ALBERT

Description: Large-scale antenna systems are considered as a viable technology to compensate for huge path loss in millimeter-wave (mmWave) communications. However, due to the massive antennas, the channel state information (CSI) acquisition is costly and challenging. In this paper, we develop a novel compressive channel estimation framework based on multiple measurement vectors (MMV). Compared with conventional single measurement vector (SMV)-based approach, the proposed framework exploits structural sparsity exhibited in the relatively rich local scattering mmWave channels to greatly reduce the training and computational overheads. Moreover, we propose a channel subspace matching pursuit (CSMP) algorithm based on the MUltiple SIgnal Classification (MUSIC) as an MMV solver. By leveraging the benefits of MUSIC, the proposed CSMP can properly exploit the diversity gain from structural sparsity, and further improve the estimation quality via the superresolution capability. Meanwhile, an efficient implementation method of the proposed CSMP is also presented. Compared to the conventional MMV solver, the proposed CSMP exhibits much lower complexity. Finally, several simulation results show that the MMV-based CSMP achieves significant performance gains over other estimation algorithms, especially when the angular resolutions are high. Regarding the computational cost, the simulation result shows that the MMV-based estimation algorithms are approximately two orders of magnitude smaller than the SMV-based estimation algorithms.

Description: Deploying a massive number of antennas at the base station side can boost the cellular system performance dramatically. This however involves significant additional radio-frequency (RF) front-end complexity, hardware cost, and power consumption. To address this issue, the beamspace-multiple-input-multiple-output (beamspace-MIMO)-based approach is considered as a promising solution. In this paper, we first show that the traditional beamspace-MIMO suffers from spatial power leakage and imperfect channel statistics estimation. A beam combination module is hence proposed, which consists of a small number (compared with the number of antenna elements) of low-resolution (possibly one-bit) digital (discrete) phase shifters after the beamspace transformation module to further compress the beamspace signal dimensionality, such that the number of RF chains can be reduced beyond beamspace transformation and beam selection. The optimum discrete beam combination weights for the uplink are obtained based on the branch-and-bound (BB) approach. The key to the BB-based solution is to solve the embodied subproblem, whose solution is derived in a closed-form. Thereby, a sequential greedy beam combination scheme with linear-complexity (w.r.t. the number of beams in the beamspace) is proposed. Link-level simulation results based on realistic channel models and long-term-evolution parameters are presented which show that the proposed schemes can reduce the number of RF chains by up to $text{25}%$ with a one-bit digital phase-shifter-network.

Description: In this paper, we investigate the noise benefits to maximum likelihood type estimators (M-estimator) for the robust estimation of a location parameter. Two distinct noise benefits are shown to be accessible under these conditions. With symmetric heavy-tailed noise distributions, the asymptotic efficiency of the estimation can be enhanced by injecting extra noise into the M-estimators. With an asymmetric contaminated noise model having a convex cumulative distribution function, we demonstrate that addition of noise can reduce the maximum bias of the median estimator. These findings extend the analysis of stochastic resonance effects for noise-enhanced signal and information processing.

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Description: In this paper, we study a frequency-modulated continuous-wave based radio-frequency identification system, which is composed of a reader with single transmitter and multiple receiving antennas as well as multiple active backscatter tags. In particular, our contribution is twofold in this paper. First, we construct a general architecture for achieving the functionality of wireless positioning based on the principle of the switched injection-locked oscillator (SILO). Unlike the previous SILO-based schemes, some limitations on the pulsed waveform generated by the tags are overcome. In addition, only one reader set up with multiple receiving antennas is used to precisely localize tags based on the delay and direction-of-arrival estimates. Second, the developed algorithms make use of a shift invariant property among the baseband signal snapshots of intra- and/or intermodulation intervals, i.e., snapshots in one modulation period and/or sets of snapshots in multiple modulation periods. A new joint singular value decomposition based ESPRIT algorithm is developed for determining the number of multiple active tags and their positions by implementing the matrix reconstruction and stacking techniques. The proposed method has its basic foundation on the processing of received data with global fusion scheme. In this way, this method can improve the performance of parameter estimates in terms of accuracy and resolution without suffering from the pair matching problem. System simulations and experimental validations are carried out to verify the proposed system architecture associated with the signal processing technique.

Description: This paper deals with the problem of analog–digital transmit beamforming under spectrum sharing constraints for backhaul systems. In contrast to fully digital designs, where the spatial processing is done at baseband unit with all the flexible computational resources of digital processors, analog–digital beamforming schemes require that certain processing is done through analog components, such as phase-shifters or switches. These analog components do not have the same processing flexibility as the digital processor, but on the other hand, they can substantially reduce the cost and complexity of the beamforming solution. This paper presents the joint optimization of the analog and digital parts, which results in a nonconvex, NP-hard, and coupled problem. In order to solve it, an alternating optimization with a penalized convex–concave method is proposed. According to the simulation results, this novel iterative procedure is able to find a solution that behaves close to the fully digital beamforming upper bound scheme.

Description: In this paper, we consider a multiuser wireless system with one full duplex (FD) base station (BS) serving a set of half duplex (HD) mobile users. To cope with the in-band self-interference (SI) and co-channel interference, we formulate a quality-of-service (QoS) based linear transceiver design problem. The problem jointly optimizes the downlink (DL) and uplink (UL) beamforming vectors of the BS and the transmission powers of UL users so as to provide both the DL and UL users with guaranteed signal-to-interference-plus-noise ratio performance, using a minimum UL and DL transmission sum power. The considered system model not only takes into account noise caused by nonideal RF circuits, analog/digital SI cancellation but also constrains the average signal power at the input of the analog-to-digital converter (ADC) for avoiding signal distortion due to finite ADC precision. The formulated design problem is not convex and challenging to solve in general. We first show that for a special case with a worst case SI channel estimation error, the QoS-based linear transceiver design problem is globally solvable by a polynomial time bisection algorithm. For the general case, we propose a suboptimal algorithm based on alternating optimization (AO). The AO algorithm is guaranteed to converge to a Karush–Kuhn–Tucker solution. To improve the computational efficiency of the AO algorithm, we further develop a fixed-point method by extending the classical uplink–downlink duality in HD systems to the FD system. Simulation results are presented to demonstrate the performance of the proposed algorithms and the comparison with HD systems.

Description: In this paper, we study the feasibility of an opportunistic radar, which exploits the probing signals transmitted during the sector level sweep of the IEEE 802.11ad beamforming training protocol. Several solutions are presented to detect the presence of prospective obstacles and estimate their position, radial velocity, and backscattered signal amplitude, which differ in the amount of prior information as to the transmitted signal and the channel fluctuation. Also, we derive the Cramér–Rao bound as a benchmark for the proposed estimators: The derivation of these bounds is per se relevant, as it generalizes classical results to the case where the echo is not entirely contained in the observation window. Numerical examples are provided to assess performance of the proposed solutions. The results indicate that the close-to-one detection probability is achievable up to 90 m with a probability of false alarm of 1e-4 and Swerling-I target fluctuation; in this region, the target delay is estimated with an accuracy smaller than the symbol interval (corresponding to a range resolution smaller than 10 cm) with probability close to one, while the velocity estimate is generally quite poor as a consequence of the very short duration of the probing signal.

Description: One-bit quantization can significantly reduce the massive multiple-input and multiple-output (MIMO) system hardware complexity, but at the same time it also brings great challenges to the system algorithm design. Specifically, it is difficult to recover information from the highly distorted samples as well as to obtain accurate channel estimation without increasing the number of pilots. In this paper, a novel inference algorithm called variational approximate message passing (VAMP) for one-bit quantized massive MIMO receiver is developed, which attempts to exploit the advantages of both the variational Bayesian inference algorithm and the bilinear generalized approximated message passing algorithm to accomplish joint channel estimation and data detection in a closed form with first-order complexity. Asymptotic state evolution analysis indicates the fast convergence rate of VAMP and also provides a lower bound for the data detection error. Moreover, through extensive simulations, we show that VAMP can achieve excellent detection performance with low pilot overhead in a wide range of scenarios.

Description: In this paper, we study the effect of downlink (DL) training on the achievable sum rate of multiuser massive MIMO channels with spatial correlations, and derive sufficient conditions of the DL channel estimation error covariance matrices that maintain the full multiplexing gain at high data signal-to-noise-ratios (SNRs). Given the derived conditions, a simple asymptotic upper bound on the average sum rate loss due to channel estimation is obtained. We derive, in closed-form, training sequences of limited duration that satisfy these conditions. The training duration is variable and increases with the data SNR, while the sequences lie in a subspace spanned by a variable number of user spatial covariance matrices’ eigenvectors. We additionally study the problem of sequence codebook design and find solutions to this problem for uniform linear and rectangular arrays using asymptotic results. For the aforementioned training structure, the designed codebooks are observed numerically to be near-optimal for a moderate number of base station antennas. Due to their ability to identify a sufficient limited number of channel directions to train, the proposed solutions can substantially reduce DL training overheads while providing achievable rates that are comparable with the rates achieved with perfect channel state information.

Description: In this paper, we consider the inference problem for a wide class of time-series models, referred to as multistate autoregressive models. The time series that we consider are composed of multiple epochs, each modeled by an autoregressive process. The number of epochs is unknown, and the transitions of states follow a Markov process of an unknown order. We propose an inference strategy that enables reliable and efficient offline analysis of this class of time series. The inference is carried out through a three-step approach: detecting the structural changes of the time series using a recently proposed multiwindow algorithm, identifying each segment as a state and selecting the most appropriate number of states, and estimating the Markov source based upon the symbolic sequence obtained from previous steps. We provide theoretical results and algorithms in order to facilitate the inference procedure described above. We demonstrate the accuracy, efficiency, and wide applicability of the proposed algorithms via an array of experiments using synthetic and real-world data.

Description: This paper considers a wireless-powered massive multi-input multioutput aided multiway amplify-and-forward relay network, where a relay equipped with massive antennas charges users through energy beamforming and assists with wireless information transmission. For this system, we propose a novel energy-efficient resource allocation scheme for the global energy efficiency (GEE) optimization. In particular, we first derive an accurate closed-form expression of GEE when zero-forcing transceivers are employed in the considered system. Second, based on this analytical expression, we formulate a resource allocation optimization problem for the GEE maximization by jointly optimizing power and time allocation, subject to limited transmit power, time duration, and minimum quality-of-service constraints. Due to the complexity of this nonconvex optimization, a two-layer iterative algorithm is proposed to address the original GEE maximization problem. Numerical results demonstrate the accuracy of our theoretical analysis and the effectiveness of the derived algorithms.

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Description: This paper studies resilient multiagent distributed estimation of an unknown vector parameter when a subset of the agents is adversarial. We present and analyze a flag raising distributed estimator ( $mathcal {FRDE}$ ) that allows the agents under attack to perform accurate parameter estimation and detect the adversarial agents. The $mathcal {FRDE}$ algorithm is a consensus+innovations estimator in which agents combine estimates of neighboring agents (consensus) with local sensing information (innovations). We establish that, under $mathcal {FRDE}$ , either the uncompromised agents' estimates are almost surely consistent, or the uncompromised agents detect compromised agents (with arbitrarily small false alarm probability) if and only if the network of uncompromised agents is connected and globally observable. Numerical examples illustrate the performance of $mathcal {FRDE}$ .

Description: Recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation problem with graph Laplacian constraints. While such problems are convex, existing methods cannot guarantee that solutions will have specific graph topology properties (e.g., being a tree), which are desirable for some applications. The problem of learning a graph with topology properties is in general non-convex. In this paper, we propose an approach to solve these problems by decomposing them into two sub-problems for which efficient solutions are known. Specifically, a graph topology inference (GTI) step is employed to select a feasible graph topology. Then, a graph weight estimation (GWE) step is performed by solving a generalized graph Laplacian estimation problem, where edges are constrained by the topology found in the GTI step. Our main result is a bound on the error of the GWE step as a function of the error in the GTI step. This error bound indicates that the GTI step should be solved using an algorithm that approximates the data similarity matrix by another matrix whose entries have been thresholded to zero to have the desired type of graph topology. The GTI stage can leverage existing methods, which are typically based on minimizing the total weight of removed edges. Since the GWE stage is an inverse covariance estimation problem with linear constraints, it can be solved using existing convex optimization methods. We demonstrate that our approach can achieve good results for both synthetic and texture image data.

Description: This paper considers the mean-reverting portfolio (MRP) design problem arising from statistical arbitrage (a.k.a. pairs trading) in the financial markets. It aims at designing a portfolio of underlying assets by optimizing the mean reversion strength of the portfolio, while taking into consideration the portfolio variance and an investment budget constraint. Several specific design problems are considered based on different mean reversion criteria. Efficient algorithms are proposed to solve the problems. Numerical results on both synthetic and market data show that the proposed MRP design methods can generate consistent profits and outperform the traditional design methods and the benchmark methods in the literature.

Description: We address the two fundamental problems of spatial field reconstruction and sensor selection in heterogeneous sensor networks. We consider the case where two types of sensors are deployed: the first consists of expensive, high quality sensors; and the second, of cheap low quality sensors, which are activated only if the intensity of the spatial field exceeds a pre-defined activation threshold (e.g., wind sensors). In addition, these sensors are powered by means of energy harvesting and their time varying energy status impacts on the accuracy of the measurement that may be obtained. We then address the following two important problems: (i) how to efficiently perform spatial field reconstruction based on measurements obtained simultaneously from both networks; and (ii) how to perform query based sensor set selection with predictive MSE performance guarantee. To overcome this problem, we solve the first problem by developing a low complexity algorithm based on the spatial best linear unbiased estimator (S-BLUE). Next, building on the S-BLUE, we address the second problem, and develop an efficient algorithm for query based sensor set selection with performance guarantee. Our algorithm is based on the Cross Entropy method which solves the combinatorial optimization problem in an efficient manner. We present a comprehensive study of the performance gain that can be obtained by augmenting the high-quality sensors with low-quality sensors using both synthetic and real insurance storm surge database known as the Extreme Wind Storms Catalogue.

Description: Detecting and tracking low-flying targets at low-grazing angles is a difficult task due to the possible beam split and radar blind area. To alleviate this issue, we propose a frequency diverse subaperturing multiple-input multiple-output (FDS-MIMO) radar with optimized low-altitude beam coverage performance. A specular echo model is first formulated in the presence of multipath propagation together with a closed-form expression for the joint transmit–receive beampattern. Then, a perturbational echo model is developed for anomalous terrain. Moreover, a notional multipath mitigation region concept is defined together with the corresponding boundary conditions. The FDS-MIMO radar beam coverage capability is evaluated by the low observability rate. Furthermore, the FDS-MIMO radar low-altitude beam coverage is improved according to the solutions of boundary conditions, and an adaptive frequency offset design strategy is proposed for the changing environment. Both theoretical analysis and numerical results demonstrate that the optimized FDS-MIMO radar outperforms conventional phased-array radar and MIMO radar in terms of low-altitude beam coverage performance.

Description: We consider in this paper how to encode a finite-energy random field via a finite number of bits. We present a method giving rise to a finite-bit representation for a given field. We analyze the overall reconstruction error associated with this method, and see that it is a summation which consists of the error coming from the sampling and quantization domains. Then, we search for the best sampling and quantization parameters to get the optimal reconstruction error for a given number of bits. This optimization leads to the number of bits versus reconstruction error curve consisting of best achievable points, which is reminiscent of rate distortion curve in information theory.

Description: Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic gradients for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multicell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

Description: Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of-arrival estimation. Recently, this problem has been addressed using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixed-norm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work, we derive an equivalent, compact reformulation of the $ell _{2,1}$ mixed-norm minimization problem that provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we prove in this case the exact equivalence between our compact problem formulation and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method.

Description: Chromatic derivatives are special, numerically robust differential operators that preserve spectral features of a signal; the associated chromatic approximations accurately capture local features of a signal. For this reason they allow digital processing of continuous time signals often superior to processing of discrete samples of such signals. We introduce a new concept of “matched filter” chromatic approximations, where the underlying basis functions are chosen to match the spectral profile of the signals being approximated. We then derive a collection of formulas and theorems that form a general framework for practical applications of chromatic derivatives and approximations. In the second part of this paper, we use such a general framework in several case studies of such applications that aim to illustrate how chromatic derivatives and approximations can be used in signal processing with an intention of motivating DSP engineers to find applications of these novel concepts in their own practice.

Description: This paper deals with the problem of sequentially detecting statistical changes. In particular, the focus is on transient change detection, in which a probability minimizing optimal criterion is desirable. This is in contrast with the traditional minimization of the detection delay, proposed in quickest change detection problems. A finite moving average stopping time is proposed for the general transient change detection problem. The statistical performance of this stopping time is investigated and compared to other methods available in the literature. The proposed stopping time and theoretical findings are applied to quality monitoring, including reliability monitoring in industrial processes and signal quality monitoring in global navigation satellite systems. Numerical simulations are presented to assess the goodness of the presented theoretical results, and the performance of the considered stopping times. This will show the superiority of the proposed scheme.

Description: This paper proposes a decentralized method for estimation of dynamic states of a power system. The method remains robust to time-synchronization errors and high noise levels in measurements. Robustness of the method has been achieved by incorporating internal angle in the dynamic model used for estimation and by decoupling the estimation process into two stages with continuous updation of measurement-noise variances. Additionally, the proposed estimation method does not need measurements obtained from phasor measurement units; instead, it just requires analog measurements of voltages and currents directly acquired from instrument transformers. This is achieved through statistical signal processing of analog voltages and currents to obtain their magnitudes and frequencies, followed by application of unscented Kalman filtering for nonlinear estimation. The robustness and feasibility of the method have been demonstrated on a benchmark power system model.

Description: In this paper, we consider the joint design of both transmit waveforms and receive filters for a colocated multiple-input-multiple-output (MIMO) radar with the existence of signal-dependent interference and white noise. The design problem is formulated into a maximization of the signal-to-interference-plus-noise ratio (SINR), including various constraints on the transmit waveforms. Compared with the traditional alternating semidefinite relaxation approach, a general and flexible algorithm is proposed based on the majorization-minimization method with guaranteed monotonicity, lower computational complexity per iteration and/or convergence to a B-stationary point. Many waveform constraints can be flexibly incorporated into the algorithm with only a few modifications. Furthermore, the connection between the proposed algorithm and the alternating optimization approach is revealed. Finally, the proposed algorithm is evaluated via numerical experiments in terms of SINR performance, ambiguity function, computational time, and properties of the designed waveforms. The experiment results show that the proposed algorithms are faster in terms of running time and meanwhile achieve as good SINR performance as the the existing methods.

Description: Multicarrier wireless communication systems, which usually operate over frequency-selective fading channels, are practically also impaired by environmental impulsive noise. In order to boost the signal-to-noise power ratio (SNR) at the receiver, this paper proposes and analyzes nonlinear estimators based on the multiple thresholding, with associated piecewise attenuation, or clipping, of the received signal amplitude. The proposed approach exploits a new heuristic criterion to set the thresholds. Although the obtained thresholds are slightly suboptimal in output SNR, the proposed approach has the nice and useful property to allow closed-form analytical derivations for both the threshold(s) and the associated attenuating/clipping parameters, when a Gaussian source is impaired by an impulsive noise. Such a quite general class of estimators, which could be applied also in other scenarios, is particularly attractive for orthogonal frequency division multiplexing communication systems in the presence of additive multicomponent impulsive noise. We are also letting to derive closed-form expressions for the output SNR in frequency-selective multipath fading channels. The SNR performance and the associated symbol error rate have been compared with those of more traditional blanking, clipping, and clipping-blanking processors. Specifically, analytical and simulation results, carried out for Class-A and symmetrical alpha-stable (S $alpha$ S) impulsive noise, show that the proposed threshold-based suppressors are superior to the traditional ones. Furthermore, as the number of thresholds increases, the proposed estimators closely approach the performance of the optimal minimum mean square error Bayesian estimator. However, as it is shown, in practical conditions only few thresholds are necessary.

Description: This paper considers the detection of a distributed target in a partial observation scenario. A distributed target model is usually adopted when the target size is larger than the range bin, for example, in some high-resolution radars. Based on the distributed target model, joint processing of several consecutive range bins can be adopted to achieve performance improvement with respect to processing just one range bin. In applications in complex electromagnetic environments, the radars may miss some of their observations, a phenomenon that usually caused by interference, spectrum sharing, and so on. This partial observation problem leads to degradation of the estimation accuracy for the disturbance (clutter plus noise) covariance matrix and target amplitude vector, which results in decline of the target detection performance. In this paper, a scheme is proposed by using the low-rank priori knowledge of clutter covariance matrix to estimate the detector's unknown parameters. Specifically, the target amplitude vector is obtained by maximizing the likelihood function, and the disturbance covariance matrix is reconstructed by solving an optimization that considers both the likelihood maximization and low-rank property of the clutter covariance matrix. The simulation results indicate that this algorithm improves the estimation accuracy, and achieves a better detection performance in the partial observation scenarios.

Description: Physical layer security is an emerging technique to protect the wireless communications in the Internet of Things (IoT). Motivated by the fact that a single IoT terminal usually occupies a very small fraction of feedback resources, we propose a novel secure transmission design with feedback compression to improve the feedback resources utilization for secure communications. Specifically, we first introduce a multiperiod one-feedback (MPOF) scheme to exploit the channel temporal correlation existing in the IoT scenarios, making the IoT terminal convey its channel knowledge to the central controller in a more efficient manner. Under this MPOF scheme, we then put forward a virtual quantizer model and design a generalized fixed-rate secure on–off transmission scheme, where the central controller adaptively adjusts the transmission parameters in one feedback interval. By averaging the total secrecy throughput of one feedback interval over all the coherence periods thereof, we further characterize the secrecy throughput of our proposed transmission scheme and facilitate the joint optimization design of the feedback interval length, the wiretap codes, and the power allocation ratios. To handle this nonconvex problem, we develop an efficient approach involving the block coordinate descent algorithm and the 1-D search method. Numerical results show that when the channel temporal correlation is high, our proposed secure transmission design achieves a significantly higher secrecy throughput than the conventional design constrained by the same amount of feedback resources.

Description: Chromatic derivatives are special, numerically robust differential operators that preserve spectral features of a signal; the associated chromatic approximations accurately capture local features of a signal. In the first part of this paper, entitled “Chromatic Derivatives and Approximations in Practice–Part I: A General Framework,” we have derived a collection of formulas and theorems which we use in this paper to demonstrate practical applications of chromatic derivatives and approximations. We present four case studies: a highly accurate (better than 170 dB) reconstruction of a signal from its nonuniformly spaced samples; a highly accurate method for obtaining timing information, such as timing of the zeros of a signal as well as timing of the zeros of its first derivative; a method of reconstruction of a sampled speech signal of 64 000 samples using such timing information only, with a reconstruction error of only about 1% of the rms of the original signal; and finally, a denoising algorithm that significantly outperforms the well-known Cadzow's denoising algorithm. The main purpose of these case studies is to illustrate the potential of chromatic derivatives and expansions and motivate DSP engineers to find applications of these novel concepts in their own practice.

Description: Quaternion adaptive filters have been widely used for the processing of three-dimensional (3-D) and 4-D phenomena, but complete analysis of their performance is still lacking, partly due to the cumbersomeness of multivariate quaternion analysis. This causes difficulties in both understanding their behavior and designing optimal filters. Based on a thorough exploration of the augmented statistics of quaternion random vectors, this paper extends an analysis framework for real-valued adaptive filters to the mean and mean square convergence analyses of general quaternion adaptive filters in nonstationary environments. The extension is nontrivial, considering the noncommutative quaternion algebra, only recently resolved issues with quaternion gradient, and the multidimensional augmented quaternion statistics. Also, for rigor, in order to model a nonstationary environment, the system weights are assumed to vary according to a first-order random-walk model. Transient and steady-state performance of a general class of quaternion adaptive filters is provided by exploiting the augmented quaternion statistics. An innovative quaternion decorrelation technique allows us to develop intuitive closed-form expressions for the performance of quaternion least mean square (QLMS) filters with Gaussian inputs, which provide new insights into the relationship between the filter behavior and the complete second-order statistics of the input signal, that is, quaternion noncircularity. The closed-form expressions for the performance of strictly linear, semiwidely linear, and widely linear QLMS filters are investigated in detail, while numerical simulations for the three classes of QLMS filters with correlated Gaussian inputs support the theoretical analysis.

Description: Compressive sensing is used to recover a sparse signal from linear measurements. Without any prior support information (PSI), least absolute shrinkage and selection operator (LASSO) is a useful method for sparse recovery. In some settings, a statistical prior about the support of the sparse signal may be provided. It is critical to optimally incorporate such statistical PSI to enhance the recovery performance. We propose a weighted LASSO algorithm to fully exploit the statistical PSI and optimize the recovery performance. In the proposed algorithm, we exploit the most general statistical PSI model, a multilevel PSI, and incorporate it into the LASSO using a weighted $l_{1}$ norm penalty function. An optimal weight policy is proposed to minimize the asymptotic normalized squared error (aNSE). We also derive the closed-form accurate expression for the minimum aNSE and characterize the minimum number of measurements required to achieve stable recovery. Based on this, we discuss the impact of PSI quality on the aNSE performance of the proposed algorithm. Both theoretical analysis and simulations show the performance advantages of our proposed solution over various baselines.

Description: The deluge of networked data motivates the development of algorithms for computation- and communication-efficient information processing. In this context, three data-adaptive censoring strategies are introduced to considerably reduce the computation and communication overhead of decentralized recursive least-squares solvers. The first relies on alternating minimization and the stochastic Newton iteration to minimize a network-wide cost, which discards observations with small innovations. In the resultant algorithm, each node performs local data-adaptive censoring to reduce computations while exchanging its local estimate with neighbors so as to consent on a network-wide solution. The communication cost is further reduced by the second strategy, which prevents a node from transmitting its local estimate to neighbors when the innovation it induces to incoming data is minimal. In the third strategy, not only transmitting, but also receiving estimates from neighbors is prohibited when data-adaptive censoring is in effect. For all strategies, a simple criterion is provided for selecting the threshold of innovation to reach a prescribed average data reduction. The novel censoring-based (C)D-RLS algorithms are proved convergent to the optimal argument in the mean-root deviation sense. Numerical experiments validate the effectiveness of the proposed algorithms in reducing computation and communication overhead.

Description: Accurately monitoring the system's operating point is central to the reliable and economic operation of an autonomous energy grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis amounts to solving a set of noise-free power flow equations, and is cast as a special case of PSSE. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel feasible point pursuit (FPP)-based solvers for power flow analysis and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming reformulation of the weighted least-squares (WLS). Relative to the prior art, the developed solvers offer superior numerical performance at the cost of higher computational complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cramér-Rao lower bound is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss–Newton iterations and SDR approaches.

Description: We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS), which is a newly proposed concept beyond massive multi-input multi-output (MIMO). In a first step, we derive Fisher-information matrix (FIM) and Cramér–Rao lower bound (CRLB) in closed form for positioning a terminal located perpendicular to the center of the LIS, whose location we refer to as being on the central perpendicular line (CPL) of the LIS. For a terminal that is not on the CPL, closed-form expressions of the CRLB seem out of reach, and we alternatively find approximations that are shown to be accurate. Under mild conditions, we show that the CRLB for all three Cartesian dimensions ( $x$ , $y$ , and $z$ ) decreases quadratically in the surface area of the LIS. In a second step, we analyze the CRLB for positioning when there is an unknown phase $varphi$ presented in the analog circuits of the LIS. We then show that the CRLBs are dramatically degraded for all three dimensions and decrease in the third order of the surface area. Moreover, with an infinitely large LIS, the CRLB for the $z$ -dimension with an unknown $varphi$ is 6 dB higher than the case without phase uncertainty, and the CRLB for estimating $varphi$ converges to a constant that is independent of the wavelength $lambda$ . At last, we extensively discuss the impact of ce- tralized and distributed deployments of LIS, and show that a distributed deployment of LIS can enlarge the coverage and improve the overall positioning performance.

Description: In an Internet of things network, multiple sensors send information to a fusion center for it to infer a public hypothesis of interest. However, the same sensor information may be used by the fusion center to make inferences of a private nature that the sensors wish to protect. To model this, we adopt a decentralized hypothesis testing framework with binary public and private hypotheses. Each sensor makes a private observation and utilizes a local sensor decision rule or privacy mapping to summarize that observation independently of the other sensors. The local decision made by a sensor is then sent to the fusion center. Without assuming knowledge of the joint distribution of the sensor observations and hypotheses, we adopt a nonparametric learning approach to design local privacy mappings. We introduce the concept of an empirical normalized risk, which provides a theoretical guarantee for the network to achieve information privacy for the private hypothesis with high probability when the number of training samples is large. We develop iterative optimization algorithms to determine an appropriate privacy threshold and the best sensor privacy mappings, and show that they converge. Finally, we extend our approach to the case of a private multiple hypothesis. Numerical results on both synthetic and real data sets suggest that our proposed approach yields low error rates for inferring the public hypothesis, but high error rates for detecting the private hypothesis.

Description: Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson–Lindenstrauss (JL) lemma and restricted isometry property (RIP) admit the use of random projection to reduce the dimension while keeping the Euclidean distance, which leads to the boom of compressed sensing and the field of sparsity related signal processing. Recently, successful applications of sparse models in computer vision and machine learning have increasingly hinted that the underlying structure of high dimensional data looks more like a union of subspaces. In this paper, motivated by JL lemma and an emerging field of compressed subspace clustering, we study for the first time the RIP of Gaussian random matrices for the compression of two subspaces based on the generalized projection $F$ -norm distance. We theoretically prove that with high probability the affinity or distance between two projected subspaces are concentrated around their estimates. When the ambient dimension after projection is sufficiently large, the affinity and distance between two subspaces almost remain unchanged after random projection. Numerical experiments verify the theoretical work.

Description: The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successfully classify nonlinearly separable data in a multitude of settings. In spite of their high clustering accuracy, SC methods incur prohibitively high computational complexity when processing large volumes of high-dimensional data. Inspired by random sketching approaches for dimensionality reduction, the present paper introduces a randomized scheme for SC, termed Sketch-SC, tailored for large volumes of high-dimensional data. Sketch-SC accelerates the computationally heavy parts of state-of-the-art SC approaches by compressing the data matrix across both dimensions using random projections, thus enabling fast and accurate large-scale SC. Performance analysis as well as extensive numerical tests on real data corroborate the potential of Sketch-SC and its competitive performance relative to state-of-the-art scalable SC approaches.

Description: 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.

Description: This paper considers the massive connectivity application in which a large number of devices communicate with a base-station (BS) in a sporadic fashion. Device activity detection and channel estimation are central problems in such a scenario. Due to the large number of potential devices, the devices need to be assigned non-orthogonal signature sequences. The main objective of this paper is to show that by using random signature sequences and by exploiting sparsity in the user activity pattern, the joint user detection and channel estimation problem can be formulated as a compressed sensing single measurement vector (SMV) or multiple measurement vector (MMV) problem depending on whether the BS has a single antenna or multiple antennas and efficiently solved using an approximate message passing (AMP) algorithm. This paper proposes an AMP algorithm design that exploits the statistics of the wireless channel and provides an analytical characterization of the probabilities of false alarm and missed detection via state evolution. We consider two cases depending on whether or not the large-scale component of the channel fading is known at the BS and design the minimum mean squared error denoiser for AMP according to the channel statistics. Simulation results demonstrate the substantial advantage of exploiting the channel statistics in AMP design; however, knowing the large-scale fading component does not appear to offer tangible benefits. For the multiple-antenna case, we employ two different AMP algorithms, namely the AMP with vector denoiser and the parallel AMP-MMV, and quantify the benefit of deploying multiple antennas.

Description: Downlink channel estimation is an important task in any wireless communication system, and 5G massive multiple-input multiple-output in particular—because the receiver must estimate and feed back to the transmitter a high-dimensional multiple-input single-output (MISO) vector channel for each receiving element. This is a serious burden in terms of mobile computation and power, as well as uplink communication overhead. The starting point of this paper is that all existing and emerging wireless communication systems provide basic Received Signal Strength (RSS) / Channel Quality Indicator (CQI) feedback to compensate for temporal channel variations. Is it possible to estimate and track the vector MISO channel from RSS/CQI feedback alone? This paper shows that the answer is affirmative, if one employs time-varying beamforming and phase modulation together with phase retrieval ideas from optics and crystallography. Three efficient algorithms that cover different model assumptions are proposed to track the vector MISO channel on the transmitter's side using only RSS/CQI feedback. Numerical simulation results under various settings validate the efficacy of the proposed algorithms in tracking a slowly time-varying vector MISO channel. Interestingly, this is the first application of phase retrieval where assuming independent and identically distributed Gaussian measurement vectors can be practically justified.

Description: Self-interference  is the main obstacle to overcome in order to enable a wireless device to simultaneously transmit and receive in overlapped frequency bands. There is much interest to suppress this interference employing compact and efficient cancelers, which operate in the digital domain, extending this way the benefits of in-band full-duplex to innumerable applications. However, this is not an easy task since the desired signal results hidden in quantization noise during analog-to-digital conversion because of the tremendous power asymmetry between the self-interference and desired signal. This paper proposes an alternative receiver structure in which the received signal is sampled at the zero-amplitude instants of the interference. Our analysis demonstrates that the resulting sampling process preserves the information conveyed in the desired signal and that demodulation is possible. The performance of this novel full-duplex receiver is evaluated using simulations, proving that this sampling strategy enables all digital self-interference cancelation.

Description: In this paper, we consider the performance of sampling associated with the linear canonical transform (LCT), which generalizes a large number of classical integral transforms and fundamental operations linked to signal processing and optics. First, we revisit sampling approximation in the LCT domain to introduce a generalized approximation operator. Then, we derive an exact closed-form expression for the integrated squared error that occurs when a signal is approximated by a basis of shifted, scaled, and chirp-modulated versions of a generating function in the LCT domain. Several basic properties of the approximation error are presented. The derived results can be applied to a wide variety of sampling approximation schemes in the LCT domain. Finally, experimental examples are given to illustrate the theoretical derivations.

Description: Modal analysis is the process of estimating a system's modal parameters, such as its natural frequencies and mode shapes. One application of modal analysis is in structural health monitoring (SHM), where a network of sensors may be used to collect vibration data from a physical structure, such as a building or bridge. There is a growing interest in developing automated techniques for SHM based on data collected in a wireless sensor network. In order to conserve power and extend battery life, however, it is desirable to minimize the amount of data that must be collected and transmitted in such a sensor network. In this paper, we highlight the fact that modal analysis can be formulated as an atomic norm minimization (ANM) problem, which can be solved efficiently and in some cases recover perfectly a structure's mode shapes and frequencies. We survey a broad class of sampling and compression strategies that one might consider in a physical sensor network, and we provide bounds on the sample complexity of these compressive schemes in order to recover a structure's mode shapes and frequencies via ANM. A main contribution of our paper is to establish a bound on the sample complexity of modal analysis with random temporal compression, and in this scenario we prove that the required number of samples per sensor can actually decrease as the number of sensors increases. We also extend an atomic norm denoising problem to the multiple measurement vector setting in the case of uniform sampling.

Description: This paper deals with adaptive radar detection of a point-like target in a homogeneous environment characterized by the presence of clutter, jamming, and radar internal noise. At the design stage, two training datasets, whose gathering is carefully motivated in the paper, are considered to get receiver adaptation. Hence, the maximum likelihood estimator of the interference covariance matrix for the cell under test is computed exploiting both the available secondary sets. This estimate is then used to build two adaptive decision rules based on the two-step generalized likelihood ratio test and Rao test criteria. Remarkably, they are not limited by the conventional constraint on the cardinality of the classic training dataset. At the analysis stage, the detection performances of the newly proposed detectors are compared with those of the analogous conventional counterparts and the interplay among the different parameters of the problem is thoroughly studied.

Description: This paper presents novel adaptive schemes and the pertinent analysis for estimation of the number of targets, their associated radar cross section (RCS) values and Doppler velocities in monostatic MIMO radar systems. These schemes are based on the fast block least mean squares (FBLMS) and fast block recursive least squares (FBRLS) algorithms considering both stationary as well as mobile targets and/or radar platform. For the stationary scenario, schemes are proposed for estimation of RCS coefficients, target number and their angle, range locations. In addition, a procedure is also developed to obtain the 2D-image of the MIMO radar scene in angle-range dimensions. Analysis is presented for the first and second order moments of the observation as well as estimation errors resulting from the proposed FBLMS, FBRLS techniques, along with their global convergence. Both the proposed schemes are shown to converge globally to the optimal Wiener filter, which is lacking in existing schemes. Further, a Bayesian information criterion based selection rule is employed to enhance the estimation and imaging performance of the proposed adaptive frameworks. Cramer-Rao bounds are derived to characterize the mean squared error of the estimated RCS coefficients for stationary scenarios and also for joint RCS, Doppler velocity estimation in mobile MIMO radar scenarios. The FBLMS and FBRLS schemes are shown to have significantly lower computational complexities in comparison to existing MIMO radar schemes. Simulation results demonstrate the improved performance of the proposed schemes and also validate the derived analytical expressions.

Description: Massive MIMO is a variant of multiuser MIMO, in which the number of antennas $M$ at the base-station is very large. It has been observed that in many realistic propagation scenarios, although the user channel vectors have a very high-dim $M$ , they lie on low-dim subspaces because of their limited angular spread (spatial correlation). This low-dim subspace structure remains stable across several coherence blocks and can be exploited to improve the system performance. In a recent work, we addressed this problem and proposed a very effective novel algorithm referred to as Approximate Maximum-Likelihood (AML), which was formulated as a semi-definite program (SDP). In this paper, we address two problems left open in our previous work, namely, computational complexity and tracking. We propose a new algorithm that is reminiscent of Multiple Measurement Vectors (MMV) problem in Compressed Sensing and prove that it is equivalent to the AML Algorithm for sufficiently dense angular grids. It has also a very low computational complexity and is able to track the sharp transitions in the channel statistics very quickly. We provide numerical simulations to assess the estimation/tracking performance of our proposed algorithm, with a particular emphasis on situations where a direct implementation of the SDP is infeasible in real-time. Our proposed algorithm is of independent interest in applications other than massive MIMO. We provide numerical simulations to compare the performance of our algorithm with that of other related subspace estimation algorithms in the literature.

Description: This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order quadratic-amplitude modulation (QAM) constellations. Four new iterative batch, BSS algorithms are presented dealing with the multimodulus (MM) and alphabet matched (AM) criteria. For the optimization of these cost functions, iterative methods of Givens and hyperbolic rotations are used. A prewhitening operation is also utilized to reduce the complexity of design problem. It is noticed that the designed algorithms using Givens rotations give satisfactory performance only for a large number of samples. However, for a small number of samples, the algorithms designed by combining both Givens and hyperbolic rotations compensate for the ill-whitening that occurs in this case and thus improves the performance. Two algorithms dealing with the MM criterion are presented for moderate-order QAM signals such as 16-QAM. The other two dealing with the AM criterion are presented for high-order QAM signals. These methods are finally compared with the state-of-the-art batch BSS algorithms in terms of signal-to-interference and noise ratio, symbol error rate, and convergence rate. Simulation results show that the proposed methods outperform the contemporary batch BSS algorithms.

Description: We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources in a distributed setting. In contrast, we propose to approximate the solution as a fixed-size vector (of larger dimension than the input space) using the previously introduced framework of random Fourier features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.

Description: We consider the problem of accelerating distributed optimization in multi-agent networks by sequentially adding edges. Specifically, we extend the distributed dual averaging (DDA) subgradient algorithm to evolving networks of growing connectivity and analyze the corresponding improvement in convergence rate. It is known that the convergence rate of DDA is influenced by the algebraic connectivity of the underlying network, where better connectivity leads to faster convergence. However, the impact of the network topology design on the convergence rate of DDA has not been fully understood. In this paper, we begin by designing network topologies via edge selection and scheduling in an offline manner. For edge selection, we determine the best set of candidate edges that achieves the optimal tradeoff between the growth of network connectivity and the usage of network resources. The dynamics of network evolution is then incurred by edge scheduling. Furthermore, we provide a tractable approach to analyze the improvement in the convergence rate of DDA induced by the growth of network connectivity. Our analysis reveals the connection between network topology design and the convergence rate of DDA, and provides quantitative evaluation of DDA acceleration for distributed optimization that is absent in the existing analysis. Lastly, numerical experiments show that DDA can be significantly accelerated using a sequence of well-designed networks, and our theoretical predictions are well matched to its empirical convergence behavior.

Description: In this paper, we tackle the problem of hidden community detection. We consider belief propagation (BP) applied to the problem of detecting a hidden Erdős-Rényi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of side-information. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when a so-called effective signal-to-noise ratio parameter falls below a threshold. In contrast, in the presence of nontrivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of a suitably defined phase-transition parameter. We validate our results on synthetic datasets and a few real world networks.

Description: Offset-quadratic-amplitude-modulation-based filterbank multicarrier (FBMC-OQAM) has been shown to be a promising alternative to cyclic prefix-orthogonal frequency division multiplexing. More recently, the use of FBMC-OQAM has been proposed in combination with massive MIMO communications. In this context, it is interesting to study the overall effect of massive MIMO on the FBMC-OQAM intrinsic interference and its interaction with channel frequency selectivity. In this paper, the performance of an FBMC-OQAM uplink massive MIMO system is theoretically characterized in terms of the output mean squared error (MSE) of the estimated transmitted symbols and for three types of linear receivers, namely, zero forcer, linear minimum mean squared error, and matched filter. Using random matrix theory, the output MSE of these receivers is asymptotically characterized as the number of base station antennas $N$ and the number of users $K$ grow large, while keeping a finite ratio $N/K$ . The obtained expressions allow to draw many conclusions, some of which were already noticed in the literature but not yet theoretically proven. First, the MSE becomes uniform across the frequency band as a result of the channel hardening effect. Second, it is shown that a good synchronization of the users is crucial in a massive MIMO scenario. Finally, if the users are well synchronized, the different terms that compose the MSE, such as noise, interuser interference, and the distortion caused by the channel frequency selectivity, become negligible for large values of the ratio $N/K$ . This effect was previously referred to as “self-equalization” in the literature.

Description: Bilinear and Volterra models are important when dealing with nonlinear systems which arise in several signal processing applications. The former can approximate a large class of systems affine in the input with relatively low parametric complexity. Such an approximate bilinear model can be derived by means of Carleman bilinearization (CB). Then, a Volterra model can be computed from it, having the advantage of being linear in the parameters, but often involving a large number of them. In this paper, we develop efficient routines for CB and for computing the Volterra kernels of a bilinear system. We argue that they are useful for studying a class of systems for which a reference physical model is known. In particular, the so-derived kernels allow assessing the suitability of a Volterra filter and of other alternatives for modeling the system of interest. Techniques exploiting sparsity and low rank of involved matrices are proposed for alleviating computing cost. Several examples are given along the paper to illustrate their use, based on existing physical models of loudspeakers.

Description: In many applications, sensors that map the positions of objects in unknown environments are installed on dynamic platforms. As measurements are relative to the observer's sensors, scene mapping requires accurate knowledge of the observer state. However, in practice, observer reports are subject to positioning errors. Simultaneous localization and mapping addresses the joint estimation problem of observer localization and scene mapping. State-of-the-art approaches typically use visual or optical sensors and therefore rely on static beacons in the environment to anchor the observer estimate. However, many applications involving sensors that are not conventionally used for Simultaneous Localization and Mapping (SLAM) are affected by highly dynamic scenes, such that the static world assumption is invalid. This paper proposes a novel approach for dynamic scenes, called GEneralized Motion (GEM) SLAM. Based on probability hypothesis density filters, the proposed approach probabilistically anchors the observer state by fusing observer information inferred from the scene with reports of the observer motion. This paper derives the general, theoretical framework for GEM-SLAM, and shows that it generalizes existing Probability Hypothesis Density (PHD)-based SLAM algorithms. Simulations for a model-specific realization using range-bearing sensors and multiple moving objects highlight that GEM-SLAM achieves significant improvements over three benchmark algorithms.

Description: The design of wireless information and power transfer (WIPT) has so far relied on an oversimplified and inaccurate linear model of the energy harvester. In this paper, we depart from this linear model and design WIPT considering the rectifier nonlinearity. We develop a tractable model of the rectifier nonlinearity that is flexible enough to cope with general multicarrier modulated input waveforms. Leveraging that model, we motivate and introduce a novel WIPT architecture relying on the superposition of multicarrier unmodulated and modulated waveforms at the transmitter. The superposed WIPT waveforms are optimized as a function of the channel state information so as to characterize the rate-energy region of the whole system. Analysis and numerical results illustrate the performance of the derived waveforms and WIPT architecture and highlight that nonlinearity radically changes the design of WIPT. We make key and refreshing observations. First, analysis (confirmed by circuit simulations) shows that modulated and unmodulated waveforms are not equally suitable for wireless power delivery, namely, modulation being beneficial in single-carrier transmissions but detrimental in multicarrier transmissions. Second, a multicarrier unmodulated waveform (superposed to a multicarrier modulated waveform) is useful to enlarge the rate-energy region of WIPT. Third, a combination of power splitting and time sharing is in general the best strategy. Fourth, a nonzero mean Gaussian input distribution outperforms the conventional capacity-achieving zero-mean Gaussian input distribution in multicarrier transmissions. Fifth, the rectifier nonlinearity is beneficial to system performance and is essential to efficient WIPT design.

Description: This paper proposes a new configuration of acoustic sensors—the collocation of three cardioid sensors in perpendicular orientation, in order to increase the mainlobe-to-sidelobe height ratio (possibly to $infty$ ). This paper will analyze such a proposed triad's “spatial matched filter” beam-pattern that is independent of the frequency/spectrum of the incident signals. Specifically, this paper will analytically derive the mainlobe's pointing error in azimuth-elevation, the mainlobe's two-dimensional beam “width,” the necessary and sufficient conditions for a sidelobe to exist, the mainlobe-to-sidelobe height ratio, and the array gain. These above characteristics depend on the cardioids’ “cardiodicity parameter” and on the beam's nominal “look direction.”

Description: We revisit the stochastic limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. By proposing a new coordinate transformation framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to previous works. In addition, we propose several practical acceleration strategies to speed up the empirical performance of such algorithms. We also provide theoretical analyses for most of the strategies. Experiments on large-scale logistic and ridge regression problems demonstrate that our proposed strategies yield significant improvements vis-à-vis competing state-of-the-art algorithms.

Description: Matrix completion refers to recovering a low-rank matrix from only a subset of its possibly noisy entries, and has a variety of important applications because many real-world signals can be modeled by a $n_1 times n_2$ matrix with rank $r ll min (n_1, n_2)$ . Most existing techniques for matrix completion assume Gaussian noise and, thus, they are not robust to outliers. In this paper, we devise two algorithms for robust matrix completion based on low-rank matrix factorization and $ell _p$ -norm minimization of the fitting error with $0 〈 p 〈 2$ . The first method tackles the low-rank matrix factorization with missing data by iteratively solving $(n_1+n_2)$ linear $ell _p$ -regression problems, whereas the second applies the alternating direction method of multipliers (ADMM) in the $ell _p$ -space. At each iteration of the ADMM, it requires performing a least squares (LS) matrix factorization and calculating the proximity operator of the $p$ th power of the $ell _p$ -norm. The LS factorization is efficiently solved using linear LS regression while the proximity operator has closed-form solution for $p=1$ or can be obtained by root finding of a scalar nonlinear equation for other values of $- $ . The two proposed algorithms have comparable recovery capability and computational complexity of $mathcal{O}(K|Omega |r^2)$ , where $|Omega |$ is the number of observed entries and $K$ is a fixed constant of several hundreds to thousands and dimension independent. It is demonstrated that they are superior to the singular value thresholding, singular value projection, and alternating projection schemes in terms of computational simplicity, statistical accuracy, and outlier-robustness.

Description: We develop a broadband channel estimation algorithm for millimeter wave (mmWave) multiple input multiple output (MIMO) systems with few-bit analog-to-digital converters (ADCs). Our methodology exploits the joint sparsity of the mmWave MIMO channel in the angle and delay domains. We formulate the estimation problem as a noisy quantized compressed-sensing problem and solve it using efficient approximate message passing (AMP) algorithms. In particular, we model the angle-delay coefficients using a Bernoulli–Gaussian-mixture distribution with unknown parameters and use the expectation-maximization forms of the generalized AMP and vector AMP algorithms to simultaneously learn the distributional parameters and compute approximately minimum mean-squared error (MSE) estimates of the channel coefficients. We design a training sequence that allows fast, fast Fourier transform based implementation of these algorithms while minimizing peak-to-average power ratio at the transmitter, making our methods scale efficiently to large numbers of antenna elements and delays. We present the results of a detailed simulation study that compares our algorithms to several benchmarks. Our study investigates the effect of SNR, training length, training type, ADC resolution, and runtime on channel estimation MSE, mutual information, and achievable rate. It shows that, in a mmWave MIMO system, the methods we propose to exploit joint angle-delay sparsity allow 1-bit ADCs to perform comparably to infinite-bit ADCs at low SNR, and 4-bit ADCs to perform comparably to infinite-bit ADCs at medium SNR.

Description: Complementary sets of sequences (CSS) and complete complementary codes (CCC) have found numerous applications in wireless communications and radar sensing owing to their perfect aperiodic correlation properties. In this paper, we first present a new algorithm for generating polyphase CSS and CCC based on paraunitary (PU) matrices which uses equivalent forms of unimodular unitary matrices. Then, we propose a multiplier-free implementation of this generator based on multiplexers and read-only memories (ROMs). Our proposed algorithm generalizes the previous PU generator for complementary pairs by Budišin and Spasojević. Some previous algorithms for CSS and CCC can also be derived from our CCC generator as special cases. In addition, we give the enumeration formula and show that the number of generated sequences is significantly higher compared to previous works.

Description: We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

Description: We introduce a truly online anomaly detection algorithm that sequentially processes data to detect anomalies in time series. In anomaly detection, while the anomalous data are arbitrary, the normal data have similarities and generally conforms to a particular model. However, the particular model that generates the normal data is generally unknown (even nonstationary) and needs to be learned sequentially. Therefore, a two stage approach is needed, where in the first stage, we construct a probability density function to model the normal data in the time series. Then, in the second stage, we threshold the density estimation of the newly observed data to detect anomalies. We approach this problem from an information theoretic perspective and propose minimax optimal schemes for both stages to create an optimal anomaly detection algorithm in a strong deterministic sense. To this end, for the first stage, we introduce a completely online density estimation algorithm that is minimax optimal with respect to the log-loss and achieves Merhav's lower bound for general nonstationary exponential-family of distributions without any assumptions on the observation sequence. For the second stage, we propose a threshold selection scheme that is minimax optimal (with logarithmic performance bounds) against the best threshold chosen in hindsight with respect to the surrogate logistic loss. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art density estimation based anomaly detection algorithms in the literature.

Description: We present novel lower bounds on the mean square error (MSE) of the location estimation of an emitting source via a network where the sensors are deployed randomly. The sensor locations are modeled as a homogenous Poisson point process. In contrast to previous bounds that are a function of the specific locations of all the sensors, we present Cramér–Rao bound (CRB) type bounds on the expected mean square error; that is, we first derive the CRB on the MSE as a function of the sensors’ location, and then take expectation with respect to the distribution of the sensors’ location. Thus, these bounds are not a function of a particular sensor configuration, but rather of the sensor statistics. Hence, these novel bounds can be evaluated prior to sensor deployment and provide insights into design issues such as the necessary sensor density, the effect of the channel model, the effect of the signal power, and others. The derived bounds are simple to evaluate and provide a good prediction of the actual network performance. Numerical results show that the novel bounds give a good approximation even in other deployment scenarios such as a square or a triangular grid.

Description: In graph signal processing, filters arise from polynomials in shift matrices that respect the graph structure, such as the graph adjacency matrix or the graph Laplacian matrix. Hence, filter design for graph signal processing benefits from knowledge of the spectral decomposition of these matrices. Often, stochastic influences affect the network structure and, consequently, the shift matrix empirical spectral distribution. Although the joint distribution of the shift matrix eigenvalues is typically inaccessible, deterministic functions that asymptotically approximate the matrix empirical spectral distribution can be found for suitable random graph models using tools from random matrix theory. We employ this information regarding the density of eigenvalues to develop criteria for optimal graph filter design. In particular, we consider filter design for distributed average consensus and related problems, leading to improvements in short-term error minimization or in asymptotic convergence rate.

Description: Multiway datasets are widespread in signal processing and play an important role in blind signal separation, array processing, and biomedical signal processing, among others. One key strength of tensors is that their decompositions are unique under mild conditions, which allows the recovery of features or source signals. In several applications, such as classification, we wish to compare factor matrices of the decompositions. Though this is possible by first computing the tensor decompositions and subsequently comparing the factors, these decompositions are often computationally expensive. In this paper, we present a similarity method that indicates whether the factors in two modes are essentially equal without explicitly computing them. Essential equality conditions, which ensure the theoretical validity of our approach, are provided for various underlying tensor decompositions. The developed algorithm provides a computationally efficient way to compare factors. The method is illustrated in a context of emitter movement detection and fluorescence data analysis.

Description: This paper presents a new scheme based on Weight vector ORthogonal Decomposition (WORD) to control the array response at a given direction and a novel WORD-based approach to pattern synthesis for arbitrary arrays. The central concept of the proposed methods stems from the adaptive array theory. More precisely, it is found that the inverse of the noise-plus-interference covariance matrix in adaptive beamforming can be regarded as a linear combination of two orthogonal projection matrices, and, accordingly, the optimal weight vector is a linear combination of two orthogonal vectors. With such an observation, the WORD scheme is developed to design the desired weight vector. It is shown that the array response at a given direction can be precisely adjusted to an arbitrary level, by simply determining appropriate combination coefficients for those two orthogonal vectors. Furthermore, a closed-form expression of the weight vector can be achieved by introducing a new cost function that measures pattern variation. By employing the WORD scheme successively, a novel approach to pattern synthesis for arbitrary arrays is devised. At each implementation step of this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. As such, both the sidelobe and mainlobe regions can be flexibly synthesized. Numerical examples are provided to demonstrate the effectiveness and flexibility of the WORD scheme in array response control at a single direction as well as pattern synthesis.

Description: We investigate an alternative solution method to the joint signal-beamformer optimization problem considered in a recent publication devoted to this topic. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and clutter power under a minimum variance distortionless response constraint, is generally nonconvex and we provide insight into the nature of the nonconvexity. Second, we employ the theory of biquadratic optimization and semidefinite relaxations to produce a relaxed version of the problem, which we show to be convex . The optimality conditions of this relaxed problem are examined and a variety of potential solutions are found, both analytically and numerically. These solutions are then compared to existing alternating minimization schemes.

Description: Antenna selection is a multiple-input multiple-output (MIMO) technology, which uses radio frequency (RF) switches to select a good subset of antennas. Antenna selection can alleviate the requirement on the number of RF transceivers, thus being attractive for massive MIMO systems. In massive MIMO antenna selection systems, RF switching architectures need to be carefully considered. In this paper, we examine two switching architectures, i.e., full-array and sub-array. By assuming independent and identically distributed Rayleigh flat fading channels, we use asymptotic theory on order statistics to derive the asymptotic upper capacity bounds of massive MIMO channels with antenna selection for the both switching architectures in the large-scale limit. We also use the derived bounds to further derive the upper bounds of the ergodic achievable spectral efficiency considering the channel state information (CSI) acquisition. It is also showed that the ergodic capacity of sub-array antenna selection system scales no faster than double logarithmic rate. In addition, optimal antenna selection algorithms based on branch-and-bound are proposed for both switching architectures. Our results show that the derived asymptotic bounds are effective and also apply to the finite-dimensional MIMO. The CSI acquisition is one of the main limits for the massive MIMO antenna selection systems in the time-variant channels. The proposed optimal antenna selection algorithms are much faster than the exhaustive-search-based antenna selection, e.g., 1000 × speedup observed in the large-scale system. Interestingly, the full-array and sub-array systems have very close performance, which is validated by their exact capacities and their close upper bounds on capacity.

Description: The columnwise Khatri–Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often contingent on proving the restricted isometry property (RIP) of a certain system matrix expressible as a Khatri–Rao product of two matrices. In this paper, we analyze the RIP of a generic columnwise Khatri–Rao product matrix by deriving two upper bounds for its $k$ th order restricted isometry constant ( $k$ -RIC) for different values of $k$ . The first RIC bound is computed in terms of the individual RICs of the real-valued input matrices participating in the Khatri–Rao product. The second RIC bound is probabilistic and is specified in terms of the input matrix dimensions. We show that the Khatri–Rao product of a pair of $m times n$ sized random matrices comprising independent and identically distributed sub-Gaussian entries satisfies $k$ -RIP with arbitrarily high probability, provided $m$ exceeds $mathcal {O}(sqrt{k}log ^{3/2}{n})$ . This is a substantially milder condition compared to $mathcal {O}(klog {n})$ rows needed to guarantee $k$ -RIP of the input sub-Gaussian random matrices participating in the Khat- i–Rao product. Our RIC bounds confirm that the Khatri–Rao product exhibits stronger restricted isometry compared to its constituent matrices for the same RIP order. The proposed RIC bounds are potentially useful in obtaining improved performance guarantees in several sparse signal recovery and tensor decomposition problems.

Description: In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the rows of the measurement matrix) is not known a priori . We consider a special case of unlabeled sensing referred to as unlabeled ordered sampling (UOS) where the ordering of the measurements is preserved. We identify a natural duality between this problem and classical compressed sensing (CS), where we show that the unknown support (location of nonzero elements) of a sparse signal in CS corresponds to the unknown indices of the measurements in UOS. While in CS, it is possible to recover a sparse signal from an underdetermined set of linear equations (less equations than the signal dimension), successful recovery in UOS requires taking more samples than the dimension of the signal. Motivated by this duality, we develop a restricted isometry property (RIP) similar to that in CS. We also design a low-complexity alternating minimization algorithm that achieves a stable signal recovery under the established RIP. We analyze our proposed algorithm for different signal dimensions and number of measurements theoretically and investigate its performance empirically via numerical simulations. The results are reminiscent of a phase transition occurring in CS.

Description: Non-orthogonal multiple access (NOMA) is one of the key techniques to address the high spectral efficiency and massive connectivity requirements for the fifth generation (5G) wireless networks. To efficiently realize NOMA, we propose a framework combining the binary polar coding and the NOMA transmission, which adequately utilizes the reliability distinctions among users. In this polar-coded NOMA (PC-NOMA) system, the NOMA transmission is recognized from the novel perspective of channel polarization. Combing the binary polar coding and signal modulation, the original NOMA channel is decomposed into multiple bit polarized channels by using a three-stage channel transform, that is, user $rightarrow$ signal $rightarrow$ bit partitions. Specifically, for the first stage channel transform, we design two schemes, namely the sequential user partition and the parallel user partition (PUP). For the SUP based PC-NOMA system, a “worst-goes-first” strategy is proposed to determine the user partition order which improves the system performance by the enhanced polarization effect among the user synthesized channels. Also, its performance is analyzed by using the channel polarization principle. In the receiver, a joint successive cancellation detection and decoding scheme is developed. For the PUP based PC-NOMA system, a parallel detection scheme is exploited to reduce the processing latency. Furthermore, a round-robin user scheduling is given for the above two PC-NOMA systems, which ensures the user fairness over multiple data blocks. The block error ratio and throughput performances indicate that the proposed PC-NOMA systems obviously outperform the state-of-the-art turbo-coded NOMA systems due to the advantages of joint design between the polar coding and the NOMA transmission.

Description: Minimizing the expected mean squared error is one of the fundamental metrics applied to adaptive waveform design for active sensing. Previously, only cost functions corresponding to a lower bound on the expected mean squared error have been expressed for optimization. In this paper, we express an exact cost function to optimize for minimum mean squared error adaptive waveform design (MMSE-AWD). This is expressed in a general form which can be applied to nonlinear systems. Additionally, we provide a general example for how this method of MMSE-AWD can be applied to a system that estimates the state using a particle filter (PF). We make the case that there is a compelling reason to choose to use the PF (as opposed to alternatives such as the unscented Kalman filter and extended Kalman filter), as our MMSE-AWD implementation can reuse the particles and particle weightings from the PF, simplifying the overall computation. Finally, we provide a numerical example, based on a simplified multiple-input-multiple-output radar system, which demonstrates that our MMSE-AWD method outperforms a simple nonadaptive radar, whose beam-pattern has a uniform angular spread, and also an existing approximate MMSE-AWD method.

Description: This paper investigates the problem of the interference among multiple simultaneous transmissions in the downlink channel of a multiantenna wireless system. A symbol-level precoding scheme is considered, in order to exploit the multiuser interference and transform it into useful power at the receiver side, through a joint utilization of the data information and the channel state information. In this context, this paper presents novel strategies that exploit the potential of symbol-level precoding to control the per-antenna instantaneous transmit power. In particular, the power peaks among the transmitting antennas and the instantaneous power imbalances across the different transmitted streams are minimized. These objectives are particularly relevant with respect to the nonlinear amplitude and phase distortions induced by the per-antenna amplifiers, which are important sources of performance degradation in practical systems. More specifically, this paper proposes two different symbol-level precoding approaches. The first approach performs a weighted per-antenna power minimization, under quality-of-service constraints and under a lower bound constraint on the per-antenna transmit power. The second strategy performs a minimization of the spatial peak-to-average power ratio, evaluated among the transmitting antennas. Numerical results are presented in a comparative fashion to show the effectiveness of the proposed techniques, which outperform the state-of-the-art symbol-level precoding schemes in terms of spatial peak-to-average power ratio, spatial dynamic range, and symbol error rate over nonlinear channels.

Description: We address the problem of sampling and reconstruction of sparse signals with finite rate of innovation. We derive general conditions under which perfect reconstruction is possible for sampling kernels satisfying Strang-Fix conditions. Previous results on the subject consider two particular cases; when the kernel is able to reproduce (complex) exponentials, or when it has the polynomial reproduction property. In this paper, we extend such analysis to the case where both properties could be found in the sampling kernel and show that the former two situations can be regarded as special cases. As a result of our analysis, we provide general conditions under which perfect recovery in the noiseless case is possible. In practice, a given sampling kernel might not satisfy Strang-Fix conditions. When dealing with arbitrary sampling kernels, we propose a unified view for sampling and reconstruction in the frequency domain. Our formulation generalizes previous approaches and provides new insights for devising optimal reconstruction schemes. We also propose a novel algorithm for denoising treating the problem as a particular instance of structured low-rank approximation. Finally, we provide some numerical experiments and a comparison between different state-of-the-art methods showing the improved estimation performance of the proposed approach.

Description: Spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing non-stationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the window length and overlap size. In addition, it undermines the dynamics of the time series as the estimate associated to each window uses only the data within. Finally, the overlap between consecutive windows hinders a precise statistical assessment. In this paper, we address these shortcomings by explicitly modeling the spectral dynamics through integrating the multitaper method with state-space models in a Bayesian estimation framework. The underlying states pertaining to the eigenspectral quantities arising in multitaper analysis are estimated using instances of the expectation–maximization algorithm, and are used to construct spectrograms and their respective confidence intervals. We propose two spectral estimators that are robust to noise and are able to capture spectral dynamics at high spectrotemporal resolution. We provide theoretical analysis of the bias-variance trade-off, which establishes performance gains over the standard overlapping multitaper method. We apply our algorithms to synthetic data as well as real data from human EEG and electric network frequency recordings, the results of which validate our theoretical analysis.

Description: Widely linear (WL) receivers have the capability to perform single antenna interference cancellation (SAIC) of one rectilinear (R) or quasi-rectilinear (QR) co-channel interference (CCI), a function which is operational in global system for mobile communications (GSM) handsets in particular. Moreover, SAIC technology for QR signals is still required for voice services over adaptive multiuser channels on one slot (VAMOS) standard, a recent evolution of both GSM and enhanced data rates for GSM evolution (EDGE) standards, to mitigate legacy GSM CCI in particular. It is also required for filter bank multicarrier offset quadrature amplitude modulation (FBMC-OQAM) networks, which are candidate for 5G mobile networks, to mitigate intercarrier interference at reception for frequency selective propagation channels in particular. In this context, the purpose of this paper is twofold. The first one is to get more insights into the existing SAIC technology, and its extension to multiple antenna called multiple antenna interference cancellation (MAIC), by showing analytically that, contrary to what is accepted as true in the literature, SAIC/MAIC implemented from standard WL filtering may be less efficient for QR signals than for R ones. From this result, the second purpose of the paper is to propose and to analyze, for QR signals and frequency selective fading channels, an SAIC/MAIC enhancement based on a three-input WL frequency shift receiver, making QR signals always almost equivalent to R ones for WL filtering in the presence of CCI. The results of the paper, completely new, may contribute to develop elsewhere new powerful WL receivers for QR signals and for both VAMOS and FBMC-OQAM networks in particular.

Description: This paper studies binary hypothesis testing based on measurements from a set of sensors, a subset of which can be compromised by an attacker. The measurements from a compromised sensor can be manipulated arbitrarily by the adversary. The asymptotic exponential rate, with which the probability of error goes to zero, is adopted to indicate the detection performance of a detector. In practice, we expect the attack on sensors to be sporadic, and therefore the system may operate with all the sensors being benign for an extended period of time. This motivates us to consider the tradeoff between the detection performance of a detector, i.e., the probability of error, when the attacker is absent (defined as efficiency) and the worst case detection performance when the attacker is present (defined as security). We first provide the fundamental limits of this tradeoff, and then propose a detection strategy that achieves these limits. We then consider a special case, where there is no tradeoff between security and efficiency. In other words, our detection strategy can achieve the maximal efficiency and the maximal security simultaneously. Two extensions of the secure hypothesis testing problem are also studied and fundamental limits and achievability results are provided: first, a subset of sensors, namely “secure” sensors, are assumed to be equipped with better security countermeasures and hence are guaranteed to be benign; and second, detection performance with unknown number of compromised sensors. Numerical examples are given to illustrate the main results.

Description: The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desired tolerance. While the first algorithm is conceptually simpler and more efficient, it is not guaranteed to converge for objective functions that are not strictly convex. This shortcoming is overcome in the second algorithm, which uses an additional outer proximal iteration, and, which is proven to converge under mild assumptions. Two examples are given to demonstrate the theoretical usefulness of the optimality conditions as well as the high efficiency and accuracy of the proposed numerical algorithms.

Description: We study detection performance of the majority dominance rule in an $m$ -ary relay tree with node and link failures. The leaves of the tree represent $N$ identical and independent sensors, the root of the tree represents a fusion center that makes the final detection decision, each of the other nodes in the tree is a relay node that combines $m$ binary messages from its immediate child nodes and forms a new binary message using the majority dominance rule. We first provide the limit performance of the detection error probability at the fusion center for the case when $N$ goes to infinity. Then, we derive upper and lower bounds for the detection error probability at the fusion center as explicit functions of $N$ . These bounds also characterize the asymptotic decay rate of the detection error probability as $N$ goes to infinity, and show that the decay rate in the failure case is not faster than that in the nonfailure case. Furthermore, we derive a necessary and sufficient condition in terms of the decay rate of the local failure probability (combination of node failure probability and link failure probability) at each level to ensure that the detection error probability of the tree with node and link failures decays as fast as that of the tree without failures.

Description: Presents an introduction from the new Editor-in-Chief.

Description: Kernel-based methods enjoy powerful generalization capabilities in learning a variety of pattern recognition tasks. When such methods are provided with sufficient training data, broadly applicable classes of nonlinear functions can be approximated with desired accuracy. Nevertheless, inherent to the nonparametric nature of kernel-based estimators are computational and memory requirements that become prohibitive with large-scale datasets. In response to this formidable challenge, this paper puts forward a low-rank, kernel-based, feature extraction approach that is particularly tailored for online operation. A novel generative model is introduced to approximate high-dimensional (possibly infinite) features via a low-rank nonlinear subspace, the learning of which lends itself to a kernel function approximation. Offline and online solvers are developed for the subspace learning task, along with affordable versions, in which the number of stored data vectors is confined to a predefined budget. Analytical results provide performance bounds on how well the kernel matrix as well as kernel-based classification and regression tasks can be approximated by leveraging budgeted online subspace learning and feature extraction schemes. Tests on synthetic and real datasets demonstrate and benchmark the efficiency of the proposed method for dynamic nonlinear subspace tracking as well as online classification and regressions tasks.

Description: In many practical filter design problems, the exact statistical information of the underlying random processes is not available. One robust filtering approach in these situations is to design an intrinsically Bayesian robust filter that provides optimal solution relative to the prior distribution governing the uncertainty class of all possible joint random process models. In this context, the intrinsically Bayesian robust Kalman filter has been recently introduced for the case that the second-order statistics of the observation and process noise in the state-space model are unknown. However, such a filter does not utilize the additional information embedded in the data being observed. In this paper, we derive the optimal Bayesian Kalman filter, which is optimal over posterior distribution obtained from incorporating data into the prior distribution. This filter has the same recursive structure as that of the classical Kalman filter, except that it is designed relative to the posterior effective noise statistics , which are found by employing the method of factor graphs through formulating the problem of computing the likelihood function as a message passing algorithm.

Description: Unresolved scatterers (separated by less than a 3-dB matched filter main lobe width) are known to degrade the matching pursuit performances in radar: It tends to generate spurious detection or miss weaker targets, hidden in strong sidelobes. In this paper, we propose a new matching pursuit algorithm performing a subspace radar resolution cell rejection. The philosophy is the following: As it is usually not possible to distinguish several unresolved scatterers, we do not try to distinguish them, but when a scatterer is detected, then every contribution in the corresponding resolution cell should be cleaned. For that, the continuous cell interval is approximated by a subspace and the corresponding orthogonal projector is build. The projector basis is chosen so that it minimizes the projection residue inside the interval and a method is proposed to select its dimension according to the rejected target SNR. We show that it enables to control the sidelobe level after rejection (orthogonal projection) so that the sidelobe detection probability can be maintained low. It allows matching pursuit to work well even if the target parameter distribution differs from a delta Dirac distribution inside the matched filter resolution cell.

Description: We consider the blind source separation (BSS) problem and the closely related approximate joint diagonalization (AJD) problem of symmetric positive definite (SPD) matrices. These two problems can be reduced to an optimization problem with three key components: the criterion to minimize, the constraint on the solution, and the optimization algorithm to solve it. This paper contains two contributions that allow us to treat these issues independently. We build the first complete Riemannian optimization framework suited for BSS and AJD handling three classical constraints, and allowing to use a large panel of general optimization algorithms on manifolds. We also perform a thorough study of the AJD problem of SPD matrices from an information geometry point of view. We study AJD criteria based on several divergences of the set of SPD matrices, provide three optimization strategies to minimize them, and analyze their properties. Our numerical experiments on simulated and pseudoreal electroencephalographic data show the interest of the Riemannian optimization framework and of the different AJD criteria we consider.

Description: We present a new approach to ensemble learning. Our approach differs from previous approaches in that it constructs and applies different predictive models to different subsets of the feature space. It does this by constructing a tree of subsets of the feature space and associating a predictor (predictive model) to each node of the tree; we call the resulting object a tree of predictors . The (locally) optimal tree of predictors is derived recursively; each step involves jointly optimizing the split of the terminal nodes of the previous tree and the choice of learner (from among a given set of base learners) and training set—hence predictor—for each set in the split. The features of a new instance determine a unique path through the optimal tree of predictors; the final prediction aggregates the predictions of the predictors along this path. Thus, our approach uses base learners to create complex learners that are matched to the characteristics of the data set while avoiding overfitting. We establish loss bounds for the final predictor in terms of the Rademacher complexity of the base learners. We report the results of a number of experiments on a variety of datasets, showing that our approach provides statistically significant improvements over a wide variety of state-of-the-art machine learning algorithms, including various ensemble learning methods.

Description: In this paper, we address the problem of spectrum estimation of multiple frequency-hopping (FH) signals in the presence of random missing observations. The signals are analyzed within the bilinear time–frequency (TF) representation framework, where a TF kernel is designed by exploiting the inherent FH signal structures. The designed kernel permits effective suppression of cross-terms and artifacts due to missing observations while preserving the FH signal autoterms. The kerneled results are represented in the instantaneous autocorrelation function domain, which are then processed using a redesigned structure-aware Bayesian compressive sensing algorithm to accurately estimate the FH signal TF spectrum. The proposed method achieves high-resolution FH signal spectrum estimation even when a large portion of data observations is missing. Simulation results verify the effectiveness of the proposed method and its superiority over existing techniques.

Description: It was shown in previous work that a vector $mathbf{x} in mathbb {R}^n$ with at most $k 〈 n$ nonzeros can be recovered from an expander sketch $mathbf{A}mathbf{x}$ in $mathcal{O}(text{nnz}(mathbf{A})log k)$ operations via the parallel- $ell _0$ decoding algorithm, where $text{nnz}(mathbf{A})$ denotes the number of nonzero entries in $mathbf{A} in mathbb {R}^{m times n}$ . In this paper, we present the robust- $ell _0$ decoding algorithm, which robustifies parallel- $ell _0$ when the sketch $mathbf{A}mathbf{x}$ is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values in the sketch given its corrupted measurements. We provide analytic expressions that approximate these posteriors under the assumptions that the nonzero entries in the signal and the noise are drawn from continuous distributions. Numerical experiments presented show that robust- $ell _0$ is superior to existing greedy and combinatorial compressed sensing algorithms in the presence of small to moderate signal-to-noise ratios in the setting of Gaussian signals and Gaussian additive noise.

Description: In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators, which incorporate prior knowledge about the organization of the nonzero coefficients. This is done by desparsifying the estimator by S. van de Geer and B. Stucky and S. van de Geer et al. , then using an appropriate estimator for the precision matrix $Theta$ . In order to estimate the precision matrix a corresponding structured matrix norm penalty has to be introduced. After normalization the result is an asymptotic pivot. The asymptotic behavior is studied and simulations are added to study the differences between the two schemes.

Description: A framework for navigation using cellular code division multiple access (CDMA) signals is studied in this paper. Theoretical lower bounds on the navigation performance using pseudorange measurements drawn from the cellular CDMA base transceiver stations (BTSs) are derived. Moreover, the navigation performance for a mapper/navigator framework is studied in the presence of timing discrepancies between the mapper and navigator. In this framework, a mapping receiver (mapper) estimates the stochastic dynamic clock biases of the BTSs and shares these estimates with a navigating receiver (navigator). The optimal navigation performance of the mapper/navigator framework in the presence of timing discrepancies is analyzed, and a practical upper bound on the resulting position error is derived. Experimental results for a ground vehicle and unmanned aerial vehicles (UAVs) are presented. The ground vehicle results show a mean distance difference of 5.51 m between the cellular CDMA-only navigation solution and a GPS navigation solution in the absence of clock bias discrepancies. The UAV results show an improvement of 10.57 m in the root-mean-square error of the cellular CDMA navigation solution, when the sector clock bias discrepancies are accounted for utilizing the statistical model relating observed clock biases from different sectors of the same BTS cell.

Description: A software-defined receiver (SDR) for navigation using cellular code-division multiple access (CDMA) signals is presented. The cellular forward link signal structure is described, and models for the transmitted and received signals are developed. Particular attention is paid to relevant information that could be extracted and subsequently exploited for positioning and timing purposes. The pseudorange from the proposed receiver is modeled and the pseudorange error is studied in an additive white Gaussian channel. Experimental results with aerial and ground vehicles utilizing the proposed SDR are presented demonstrating a close match between the variation in pseudoranges and the variation in true ranges between the receiver and two cellular CDMA base transceiver stations (BTSs). Moreover, the dynamics of the discrepancy between the observed clock biases of different sectors of the same BTS cell is modeled and validated experimentally. The consistency of the obtained model is analyzed through experimental tests in different locations, at different times, and for different cellular providers.

Description: As a branch of sphere decoding, the K -best method has played an important role in detection in large-scale multiple-input-multiple-output (MIMO) systems. However, as the numbers of users and antennas grow, the preprocessing complexity increases significantly, which is one of the major issues with the K -best method. To address this problem, this paper proposes a preprocessing algorithm combining Cholesky sorted QR decomposition and partial iterative lattice reduction (CHOSLAR) for K -best detection in a 64-quadrature amplitude modulation (QAM) 16 $times$ 16 MIMO system. First, Cholesky decomposition is conducted to perform sorted QR decomposition. Compared with conventional sorted QR decomposition, this method reduces the number of multiplications by 25.1% and increases parallelism. Then, a constant-throughput partial iterative lattice reduction method is adopted to achieve near-optimal detection accuracy. This method further increases parallelism, reduces the number of matrix swaps by 45.5%, and reduces the number of multiplications by 67.3%. Finally, a sorting-reduced K -best strategy is used for vector estimation, thereby, reducing the number of comparators by 84.7%. This method suffers an accuracy loss of only approximately 1.44 dB compared with maximum likelihood detection. Based on CHOSLAR, this paper proposes a fully pipelined very-large-scale-integration architecture. A series of different systolic arrays and parallel processing units achieves an optimal tradeoff among throughput, area consumption, and power consumption. This architectural layout is obtained via TSMC 65-nm 1P9M CMOS technology, and throughput metrics of 1.40 Gbps/W (throughput/power) and 0.62 Mbps/kG (throughput/area) are a- hieved, demonstrating that the proposed system is much more efficient than state-of-the-art designs.

Description: Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain faster convergence to a minimizer achieving the allowed error without increasing the computational cost of each iteration considerably. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to faster convergence at the cost of an additional reconstruction error related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing, and deep learning. Particularly, it may provide a possible explanation to the successful approximation of the $ell _1$ -minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm.