In communication systems where full-duplex transmission is required, echo cancellers are deployed to cancel the interference of the transmitted signal at the collocated receiver. For systems using discrete multitone (DMT) modulation, echo cancellation is performed partially in the time and frequency domains to decrease the processing complexity. In this paper, echo cancellation for DMT systems is reformulated as a constrained optimization problem, where a cost function is minimized over an extended linear space. This extended space contains the weights of the finite-impulse-response (FIR) filter emulating the echo channel in the time and the frequency domains, while linear constraints are used to ensure the proper mapping between these two domains. Based on this proposed formulation, a new constrained adaptive echo cancellation structure for DMT-based digital subscriber lines (DSL) systems is proposed. The proposed formulation provides a unifying framework for different practical DSL systems (i.e., frame asynchronous and multirate), as well as additional flexibility in implementation by allowing the incorporation of supplementary constraints that can improve the performance of the system. As an illustrative example, we show how the robustness of the echo canceller can be improved in the presence of radio frequency interference by adding appropriate constraints on the extended linear space. [ABSTRACT FROM AUTHOR]

The generation of Hermite-Gaussian-like orthonormal eigenvectors of the discrete Fourier transform (DFT) matrix F is an essential step in the development of the discrete fractional Fourier transform (DFRFT). Most existing techniques depend on the generation of orthonormal eigenvectors of a nearly tridiagonal matrix S which commutes with matrix F. More sophisticated methods view the eigenvectors of S as only initial ones and use them for generating final ones which better approximate the Hermite-Gaussian functions employing a technique like the orthogonal procrustes algorithm (OPA). Here, a direct technique for the collective (batch) evaluation of optimal Hermite-Gaussian-like eigenvectors of matrix F is contributed. It is a direct technique in the sense that it does not require the generation of initial eigenvectors to be used for computing the final superior ones. It is a batch method in the sense that it solves for the entire target modal matrix of F instead of the sequential generation of the eigenvectors. The simulation results show that the proposed method is faster than the OPA. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal power and rate allocation control in multiple-input multiple-output (MIMO) wireless systems over Markovian fading channels. The problem is posed as an infinite horizon average-cost constrained Markov decision process (CMDP) with the goal of minimizing the average transmission power subject to delay constraints. By using a Lagrangian formulation of the CMDP, we use the concepts of stochastic dominance, submodularity, and multimodularity to prove that the optimal randomized policies are monotone. Three important structural results on the nature of the optimal randomized policies are derived. First, we show that the action space can be exponentially reduced by decomposing the rate allocation problem into bit-loading problem across individual antennas and the total rate allocation based on the current buffer occupancy and channel state. Second, we show that the optimal rate allocation policy is a randomized mixture of two pure policies that are monotonically increasing in the buffer occupancy. Finally, we show that the optimal power allocation is piecewise linear in the delay constraint. These three structural results can be exploited to devise efficient online reinforcement learning algorithms for optimal rate allocation. [ABSTRACT FROM AUTHOR]

We consider multi-input multi-output-orthogonal frequency division multiplexing (MIMO-OFDM) transmission in a scenario that the adopted cyclic-prefix (CP) length is shorter than the channel delay spread for boosting data rate and, moreover, the channel parameters are not exactly known but are estimated using the least-squares (LS) training technique. By exploiting the receiver spatial resource, we propose a constrained-optimization-based linear equalizer which can mitigate inter-symbol interference and inter-carrier interference incurred by insufficient CP interval, and is robust against the net detrimental effects caused by channel estimation errors. The optimization problem is formulated in an equivalent unconstrained generalized-sidelobe-canceller (GSC) setup. The channel parameter error is explicitly incorporated into the constraint-free GSC system model through the perturbation technique; this allows us to exploit the presumed LS channel error property for deriving a closed-form solution, and can also facilitate an associated analytic performance analysis. A closed-form approximate signal-to-interference-plus-noise ratio (SINR) expression for the proposed robust scheme is given, and an appealing formula of the achievable SINR improvement over the nonrobust counterpart is further specified. Our analytic results bring out several intrinsic features of the proposed solution. Simulation study confirms the effectiveness of the proposed method and corroborates the predicted SINR results [ABSTRACT FROM PUBLISHER]

In this correspondence, three methods are proposed to design the look-direction amplitude/phase response to optimize the Frost beamformer. With some constrained optimization criteria, the new constraint vector and thus the new weight vector are designed to improve the output signal-to-interference-plus-noise ratio (SINR) relative to the beamformer with the distortionless constraint. Simulation results are presented to demonstrate the improved interference and noise suppression performance of the optimized beamformer. [ABSTRACT FROM AUTHOR]

The minimum bit-error rate (MBER) linear multiuser detection of direct-sequence code-division multiple-access (DS-CDMA) communications is considered, It is shown that the problem of MBER linear multiuser detection is equivalent to a constraitied optimization problem where the constrained space is the surface and interior of a hyperellipsoid. It is further shown that any solution of the constrained optimization problem must be a solution of a set of nonlinear equations. Based on these the MBER linear multiuser detector of the two-user case is obtained. For general cases, we propose a convex subspace of the constrained space and show that the BER cost function is convex on the subspace and therefore has a unique solution. Some sufficient conditions that guarantee the convex subspace always contains the global minimizer are provided, which show that if the signal-to-noise ratio (SNR) is sufficiently large, the convex subspace always contains the global minimizer. A Newton method is developed for the set of nonlinear equations and computer simulation gives some illustrative examples. [ABSTRACT FROM AUTHOR]

By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a test is required to indicate whether the model for brain activity fits. A problem in using such tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald test for these cases. One of the advantages of the Wald test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald tests in electromagnetic source analysis (EMSA) are examined: a test on source amplitudes and a test on the closeness of source pairs. The Wald test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Cramér-Rao bound (CRB) is required for the use of the Wald test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald test are still good, with a moderate number of trials. Additionally, the CRB and Wald test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude. [ABSTRACT FROM AUTHOR]

Based on the linear prediction (LP) property of sinusoidal signals, a closed-form unbiased frequency estimator for a real sinusoid in white noise is proposed. The frequency estimator, which is derived by minimizing a constrained least squares cost function, can be considered as a reformulation of the well known Pisarenko harmonic decomposer (PHD). Online computation of the frequency estimate can be achieved in a very simple manner, and its variance is derived. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the PHD, maximum likelihood, and LP-based methods as well as Cramér-Rao lower bound. [ABSTRACT FROM AUTHOR]