In this paper, we develop a low-complexity cooperative relay network based on generalized frequency division multiplexing (GFDM) system. In this network, multiple relay nodes (RNs) are used to relay GFDM symbols from a source node (SN) toward a destination node (DN). We propose three methods to design the RNs based on the minimization of the total power of the noise after symbol estimation at the DN

This paper proves that every non-trivial, linear time-invariant (LTI) system of the first order shows a complexity blowup if it is simulated on a digital computer. This means that there exists a low-complexity input signal, which can be generated on a Turing machine in polynomial time, but such that the output signal of the LTI system has high complexity in the sense that the computation time for determining

This paper reports the design of a high-accuracy spatial location estimation method using ultrasound waves by exploiting the fixed geometry of the transmitters. Assuming an isosceles triangle antenna configuration, where three antennas are placed as the vertices of an isosceles triangle, the spatial location problem can be formulated as a non-convex optimization problem whose interior is shown to admit

Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern, or the wave-shape function, far from a sinusoidal function, and the oscillatory pattern is even changing from time to time. In practice, if multiple components exist

Practical systems often suffer from hardware impairments that already appear during signal generation. Despite the limiting effect of such input-noise impairments on signal processing systems, they are routinely ignored in the literature. In this paper, we propose an algorithm for data detection and signal estimation, referred to as Approximate Message Passing with Input noise (AMPI), which takes into

In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments. The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream

In asynchronous (intermittent) interference scenarios, the content of co-channel interference sources over the data interval may be different from the interferers content over the training interval, typically with extra interference sources presented over the data interval. Under such conditions, conventional adaptive beamformer designed over the training interval may lose its efficiency when applied

This paper reports a solution to a linear blind equalizer used in communication systems under the effect of two factors: i) An unknown linear inter symbol interference and ii) the impulsive noise satisfying the $\alpha$ -stable distribution. First, a constellation matching error-based cost function associated with the linear equalizer is designed to effectively compensate for the inter symbol interference

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon Fourier transform and linear shift invariant graphon filters , the graphon counterparts of the graph Fourier transform and graph filters. It is shown that for convergent

Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used

Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between the maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem. The drawback of the MPRF method is that the received samples are not processed jointly, decreasing signal to noise ratio (SNR). To overcome the drawbacks of

A Savitzky-Golay (SG) filter, widely used in signal processing applications, is a finite-impulse-response low-pass filter obtained by a local polynomial regression on noisy observations in the least-squares sense. The problem addressed in this paper is one of optimal order (or filter length) selection of SG filter in the presence of non-Gaussian noise, such that the mean-squared-error (or risk) between

We investigate numerically efficient approximations of eigenspaces associated with symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated which we consider to be extended orthogonal Givens or scaling and shear transformations. The number of these components controls the trade-off between approximation accuracy and

The performance of a single neural network can vary unexpectedly corresponding to different classification tasks, and thus the network with fixed structure may lack flexibility and often lead to overfitting or underfitting. It is urgent, also the main objective of this paper, to deal with the limitation of the fixed neural network structure on classifying radar signals in different electromagnetic

In this paper, we investigate the robust beamforming for the magnetic-based wireless power transfer (WPT) with multiple transmitters and multiple receivers to improve the power efficiency and reliability. By taking into account the imperfection of the magnetic mutual inductances information (MII), we firstly formulate a beamforming optimization problem to minimize the total transmit power while guaranteeing

This work focuses on the problem of unraveling nonlinearly mixed latent components in an unsupervised manner. The latent components are assumed to reside in the probability simplex, and are transformed by an unknown post-nonlinear mixing system. This problem finds various applications in signal and data analytics, e.g., nonlinear hyperspectral unmixing, image embedding, and nonlinear clustering. Linear

Deep neural networks (DNNs) have surpassed human-level accuracy in various learning tasks. However, unlike humans who have a natural cognitive intuition for probabilities, DNNs cannot express their uncertainty in the output decisions. This limits the deployment of DNNs in mission-critical domains, such as warfighter decision-making or medical diagnosis. Bayesian inference provides a principled approach

We correct errors in step 6 of Algorithm 1 given in the paper ‘`Sparse-Group Lasso for Graph Learning from Multi-Attribute Data.’' Other parts of the paper including numerical results are unchanged as the algorithm was implemented correctly.

A key objective in multiview learning is to model the information common to multiple parallel views of a class of objects/events to improve downstream tasks such as classification and clustering. In this context, two open research challenges remain; achieving scalability: how can we incorporate information from hundreds of views per event into a model? and being view-agnostic: how to learn robust multiview

To achieve high resolution, orthogonal frequency division multiplex (OFDM) radars deploy two-dimensional multiple signal classification (2D-MUSIC) in the joint range-velocity estimator. However, it is obvious that both of the signal reconstruction and 2D smoothing affect the noise statistical distribution and virtual array aperture in the joint range-velocity estimator with 2D-MUSIC. Therefore, the

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

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so degrades when the noise is heteroscedastic across samples, as occurs, e.g., when samples come from sources of heterogeneous quality. This paper develops a probabilistic

We consider Fair Principal Component Analysis (FPCA) and search for a low dimensional subspace that spans multiple target vectors in a fair manner. FPCA is defined as a non-concave maximization of the worst projected target norm within a given set. The problem arises in filter design in signal processing, and when incorporating fairness into dimensionality reduction schemes. The state of the art approach

Traditional networked radar systems for target tracking usually suffer from a heavy data processing burden, and do not consider the sensor location uncertainties (SLUs), by assuming that radar locations are known perfectly, which is applicable only for static platforms. In this paper, considering sensors mounted on moving platforms, we propose a joint power allocation and measurement selection (JPAMS)

In this work, a gradient-based primal-dual method of multipliers is proposed for solving a class of linearly constrained non-convex problems. We show that with random initialization of the primal and dual variables, the algorithm is able to compute second-order stationary points (SOSPs) with probability one. Further, we present applications of the proposed method in popular signal processing and machine

This paper presents algorithms for the parallelization of inference in hidden Markov models (HMMs). In particular, we propose a parallel forward-backward type of filtering and smoothing algorithm as well as a parallel Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements and operators to pose these inference problems as all-prefix-sums computations and parallelize them using

Among various array configurations, superdirective beamforming based on linear differential arrays has attracted much attention. It is well known that its directivity performance degrades at higher frequencies due to the limitation of finite difference approximation, and its robustness deteriorates due to the mismatch of practical systems. In this paper, we develop a wavenumber-domain superdirective

Partitioned-block frequency-domain adaptive filter (PBFDAF) algorithms have become very popular, in particular, for acoustic signal processing. However, the stochastic behavior of PBFDAFs has not been extensively examined. This paper presents a comprehensive statistical analysis for a family of the overlap-save PBFDAF algorithms with 50% overlap, including the transient and steady-state performance

In this paper, we investigate widely-linear channel estimation and data detection for the uplink of the massive multiple-input multiple-output (MIMO) with in-phase or quadrature-phase imbalance (IQI). We firstly investigate widely-linear minimum mean square error (WL-MMSE) estimation for the effective channel which is the product of the IQI coefficients and the wireless channel. We reuse pilots among

This paper derives the optimal Bayesian processing of an out-of-sequence (OOS) set of measurements in continuous-time for multiple target tracking. We consider a multi-target system modelled in continuous time that is discretised at the time steps when we receive the measurements, which are distributed according to the standard point target model. All information about this system at the sampled time

This paper deals with the problem of testing for equality between the location parameters of two unknown symmetric distributions that may belong to different families. Under this framework, we develop a new robust extension of the two-sample Hotelling test (HT). The proposed extension, called measure-transformed HT (MT-HT), operates by applying a transform to the probability measures of some reshaped

Deep convolutional neural networks (DCNNs) have recently emerged as a powerful tool to deliver breakthrough performances in various image analysis and processing applications. However, DCNNs lack a strong theoretical foundation and require massive amounts of training data. More recently, the deep scattering network (DSN), a variant of DCNNs, has been proposed to address these issues. DSNs inherit the

We consider the problem of minimizing the $\ell _1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show

In this paper, we investigate designs of linear precoders for vector Gaussian channels via stochastic optimizations and deep neural networks (DNNs). We assume that the channel inputs are drawn from practical finite alphabets, and we search for precoders maximizing the mutual information between channel inputs and outputs. Though the problem is generally non-convex, we prove that when the right singular

This paper proposes an efficient algorithm for robust sensor placement with the purpose of recovering a source signal from noisy measurements. To model uncertainty on the spatially-variant sensors gain and on the spatially correlated noise, we assume that both are realizations of Gaussian processes. Since the signal to noise ratio (SNR) is also uncertain in this context, to achieve a robust signal

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm

We consider a modern radar system which has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. A generalized likelihood ratio test (GLRT) was proposed in this context for target detection and direction of arrival estimation. However, the analytical performance of the GLRT has not been provided yet. In this paper, we

In this correspondence, we make a few corrections to the geodesic projection method of estimation fusion presented in [M. Tang, Y. Rong, J. Zhou, and X. R. Li, IEEE TSP, vol. 67, no. 2, pp. 279-292, 2019].

This paper introduces a collection of scaling methods for generating $\text{2}\,N$ -point DCT-II approximations based on $N$ -point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $\text{2}\,N$ -point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations

The high precision positioning of global navigation satellite systems (GNSS), which essentially corresponds to solving the integer least-squares (ILS) problem in the integer phase ambiguity estimation, has emerged as a key problem for the development of industrial internet-of-things (IIoT). In this paper, a novel paradigm for solving the ILS problem is introduced to the integer phase ambiguity estimation

We present novel generalized non-redundant sparse array design strategies that achieve the highest possible number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation. These array designs offer difference co-arrays that do not contain any lag redundancies except the unavoidable redundancies at lag zero. We first develop a co-array-based zero-redundancy design rule which serves as

In this paper, we propose a novel channel estimation method and optimize the pilot symbols based on intrinsic interference utilization for offset quadrature amplitude modulation based filter-bank multicarrier (OQAM/FBMC) systems. Specifically, we firstly propose a line fitting based channel estimation method by analyzing and utilizing the distribution characteristics of the demodulated OQAM symbols

Distributed or decentralized estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years, and applications in array processing have been indicated in some detail. Inspired by these, this paper provides a detailed development of several distributed algorithms for array processing. New distributed algorithms

Deep multi-view clustering utilizes neural networks to extract the potential peculiarities of complementarity and consistency information among multi-view features. This can obtain a consistent representation that improves clustering performance. Although a multitude of deep multi-view clustering approaches have been proposed, most lack theoretic interpretability while maintaining the advantages of

This paper targets developing algorithms for solving distributed learning problems in a communication-efficient fashion, by generalizing the recent method of lazily aggregated gradient (LAG) to deal with stochastic gradient — justifying the name of the new method LASG. While LAG is effective at reducing communication without sacrificing the rate of convergence, we show it only works with deterministic

In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where the cost of communication and/or computation can be expensive. We extend and generalize the analysis for a class of nested gradient-based distributed algorithms [NEAR-DGD, (Berahas et al. , 2019)] to account for multiple gradient steps at every iteration. We show the effect of performing

Methods for information-theoretic control for networks of sensors are of interest for enabling the development of autonomous sensor systems. In this paper we revisit the fundamentals of information theoretic-based control for multi-target systems and present a systematic approach for determining information-theoretic situational awareness based on mutual information for point processes. The extension

Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the Cramér-Rao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution, which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation

Neural networks with non-linear rectified linear unit (ReLU) activation functions have demonstrated remarkable performance in many fields. It has been observed that a sufficiently wide and/or deep ReLU network can accurately fit the training data, with a small generalization error on the testing data. Nevertheless, existing analytical results on provably training ReLU networks are mostly limited to

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link fluctuations that occur due to environment, human factors, or external attacks. In these situations, the GNN fails to address its distributed task if the topological randomness

In this paper, we study the problem of wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs), where a number of uncorrelated wideband signals impinge on an SLA and the data is collected from multiple frequency bins. To boost the performance and perform underdetermined DoA estimation, the difference co-array response matrices for all frequency bins are constructed first. Then

Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally different performances in many practical applications. In this paper, we propose a total Bregman divergence-based matrix information geometry (TBD-MIG) detector

We consider a wireless source localization network in which a target node emits localization signals that are used by anchor nodes to estimate the target node position. In addition to target and anchor nodes, there can also exist eavesdropper nodes and jammer nodes which aim to estimate the position of the target node and to degrade the accuracy of localization, respectively. We first propose the problem

This paper presents a new radar system that combines any number and any kind of radar signals and transmits them simultaneously, thereby obtaining all the advantages of each of the radar waveforms used. This new system is based on a low-rate coded time compression overlap-add (TC-OLA) technique, and allows radar designers to address the challenge of having many features, such as high-time resolution

We study a new stochastic multi-player multi-armed bandits (MP-MAB) problem, where the reward distribution changes if a collision occurs on the arm. Existing literature always assumes a zero reward for involved players if collision happens, but for applications such as cognitive radio, the more realistic scenario is that collision reduces the mean reward but not necessarily to zero. We focus on the

We consider the sparse phase retrieval problem of recovering a sparse signal $\mathbf {x}$ in $\mathbb {R}^d$ from intensity-only measurements in dimension $d \geq 2$ . Sparse phase retrieval can often be equivalently formulated as the problem of recovering a signal from its autocorrelation, which is in turn directly related to the combinatorial problem of recovering a set from its pairwise differences

This paper analyzes the detection of a $M$ –dimensional useful signal modeled as the output of a $M \times K$ MIMO filter driven by a $K$ –dimensional white Gaussian noise, and corrupted by a $M$ –dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained

We present spatial-Slepian transform (SST) for the joint spatial-Slepian domain representation of signals on the sphere to support localized signal analysis. We employ well-optimally concentrated Slepian functions, which are obtained as a solution of the Slepian spatial-spectral concentration problem of finding bandlimited and spatially optimally concentrated functions on the sphere, to formulate the

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that

Spherical harmonics representations are widely adopted in applications such as analysis, manipulation, and synthesis of wave fields that are either captured or simulated. Recent studies have shown that, for broadband fields, a time domain representation of spherical harmonics expansions can benefit from computational efficiency and favorable transient properties. For practical usage, an accurate discrete-time