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We provide a rigorous account of the equivalence between the complex-valued widely linear estimation method and the quaternion involution widely linear estimation method with their vector-valued real linear estimation counterparts. This is achieved by an account of degrees of freedom and by providing matrix mappings between a complex variable and an isomorphic bivariate real vector, and a quaternion variable versus a quadri-variate real vector. Furthermore, we show that the parameters in the complex-valued linear estimation method, the complex-valued widely linear estimation method, the quaternion linear estimation method, the quaternion semi-widely linear estimation method, and the quaternion involution widely linear estimation method include distinct geometric structures imposed on complex numbers and quaternions, respectively, whereas the real-valued linear estimation methods do not exhibit any structure. This key difference explains, both in theoretical and practical terms, the advantage of estimation in division algebras (complex, quaternion) over their multivariate real vector counterparts. In addition, we discuss the computational complexities of the estimators of the hypercomplex widely linear estimation methods. [ABSTRACT FROM AUTHOR]

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional GSP as a special case, but also includes a hybrid framework of graph and classical signal processing over a continuous domain. Our framework relies extensively on concepts and tools from functional analysis to generalize traditional GSP to graph signals in a separable Hilbert space with infinite dimensions. We develop a concept analogous to Fourier transform for generalized GSP and the theory of filtering and sampling such signals. [ABSTRACT FROM AUTHOR]

It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to smoothen or interpolate circle-valued signals defined on arbitrary graphs. We propose a convex relaxation of this nonconvex problem as a semidefinite program, and an efficient algorithm to solve it. [ABSTRACT FROM AUTHOR]

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, “divide-and-conquer” is probably the most common strategy to address the problem. In other words, the captured signal is decomposed into signal components for each individual component to be processed. Unfortunately, for signals that are superimposition of non-stationary amplitude-frequency modulated (AM-FM) components, the “divide-and-conquer” strategy is bound to fail, since there is no way to be sure that the decomposed components take on the AM-FM formulations which are necessary for the extraction of their instantaneous frequencies (IFs) and amplitudes (IAs). In this paper, we propose an adaptive signal separation operation (ASSO) for effective and accurate separation of a single-channel blind-source multi-component signal, via introducing a time-varying parameter that adapts locally to IFs and using linear chirp (linear frequency modulation) signals to approximate components at each time instant. We derive more accurate component recovery formulae based on the linear chirp signal local approximation. In addition, a recovery scheme, together with a ridge detection method, is also proposed to extract the signal components one by one, and the time-varying parameter is updated for each component. The proposed method is suitable for engineering implementation, being capable of separating complicated signals into their components or sub-signals and reconstructing the signal trend directly. Numerical experiments on synthetic and real-world signals are presented to demonstrate our improvement over the previous attempts. [ABSTRACT FROM AUTHOR]

Conventionalliterature on array signal processing (ASP) is based on the “capture first, process later” philosophy and to this end, signal processing algorithms are typically decoupled from the hardware. This poses fundamental limitations because if the sensors result in information loss, the algorithms may no longer be able to achieve their guaranteed performance. In this paper, our goal is to overcome the barrier of information loss via sensor saturation and clipping. This is a significant problem in application areas including physiological monitoring and extra-terrestrial exploration where the amplitudes may be unknown or larger than the dynamic range of the sensor. To overcome this fundamental bottleneck, we propose “computational arrays” which are based on a co-design approach so that a collaboration between the sensor array hardware and algorithms can be harnessed. Our work is inspired by the recently introduced unlimited sensing framework. In this context, our computational arrays encode the high-dynamic-range information by folding the signal amplitudes, thus introducing a new form of information loss in terms of the modulo measurements. On the decoding front, we develop mathematically guaranteed recovery algorithms for spatio-temporal array signal processing tasks that include DoA estimation, beamforming and signal reconstruction. Numerical examples corroborate the applicability of our approach and pave a path for the development of novel computational arrays for ASP. [ABSTRACT FROM AUTHOR]

A reconfigurable intelligent surface (RIS) is a nearly-passive flat layer made of inexpensive elements that can add a tunable phase shift to the impinging electromagnetic wave and are controlled by a low-power electronic circuit. This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar. At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the radar transmitter and one close to the radar receiver) and subsumes both a monostatic and a bistatic radar configuration with or without a line-of-sight view of the prospective target. Upon resorting to a generalized likelihood ratio test (GLRT), the design of the phase shifts introduced by the RIS elements is formulated as the maximization of the probability of detection in the location under inspection for a fixed probability of false alarm, and suitable optimization algorithms are proposed. The performance analysis shows the benefits granted by the presence of the RISs and shed light on the interplay among the key system parameters, such as the radar-RIS distance, the RIS size, and the location of the prospective target. A major finding is that the RISs should be better deployed in the near-field of the radar arrays at both the transmit and the receive side. The paper is concluded by discussing some open problems and foreseen applications. [ABSTRACT FROM AUTHOR]

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima. This is complemented by a recent interest in their zeros or minima, following seminal work by Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, the zero sets (or extrema) of GAFs have a complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from the analysis of spatial data, whose distributional properties for spectrograms are mostly understood only at an empirical level. In this work, we investigate spectrogram analysis via an examination of the stochastic geometric properties of their level sets. We obtain rigorous theorems demonstrating the efficacy of a spectrogram level sets based approach to the detection and estimation of signals, framed in a concrete inferential set-up. Exploiting these ideas as theoretical underpinnings, we propose a level sets based algorithm for signal analysis that is intrinsic to given spectrogram data, and substantiate its effectiveness via extensive empirical studies. Our results also have theoretical implications for spectrogram zero based approaches to signal analysis. To our knowledge, these results are arguably among the first to provide a rigorous statistical understanding of signal detection and reconstruction in this set up, complemented with provable guarantees on detection thresholds and rates of convergence. [ABSTRACT FROM AUTHOR]

In millimeter wave (mmWave) systems, it is challenging to ensure reliable communication links due to the high sensitivity to the presence of blockages. In order to improve the robustness of mmWave systems in the presence of random blockages, we consider the deployment of multiple reconfigurable intelligent surfaces (RISs) to enhance the spatial diversity gain, and the design of robust beamforming schemes based on stochastic optimization methods that minimize the maximum outage probability among multiple users so as to ensure fairness. Under the stochastic optimization framework, we adopt the stochastic majorization–minimization (SMM) method and the stochastic successive convex approximation (SSCA) method to construct deterministic surrogate problems at each iteration, and to obtain closed-form solutions of the precoding matrix at the base station (BS) and the beamforming vectors at the RISs. Both stochastic optimization methods are proved to converge to the set of stationary points of the original stochastic problems. Simulation results show that the proposed robust beamforming for RIS-aided systems can effectively compensate for the performance loss caused by the presence of random blockages, especially when the blockage probability is high. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is a promising device that can reconfigure the electromagnetic propagation environment through adjustment of the phase shifts of its reflecting elements. However, channel estimation in RIS-aided multiuser multiple-input single-output (MU-MISO) wireless communication systems is challenging due to the passive nature of the RIS and the large number of reflecting elements that can lead to high channel estimation overhead. To address this issue, we propose a novel cascaded channel estimation strategy with low pilot overhead by exploiting the sparsity and the correlation of multiuser cascaded channels in millimeter-wave MISO systems. Based on the fact that the physical positions of the BS, the RIS and users do not appreciably change over multiple consecutive channel coherence blocks, we first estimate the full channel state information (CSI) including all the angle and gain information in the first coherence block, and then only re-estimate the channel gains in the remaining coherence blocks with much lower pilot overhead. In the first coherence block, we propose a two-phase channel estimation method, in which the cascaded channel of one typical user is estimated in Phase I based on the linear correlation among cascaded paths, while the cascaded channels of other users are estimated in Phase II by utilizing the reparameterized CSI of the common base station (BS)-RIS channel obtained in Phase I. The minimum pilot overhead is much less than the existing works. Simulation results show that the performance of the proposed method outperforms the existing methods in terms of the estimation accuracy when using the same amount of pilot overhead. [ABSTRACT FROM AUTHOR]

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

In signal processing and data analytics, Wiener filter is a classical powerful tool to transform an input signal to match a desired or target signal by a linear time-invariant (LTI) filter. The input signal of a Wiener filter is one-dimensional while its associated least-squares solution, namely Wiener-Hopf equation, involves a two-dimensional data-array, or correlation matrix. However, the actual match should often be carried out between a multi-dimensional filtered signal-sequence, which is the output of a multi-channel filter characterized as a linear-time-invariant MIMO (multi-input and multi-output) system, and a multi-dimensional desired signal-sequence simultaneously. In the presence of such a multi-channel filter, the solution to the corresponding Wiener filter, which we call MIMO Wiener-Hopf equation now, involves a correlation tensor. Therefore, we call this optimal multi-channel filter Tensor Wiener Filter (TWF). Due to lack of the pertinent mathematical framework of needed tensor operations, TWF has never been investigated so far. Now we would like to make the first-ever attempt to establish a new mathematical framework for TWF, which relies on the inverse of the correlation tensor. We propose the new parallel block-Jacobi tensor-inversion algorithm for this tensor inversion. A typical application of the new TWF approach is illustrated as a multi-channel linear predictor (MCLP) built upon a multi-channel autoregressive (MCAR) filter with multi-dimensional input data. Numerical experiments pertaining to seismic data, optical images, and macroeconomic time-series are conducted in comparison with other existing methods. The memory- and computational-complexities corresponding to our proposed parallel block-Jacobi tensor-inversion algorithm are also studied in this paper. [ABSTRACT FROM AUTHOR]

The great success of deep learning (DL) has inspired researchers to develop more accurate and efficient symbol detectors for multi-input multi-output (MIMO) systems. Existing DL-based MIMO detectors, however, suffer several drawbacks. To address these issues, in this paper, we develop a model-driven DL detector based on variational Bayesian inference. Specifically, the proposed unrolled DL architecture is inspired by an inverse-free variational Bayesian learning framework which circumvents matrix inversion via maximizing a relaxed evidence lower bound. Two networks are respectively developed for independent and identically distributed (i.i.d.) Gaussian channels and arbitrarily correlated channels. The proposed networks, referred to as VBINet, have only a few learnable parameters and thus can be efficiently trained with a moderate amount of training samples. The proposed VBINet-based detectors can work in both offline and online training modes. An important advantage of our proposed networks over state-of-the-art MIMO detection networks such as OAMPNet and MMNet is that the VBINet can automatically learn the noise variance from data, thus yielding a significant performance improvement over the OAMPNet and MMNet in the presence of noise variance uncertainty. Simulation results show that the proposed VBINet-based detectors achieve competitive performance for both i.i.d. Gaussian and realistic 3GPP MIMO channels. [ABSTRACT FROM AUTHOR]

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

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

The large antenna arrays with hybrid analog and digital (HAD) architectures can provide a large aperture with low cost and hardware complexity, resulting in enhanced direction-of-arrival (DOA) estimation and reduced power consumption. This paper investigates the trade-off between DOA estimation and power consumption in large antenna arrays with HAD architectures. Particularly, the DOA estimation problem of fully-connected, sub-connected (SC), and switches-based (SE) hybrid architectures is formulated into a unified expression, with the compression matrix in a time-varying form. Based on this model, we derive a dynamic maximum likelihood (D-ML) estimator that is suitable for both HAD and conventional fully digital (FD) structures, and the closed-form expression of Cramér-Rao bound (CRB) to evaluate the performance limit of the D-ML estimator for different HAD structures. The theoretical CRB analysis in the single-source case reveals that, the SC structure has the ability to achieve approximately the same performance as the FD structures at DOAs around zero, but suffers from the inherent angle ambiguity because of the antenna grouping. In addition, we propose a dynamic SC (D-SC) structure that is proved to eliminate the angle ambiguity with time-varying phase shifters, and a switch optimization (SWO) algorithm to minimize the CRB of SE structures. Finally, we introduce a new metric, DOA efficiency, to measure the trade-off between the DOA estimation performance and power consumption of different structures. Simulation results verify our theoretical analysis and the superiority of the proposed D-SC structure and the SWO algorithm. [ABSTRACT FROM AUTHOR]

The temporal variations in the wireless propagation channel, referred to as channel aging, cause a mismatch between the estimated channel and the channel state at the time of data detection. This mismatch has been shown to severely impair the performance of massive MIMO systems. In this paper, we present data aided MSE-optimal channel tracking algorithms to decode the received symbols and update the channel estimates at the base station (BS) and the UEs. These algorithms combine ideas from Kalman filtering for channel tracking and deterministic equivalent analysis for symbol estimation. In the uplink case, we first develop a minimum mean squared error (MMSE) data estimator and the MSE-optimal channel predictor based on the Kalman filtering algorithm. We analytically show that the updated channel estimate obtained from the estimates of the data symbols leads to significantly larger signal to interference-plus-noise ratio (SINR), and hence achievable rate, compared to that obtained from the channel estimate based on pilot symbols. Following this, in the downlink case, we develop an algorithm to track the effective channel at the UEs and analyze its MSE, SINR and achievable rate performance. We show that tracking the effective downlink channel mitigates the effects of channel aging and leads to improved performance. However, since the beamforming matrices at the BS are not updated, downlink channel tracking is not as effective as uplink channel tracking. Finally, via Monte Carlo simulations, we validate our derived results, and demonstrate the gains achievable by tracking the time-varying channels in massive MIMO systems. [ABSTRACT FROM AUTHOR]

Frequency agile radar (FAR) has improved anti-jamming performance over traditional pulse-Doppler radars under complex electromagnetic circumstances. To reconstruct the range-Doppler information in FAR, many compressed sensing (CS) methods including standard and block sparse recovery have been applied. In this paper, we study phase transitions of range-Doppler recovery in FAR using CS. In particular, we derive closed-form phase transition curves associated with block sparse recovery and complex Gaussian matrices, based on prior results of standard sparse recovery under real Gaussian matrices. We further approximate the obtained curves with elementary functions of radar and target parameters, facilitating practical applications of these curves. Our results indicate that block sparse recovery outperforms the standard counterpart when targets occupy more than one range cell, which are often referred to as extended targets. Simulations validate the availability of these curves and their approximations in FAR, which benefit the design of the radar parameters. [ABSTRACT FROM AUTHOR]

This paper deals with adaptive radar detection problems where several alternative hypotheses may be plausible. This kind of problems naturally extends the conventional binary tests that often occur in radar (as well as in other application fields) by including a further uncertainty degree related to the number of unknown signal parameters (model order). Such a modification consequently leads to multiple composite alternative hypotheses. In the companion paper (Addabbo et al., 2021), we have defined a new design framework which allows us to come up with decision schemes for these hypothesis testing problems by exploiting the Kullback-Leibler Information Criterion and without resorting to heuristic design criteria. The architectures devised within the proposed framework consist of the sum between the compressed log-likelihood ratio and a penalty term inherited from model order selection rules. Such a penalty term accounts for the number of unknown parameters to overcome the limitation of the generalized likelihood ratio test in the presence of nested hypotheses. In the present paper, we apply the new design framework to different detection problems related to both real aperture and (polarimetric) synthetic aperture radar. The analysis is carried out in comparison with suitable competitors (possibly based upon heuristic design criteria) and shows that the architectures devised within the proposed theoretically-founded design framework represent an effective means to deal with detection problems where the uncertainty on some parameters leads to multiple alternative hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of target detection in the presence of coherent (or fully correlated) signals, which can be due to multipath propagation effects or electronic attacks by smart jammers. To this end, we formulate the problem at hand as a multiple-hypothesis test that, besides the conventional radar alternative hypothesis, contains additional hypotheses accounting for the presence of an unknown number of interfering signals. In this context and leveraging the classification capabilities of the Model Order Selection rules, we devise penalized likelihood-ratio-based detection architectures that can establish, as a byproduct, which hypothesis is in force. Moreover, we propose a suboptimum procedure to estimate the angles of arrival of multiple coherent signals ensuring (at least for the considered parameters) almost the same performance as the exhaustive search. Finally, the performance assessment, conducted over simulated data and in comparison with conventional radar detectors, highlights that the proposed architectures can provide satisfactory performance in terms of probability of detection and correct classification. [ABSTRACT FROM AUTHOR]

A blind Direction-of-Arrivals (DOAs)estimate of narrowband signals for Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special structure of the signal measured by an AVS, we show that the covariance matrix of all the received signals from the array admits a natural low-rank 4-way tensor representation. Thus, rather than estimating the DOAs directly from the raw data, our estimate arises from the unique parametric Canonical Polyadic Decomposition (CPD) of the observations’ Second-Order Statistics (SOSs) tensor. By exploiting results from fundamental statistics and the recently re-emerging tensor theory, we derive a consistent blind CPD-based DOAs estimate without prior assumptions on the array configuration. We show that this estimate is a solution to an equivalent approximate joint diagonalization problem, and propose an ad hoc iterative solution. Additionally, we derive the Cramér-Rao lower bound for Gaussian signals, and use it to derive the iterative Fisher scoring algorithm for the computation of the Maximum Likelihood Estimate (MLE) in this particular signal model. We then show that the MLE for the Gaussian model can in fact be used to obtain improved DOAs estimates for non-Gaussian signals as well (under mild conditions), which are optimal under the Kullback-Leibler divergence covariance fitting criterion, harnessing additional information encapsulated in the SOSs. Our analytical results are corroborated by simulation experiments in various scenarios, which also demonstrate the considerable improved accuracy w.r.t. a previously proposed state-of-the-art blind DOAs estimate for AVS arrays, reducing the resulting root mean squared error by up to more than an order of magnitude. [ABSTRACT FROM AUTHOR]

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

In this paper, we study the resource allocation design for non-orthogonal multiple access (NOMA)-based cellular massive Internet-of-Things (IoT) enabled with simultaneous wireless information and power transfer (SWIPT). The design is formulated as a non-convex optimization problem, which takes into account practical and adverse factors, e.g., the channel uncertainty during channel state information (CSI) acquisition, the non-linear receiver during energy harvesting (EH) and the imperfect successive information cancellation (SIC) during the information decoding (ID). The originally harmful co-channel interference in massive access is coordinated to strike a balance between efficient information transmission and efficient energy harvesting via spatial beamforming. Subsequently, two robust beamforming algorithms are designed from the aspects of the weighted sum rate maximization and the total power consumption minimization, respectively. It is found that overall performance can be improved by adding BS antennas due to more array gains. Moreover, it is proved that the proposed algorithms can effectively alleviate the influence of adverse practical conditions and achieve the best performance compared to the baseline ones, which demonstrates the effectiveness and robustness of proposed algorithms for cellular massive IoT. [ABSTRACT FROM AUTHOR]

Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. The computational performance is further improved by bounds on the pole location and an approximate iteration step. We demonstrate how explicit knowledge of the FDN's modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that relatively few modes contribute a large portion of impulse response energy. [ABSTRACT FROM AUTHOR]

This paper proposes a new method called multiscale quaternion Weber local descriptor histogram (MQWLDH) for feature extraction of hyperspectral images (HSIs), which is used to model spatial information based on the corresponding spectral features. The proposed method first transforms spectral data into an orthogonal space using principal component analysis, and extracts the first three principal components (PCs) based on the maximum variance theory. Then, construct the MQWLDH to extract spatial features based on those first three PCs. The proposed method uses the algebraic structure of quaternions to unify the process of processing the first three PCs, which reduces the computational cost and the dimensionality of the extracted spatial feature vector. Moreover, the constructed quaternion Weber local descriptor effectively characterizes the variations of each pixel neighborhood and detects the edges of HSIs. To capture more intrinsic spatial information contained in homogeneous regions of different sizes and shapes, multiscale feature histograms are constructed. Finally, a feature fusion framework is proposed to fuse spectral and spatial features so that spectral information can be fully utilized. The experimental results on three HSI datasets demonstrate that the proposed method provides effective features to different classifiers and achieves excellent classification performance. [ABSTRACT FROM AUTHOR]

Two-dimensional (2-D) spectrum sensing is addressed in the context of a cognitive radar to gather real-time space-frequency electromagnetic awareness. Assuming a sensor equipped with multiple receive antennas, a discrete-time sensing signal model formally accounting for multiple snapshots of observations is introduced. Hence, a new signal processing strategy exploiting the inherent block-sparsity of the overall profile is developed to glean a reliable 2-D occupancy awareness. Specifically, the proposed approach resorts to the regularized maximum likelihood estimation paradigm including a term promoting the block-sparsity of the 2-D profile so as to automatically foster this peculiarity in the profile evaluation. Some illustrative examples (both on simulated and measured data) are provided to compare the novel strategy with a relevant counterpart available in the open literature and highlight the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

We address the downlink channel estimation problem for massive multiple-input multiple-output (MIMO) systems in this paper, where the inherit burst-sparsity structure is exploited to improve the channel estimation performance. In the literature, the commonly used burst-sparsity model assumes a uniform burst-sparse structure in which all bursts have similar sizes. However, such assumption is oversimplified to hold in practice. Outliers deviated from such uniform burst structures can significantly degrade the accuracy of the existing burst-sparsity models, which may result in a reduced recovery performance. To capture a more general burst-sparsity structure in practice, we propose a novel non-uniform burst-sparsity model and introduce an improved pattern-coupled prior to account for more realistic non-uniform burst structures. A generic sparse Bayesian learning based framework to exploit the non-uniform burst-sparsity and to enhance massive MIMO channel estimation performance is then developed. We further prove that our solution converges to a stationary point of the associated optimization problem, and our framework includes the state-of-the-art pattern-coupled method as a special case. Simulation results verify the robust performance of the devised method. [ABSTRACT FROM AUTHOR]

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification, and matrix completion tasks. [ABSTRACT FROM AUTHOR]

In this paper, we consider compressive sensing (CS)-based recovery of delays and Doppler frequencies of targets in high resolution radars. We propose a novel sub-Nyquist sampling method in the Fourier domain based on difference sets (DS), called DS-sampling, to create dictionaries with highly incoherent atoms. The coherence of the dictionary reaches the Welch minimum bound if the DS-sampling is employed. This property let us to implement sub-Nyquist high resolution radars with minimum number of samples.1 Two low-complexity recovery methods are developed and sufficient condition of target recovery with specific resolution obtained theoretically for noisy and noiseless conditions. We also propose a new waveform, called DS-frequency coded modulated waveform, to boost the recovery performance of the sub-Nyquist radar in noisy environments. The proposed method solves some of the common problems in many CS-based radars and overcome disadvantages of the conventional Nyquist processing (i.e., matched filtering) in high resolution radar systems. The proposed method allows us to design sub-Nyquist radars, which require less than $\text{2}{\%}$ of Nyquist samples and recover targets without resolution degradation in comparison to the conventional Nyquist processing. [ABSTRACT FROM AUTHOR]

For colocated multiple-input multiple-output (MIMO) radar, we investigate the target detection problem in Gaussian clutter with unknown covariance matrix with known inverse complex Wishart distribution as its prior probability density function. We propose three detectors in the Bayesian framework according to the criteria of the generalized likelihood ratio test, Rao test, and Wald test. The two main advantages of the proposed Bayesian detectors are as follows: first, no training data are required; and second, a priori knowledge about the clutter is incorporated in the decision rules to achieve detection performance gains. Numerical simulations show that the proposed Bayesian detectors outperform their non-Bayesian counterparts, especially when the sample number of the transmitted waveform is small. In addition, the proposed Bayesian Wald test is the most robust against the mismatch in the receive steering vector, and the proposed Bayesian Rao test exhibits the strongest rejection capability of mismatched signals. [ABSTRACT FROM AUTHOR]

The linear canonical transform (LCT) is a multiparameter unitary transform that generalizes a large number of classical transforms with application to signal processing and optics. Many of its fundamental properties are already known; however, little attention has been paid to the design and implementation of matched filters in the LCT domain. The objective of this paper is to design this type of filters that maximize the output signal-to-noise ratio, dubbed the linear canonical matched filter (LCMF). We first derive some facts of the LCT spectral analysis for random signals. Then, by applying the derived results, the LCMF design theory associated with the LCT is developed. Moreover, the implementation and basic properties of the LCMF are presented. The introduction of the LCMF invites a new interpretation of the ambiguity function and the correlation function of the LCT. Finally, we provide several applications for the theoretical derivations. [ABSTRACT FROM AUTHOR]

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated by incorporating persymmetric structure of received data. The signal of interest is described with a subspace model, namely, it belongs to a subspace spanned by the columns of a known matrix, but with unknown coordinates. We propose a persymmetric detector with two tunable parameters, which includes many existing persymmetric detectors as special cases. Approximate expressions for the probabilities of false alarm and detection of the proposed detector are derived, which are verified via Monte Carlo simulations. Numerical results reveal that the exploitation of the persymmetric structure leads to a significant gain in the detection performance, especially in the case of limited training data. In addition, a further gain in the detection performance can be obtained by optimally selecting the tunable parameters. [ABSTRACT FROM AUTHOR]

This paper studies the existence of optimal invariant detectors for determining whether $P$ multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the retrieval of the modes of multicomponent signals from their downsampled short-time Fourier transform. To this end, we first recall signal reconstruction techniques based on shifted downsampled short-time Fourier transform, and then explain how to adapt these to the context of the retrieval of the modes of a multicomponent signal. We then show, on simulated and real data, that downsampling the short-time Fourier transform does not result in a significant performance loss of the mode retrieval procedures. Finally, comparisons with recent mode retrieval techniques based on synchrosqueezing transform are carried out, the focus being put on the amount of information needed to perform the recovery of the modes. [ABSTRACT FROM AUTHOR]

This paper studies the relative position based node-localization problem for a sensor network without all nodes sharing a common reference frame in the presence of both measurement and communication noises. To solve the problem, a robust distributed orientation estimate algorithm and a robust distributed node-localization algorithm are designed, where unbiased estimators are constructed based on the historical measurement information to inhibit the measurement noise and the stochastic approximation method is adopted to inhibit the communication noise. Under the zero-mean and independence assumption on the measurement/communication noise, we show that all sensor nodes can asymptotically determine their own orientation angles and positions almost surely under the designed algorithms, if and only if the network contains at least one anchor node, and its communication and distance-sensing topology is 1-rooted at the anchor node set and the corresponding bearing sensing topology is connected. Moreover, the convergence rate is quantified if only the measurement noise or communication noise is involved. Simulation experiments are conducted to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of detecting a subspace signal in the presence of spatially and temporally colored disturbance. A new subspace parametric signal model that takes into account a multi-rank subspace structure for the target signal and employs a multi-channel auto-regressive process for the disturbance signal is proposed. Following this model, a new subspace parametric Rao detector (SP-Rao) is developed for training-limited scenarios. Unlike conventional parametric detectors that are designed for only rank-one signal detection, the SP-Rao has a new multi-rank structure with a pairwise successive spatio-temporal whitening and cross-correlation process between the observed signal and each subspace basis vector. Additionally, a non-parametric subspace detector (NSD) is derived based upon a frequency-domain representation of the SP-Rao test statistic. The NSD is distinctively different from conventional subspace detectors, in which the former involves pairwise whitening and cross-correlation between the test signal and each subspace basis vector but the latter employs the whole subspace matrix. Numerical results are presented to illustrate the performance of the proposed subspace detectors in comparison with several leading existing methods, especially in the case of limited data. [ABSTRACT FROM AUTHOR]

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

This paper presents an approximate minimum mean squared error (MMSE) adaptive beam-pattern design (ABD) method for MIMO active sensing systems. The proposed approximate MMSE ABD method leverages the physics of the MIMO arrays to provide a linear-Gaussian approximation that is specific to MIMO active sensing systems, and yields a computationally simple optimization problem. Computational complexity analysis confirms this theoretical reduction in the number of floating-point operations required, most notably that evaluation of the proposed approximate optimization cost function grows polynomially with the number of targets being tracked, whereas for evaluation of the exact cost the growth is exponential. Additionally, numerical results indicate that, even for a simple scenario with a single target being tracked, the proposed approximate MMSE ABD method does indeed reduce the mean squared error of target parameter estimation compared to the nonadaptive case, with a reduction in computation time of four orders of magnitude compared to exact MMSE ABD. [ABSTRACT FROM AUTHOR]

In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is slightly above the number of frequency channels. [ABSTRACT FROM AUTHOR]

We study downlink of multiantenna cloud radio access networks with finite-capacity fronthaul links. The aim is to propose joint designs of beamforming and remote radio head (RRH)-user association, subject to constraints on users’ quality-of-service, limited capacity of fronthaul links and transmit power, to maximize the system energy efficiency. To cope with the limited-capacity fronthaul we consider the problem of RRH-user association to select a subset of users that can be served by each RRH. Moreover, different to the conventional power consumption models, we take into account the dependence of the baseband signal processing power on the data rate, as well as the dynamics of the efficiency of power amplifiers. The considered problem leads to a mixed binary integer program which is difficult to solve. Our first contribution is to derive a globally optimal solution for the considered problem by customizing a discrete branch-reduce-and-bound approach. Since the global optimization method requires a high computational effort, we further propose two suboptimal solutions able to achieve the near optimal performance but with much reduced complexity. To this end, we transform the design problem into continuous (but inherently nonconvex) programs by two approaches: penalty and $\ell _{0}$ -approximation methods. These resulting continuous nonconvex problems are then solved by the successive convex approximation framework. Numerical results are provided to evaluate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed. [ABSTRACT FROM AUTHOR]

Kernel methods have been successfully applied to nonlinear problems in machine learning and signal processing. Various kernel-based algorithms have been proposed over the last two decades. In this paper, we investigate the kernel conjugate gradient (KCG) algorithms in both batch and online modes. By expressing the solution vector of CG algorithm as a linear combination of the input vectors and using the kernel trick, we developed the KCG algorithm for batch mode. Because the CG algorithm is iterative in nature, it can greatly reduce the computations by the technique of reduced-rank processing. Moreover, the reduced-rank processing can provide the robustness against the problem of overlearning. The online KCG algorithm is also derived, which converges as fast as the kernel recursive least squares (KRLS) algorithm, but the computational cost is only a quarter of that of the KRLS algorithm. Another attractive feature of the online KCG algorithm compared with other kernel adaptive algorithms is that it does not require the user-defined parameters. To control the growth of data size in online applications, a simple sparsification criterion based on the angles among elements in reproducing kernel Hilbert space is proposed. The angle criterion is equivalent to the coherence criterion but does not require the kernel to be unit norm. Finally, numerical experiments are provided to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The current trend of acquiring data pervasively calls for some data-selection strategy, particularly in the case a subset of the data does not bring enough innovation. In this paper, we present some extensions of the existing adaptive filtering algorithms enabling data selection, which also address the censorship of outliers measured through unexpected high estimation errors. The resulting algorithms allow the prescription of how often the acquired data are expected to be incorporated in the learning process based on some a priori assumptions regarding the environment data. A detailed derivation of how to implement the data selection in a computationally efficient way is provided along with the proper choice of the parameters inherent to the data-selective affine projection algorithms. Similar discussions lead to the proposal of the data-selective least mean square and data-selective recursive least squares algorithms. Simulation results show the effectiveness of the proposed algorithms for selecting the innovative data without sacrificing the estimation accuracy, while reducing the computational cost. [ABSTRACT FROM AUTHOR]

We perform an asymptotic study of the performance of filter bank multicarrier in the context of massive multi-input multi-output. We show that the effects of channel distortions, i.e., intersymbol interference and intercarrier interference, do not vanish as the base station (BS) array size increases. As a result, the signal-to-interference-plus-noise ratio (SINR) cannot grow unboundedly by increasing the number of BS antennas, and is upper bounded by a certain deterministic value. We show that this phenomenon is a result of the correlation between the multiantenna combining tap values and the channel impulse responses between the mobile terminals and the BS antennas. To resolve this problem, we introduce an efficient equalization method that removes this correlation, enabling us to achieve arbitrarily large SINR values by increasing the number of BS antennas. We perform a thorough analysis of the proposed system and find analytical expressions for both equalizer coefficients and the respective SINR. [ABSTRACT FROM AUTHOR]

The recently proposed multilayer convolutional sparse coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of convolutional neural networks (CNNs). Under this framework, the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking. In this paper, we propose a sound pursuit algorithm for the ML-CSC model by adopting a projection approach. We provide new and improved bounds on the stability of the solution of such pursuit and we analyze different practical alternatives to implement this in practice. We show that the training of the filters is essential to allow for nontrivial signals in the model, and we derive an online algorithm to learn the dictionaries from real data, effectively resulting in cascaded sparse convolutional layers. Last, but not least, we demonstrate the applicability of the ML-CSC model for several applications in an unsupervised setting, providing competitive results. Our work represents a bridge between matrix factorization, sparse dictionary learning, and sparse autoencoders, and we analyze these connections in detail. [ABSTRACT FROM AUTHOR]

In this paper, we study the tone reservation method for reducing the peak-to-average power ratio (PAPR) in general orthonormal transmission systems. We prove that strong solvability, where the peak value of the transmit signal has to be bounded by a constant times the energy of the information symbols, is equivalent to weak solvability, where the peak value of the transmit signal has to be only bounded. Further, we show that in the case where the PAPR problem is not weakly solvable, almost all information sequences lead to an unbounded transmit signal. [ABSTRACT FROM AUTHOR]

When there are a large number of antennas in massive MIMO systems, the transmitted wideband signal will be sensitive to the physical propagation delay of electromagnetic waves across the large array aperture, which is called the spatial-wideband effect. In this scenario, the transceiver design is different from most of the existing works, which presume that the bandwidth of the transmitted signals is not that wide, ignore the spatial-wideband effect, and only address the frequency selectivity. In this paper, we investigate spatial- and frequency-wideband effects, called dual-wideband effects in massive MIMO systems from the array signal processing point of view. Taking millimeter-wave-band communications as an example, we describe the transmission process to address the dual-wideband effects. By exploiting the channel sparsity in the angle domain and the delay domain, we develop the efficient uplink and downlink channel estimation strategies that require much less amount of training overhead and cause no pilot contamination. Thanks to the array signal processing techniques, the proposed channel estimation is suitable for both TDD and FDD massive MIMO systems. Numerical examples demonstrate that the proposed transmission design for massive MIMO systems can effectively deal with the dual-wideband effects. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of downlink channel estimation in frequency-division duplexing massive multiple-input multiple-output systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the downlink channel. However, there are at least two shortcomings of these DFT-based methods: first, they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs; and second, they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above-mentioned shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary two-dimensional-array antenna geometry, and propose an efficient sparse Bayesian learning approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization–minimization algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplink-aided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This contribution considers the non-Bayesian Cramér-Rao bound (CRB) related to parameter estimation from a linearly modulated signal observed in additive white Gaussian noise. We compare the exact CRB expression for coded modulation with two ad hoc CRB (ACRB) expressions; the first ACRB is obtained by substituting in the exact CRB expression for uncoded modulation the a priori symbol probabilities by the extrinsic symbol probabilities; the second ACRB, which has received some attention in recent scientific publications, additionally assumes that the real and imaginary parts of the symbols are independent. Our exposition focuses on the particular case of phase shift estimation. By means of examples we show that although for some coded modulation schemes the exact and ACRBs yield virtually the same numerical result, for other coded modulation schemes the ACRBs differ considerably among themselves and from the exact CRB. We provide some explanations for this behavior. We also argue that both ACRBs are expected to virtually coincide with the exact CRB in the case of bit-interleaved coded modulation combined with a rectangular constellations with independent in-phase and quadrature mapping and a binary code for which the factor graph does not contain short cycles. [ABSTRACT FROM AUTHOR]

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 highresolution FH signal spectrum estimation evenwhen a large portion of data observations is missing. Simulation results verify the effectiveness of the proposed method and its superiority over existing techniques. [ABSTRACT FROM AUTHOR]