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Integrated passive radar (IPR) can be regarded as next-generation passive radar technology, which aims to integrate communication and radar systems. Unlike conventional passive radar, which does not prioritize communication-centric radar technology, IPR technology places a higher priority on incorporating specific radar constraints to develop waveforms that are better suited for radar applications. This paper deals with the problem of distributed MIMO IPR target detection under uncalibrated surveillance/reference receivers. We focus on a communication-centric radar system consisting of several opportunity transmitters non-overlapping in frequency with the same bandwidth and several spatially separated receivers. Five new detectors are devised according to the likelihood ratio test (LRT), Rao, Wald, Gradient, and Durbin criteria. Although it is shown that these detectors are asymptotically equivalent, they provide different performances in the presence of noisy reference channels. The invariance principle is applied in this paper to show that all uncertainties affecting threshold setting can be unified in the direct-path signal power-to-noise power ratio (DNR) of the reference channels. To ensure effective detection threshold setting regardless of the DNR values in the reference channels, we introduce a novel strategy to adjust the level of the proposed detectors rather than their sizes. Then, we examine false alarm regulations and the detection performance of the fixed-level proposed detectors to demonstrate their effectiveness compared to several existing detectors. Thus, we create a unified framework for uncalibrated MIMO IPR target detection in the presence of noisy reference channels.

Existing multilayer graph clustering models focus on integrating the monolithic structure of each layer, but the local preference between layers and clusters has not been fully exploited. To alleviate this problem, this paper proposes a novel multilayer graph clustering model with Adaptive Local Modularity Learning (ALML), which mines truncated layer-cluster relationships adaptively with graph modularity learning paradigm, to reveal the local preference in multilayer graphs. More importantly, ALML reveals the equivalence between graph cut and graph modularity learning in multilayer graph scenarios in theory. To solve the optimization problem involved in ALML, this paper proposes an efficient alternating algorithm with quadratic-level time complexity, which is satisfactory in multilayer graph clustering scenarios, and provides corresponding analyses. In the simulations, extensive experimental results demonstrate that ALML outperforms state-of-the-art competitors in terms of effectiveness as well as efficiency.

Existing algorithms in online optimization usually rely on trustful information, e.g., reliable knowledge of gradients, which makes them vulnerable to attacks. To take into account the security issue in online optimization, this paper investigates the effect of randomly corrupted attacks, which can corrupt gradient information arbitrarily. To conquer the randomly corrupted attack, an onLine muLtiple normaLized Gradient Descent (L3GD) algorithm is proposed. Under mild conditions, the algorithm is proven to achieve satisfactory expected dynamic regret, i.e, $\mathcal{O}(\min\{P_{T}^{*}+T^{\frac{3}{4}},S_{T}^{*}+\sqrt{T}+\sum_{t=1}^{T} \|\nabla f_{t}(x_{t}^{*})\|^{2}\})$ and $\mathcal{O}(F_{T}+T^{\frac{3}{4}})$, without convex assumption, where $P_{T}^{*}$, $S_{T}^{*}$, and $F_{T}$ denote the path-length, squared path-length, and the functional variation, respectively. The results are comparable to state-of-the-art algorithms in the absence of randomly corrupted attacks. To our best knowledge, this paper is the first to consider randomly corrupted attacks in online optimization. Simulations conducted on both synthetic examples and real-world datasets, namely MNIST and CIFAR-10, corroborate the resilience of L3GD.

The paper defines and studies manifold (M) convolutional filters and neural networks (NNs). Manifold filters and MNNs are defined in terms of the Laplace-Beltrami operator exponential and are such that graph (G) filters and neural networks (NNs) are recovered as discrete approximations when the manifold is sampled. These filters admit a spectral representation which is a generalization of both the spectral representation of graph filters and the frequency response of standard convolutional filters in continuous time. The main technical contribution of the paper is to analyze the stability of manifold filters and MNNs to smooth deformations of the manifold. This analysis generalizes known stability properties of graph filters and GNNs and it is also a generalization of known stability properties of standard convolutional filters and neural networks in continuous time. The most important observation that follows from this analysis is that manifold filters, same as graph filters and standard continuous time filters, have difficulty discriminating high frequency components in the presence of deformations. This is a challenge that can be ameliorated with the use of manifold, graph, or continuous time neural networks. The most important practical consequence of this analysis is to shed light on the behavior of graph filters and GNNs in large scale graphs.

The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present a fast inertial/momentum based algorithm for the phase retrieval problem. Our method can be seen as an extended algorithm of the Fast Griffin-Lim Algorithm, a method originally designed for phase retrieval in acoustics. The new numerical algorithm can be applied to a more general framework than acoustics, and as a main result of this paper, we prove a convergence guarantee of the new scheme. Consequently, we also provide an affirmative answer for the convergence of its ancestor Fast Griffin-Lim Algorithm, whose convergence remained unproven in the past decade. In the final chapter, we complement our theoretical findings with numerical experiments for the Short Time Fourier Transform phase retrieval and compare the new scheme with the Griffin-Lim Algorithm, the Fast Griffin-Lim Algorithm, and two other iterative algorithms typically used in acoustics.

Recently, the compressive diffusion strategies have been proposed to reduce the communication load of adaptive networks in the absence of link noises. In this paper, we are the first to study the compressive diffusion double normalized least mean square (CD${}^{2}$-NLMS) algorithm in the presence of noisy communication links. By means of the single update global weight error model, the transient and steady-state results of the CD${}^{2}$-NLMS algorithm are formulated analytically. One of the main findings is that the impact of link noises is well suppressed by use of small step-sizes and randomized projection vectors with a large variance in the second step of the algorithm. Taking advantage of the anti-link noise method and further combining with the traditional diffusion scheme, we ultimately design a novel auxiliary diffusion strategy to resist link noises in this paper. Different from the existing diffusion schemes, the designed auxiliary diffusion strategy consists of three steps: (i) weight update, (ii) auxiliary interaction, and (iii) weight combination, where the second step introduces an auxiliary estimation process to achieve the purpose of anti-link noise. Finally, numerical simulations are presented to demonstrate our theoretical analysis and the effectiveness of the proposed algorithms.

In this paper, we consider a wireless federated inference scenario in which devices and a server share a pre-trained machine learning model. The devices communicate statistical information about their local data to the server over a common wireless channel, aiming to enhance the quality of the inference decision at the server. Recent work has introduced federated conformal prediction (CP), which leverages devices-to-server communication to improve the reliability of the server's decision. With federated CP, devices communicate to the server information about the loss accrued by the shared pre-trained model on the local data, and the server leverages this information to calibrate a decision interval, or set, so that it is guaranteed to contain the correct answer with a pre-defined target reliability level. Previous work assumed noise-free communication, whereby devices can communicate a single real number to the server. In this paper, we study for the first time federated CP in a wireless setting. We introduce a novel protocol, termed wireless federated conformal prediction (WFCP), which builds on type-based multiple access (TBMA) and on a novel quantile correction strategy. WFCP is proved to provide formal reliability guarantees in terms of coverage of the predicted set produced by the server. Using numerical results, we demonstrate the significant advantages of WFCP against digital implementations of existing federated CP schemes, especially in regimes with limited communication resources and/or large number of devices.

Activity detection is an important task in the next generation grant-free multiple access. While there are a number of existing algorithms designed for this purpose, they mostly require precise information about the network, such as large-scale fading coefficients, small-scale fading channel statistics, noise variance at the access points, and user activity probability. Acquiring these information would take a significant overhead and their estimated values might not be accurate. This problem is even more severe in cell-free networks as there are many of these parameters to be acquired. Therefore, this paper sets out to investigate the activity detection problem without the above-mentioned information. In order to handle so many unknown parameters, this paper employs the Bayesian approach, where the unknown variables are endowed with prior distributions which effectively act as regularizations. Together with the likelihood function, a maximum a posteriori (MAP) estimator and a variational inference algorithm are derived. Extensive simulations demonstrate that the proposed methods, even without the knowledge of these system parameters, perform better than existing state-of-the-art methods, such as covariance-based and approximate message passing methods.

In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional iterative methods for minimizing nonconvex problems are sensitive to the initialization, have high computational complexity, and do not utilize the underlying graph structure behind the data. In this paper we propose three new estimators that are based on the Gauss-Newton method: 1) the elementwise graph-frequency-domain MAP (eGFD-MAP) estimator; 2) the sample graph signal processing MAP (sGSP-MAP) estimator; and 3) the GSP-MAP estimator. At each iteration, these estimators are updated by the outputs of two graph filters, with the previous state estimator and the residual as the input graph signals. The eGFD-MAP estimator is based on neglecting the mixed-derivatives of different graph frequencies in the Jacobian matrix and the off-diagonal elements in the covariance matrices. Consequently, it updates the elements of the graph signal in the graph-frequency domain independently, which reduces the computational complexity compared to the conventional MAP estimator. The sGSP-MAP and GSP-MAP estimators are based on optimizing the graph filters at each iteration of the Gauss-Newton algorithm. We state conditions under which the new estimators coincide with the MAP estimator in the case of an observation model with orthogonal graph frequencies. We evaluate the performance of the estimators for nonlinear graph signal recovery tasks, both with synthetic data and with the real-world problem of state estimation in power systems. These simulations show the advantages of the proposed estimators in terms of computational complexity, mean-squared-error, and robustness to the initialization of the algorithms.

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs.

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cramér-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB (BCRB) in the Bayesian framework. However, unlike the CRB, the BCRB is asymptotically unattainable in general, and its equality condition is restrictive. This paper introduces an extension of the Bobrovsky–Mayer-Wolf–Zakai class of bounds, also known as the weighted BCRB (WBCRB). The WBCRB is optimized by tuning the weighting function in the scalar case. Based on this result, we propose an asymptotically tight version of the bound called AT-BCRB. We prove that the AT-BCRB is asymptotically attained by the maximum a-posteriori probability (MAP) estimator. Furthermore, we extend the WBCRB and the AT-BCRB to the case of vector parameters. The proposed bounds are evaluated in several fundamental signal processing examples, such as variance estimation of white Gaussian process, direction-of-arrival estimation, and mean estimation of Gaussian process with unknown variance and prior statistical information. It is shown that unlike the BCRB, the proposed bounds are asymptotically attainable and coincide with the expected CRB (ECRB). The ECRB, which imposes uniformly unbiasedness, cannot serve as a valid lower bound in the Bayesian framework, while the proposed bounds are valid for any estimator.

This paper proposes a blind detection problem for low pass graph signals. Without assuming knowledge of the exact graph topology, we aim to detect if a set of graph signal observations are generated from a low pass graph filter. Our problem is motivated by the widely adopted assumption of low pass (a.k.a. smooth) signals required by existing works in graph signal processing (GSP), as well as the longstanding problem of network dynamics identification. Focusing on detecting low pass graph signals on modular graphs whose cutoff frequency coincides with the number of clusters in the graph, we study and leverage the unique spectral pattern exhibited by such low pass graph signals to devise two detectors: one is based on Perron-Frobenius theorem, one is based on the K-means score. We analyze the sample complexity of these detectors considering the effects of graph filter's properties, random delays, and other parameters. We show novel applications of the blind detector on robustifying graph learning, identifying antagonistic ties in opinion dynamics, and detecting anomalies in power systems. Numerical experiments validate our findings.

While traditional electromagnetic stealth materials/metasurfaces can render a target virtually invisible to some extent, they lack flexibility and adaptability, and can only operate within a limited frequency and angle/direction range, making it challenging to ensure the expected stealth performance. In view of this, we propose in this paper a new intelligent reflecting surface (IRS)-aided electromagnetic stealth system mounted on targets to evade radar detection, by utilizing the tunable passive reflecting elements of IRS to achieve flexible and adaptive electromagnetic stealth in a cost-effective manner. Specifically, we optimize the IRS’s reflection at the target to minimize the sum received signal power of all adversary radars. We first address the IRS’s reflection optimization problem using the Lagrange multiplier method and derive a semi-closed-form optimal solution for the single-radar setup, which is then generalized to the multi-radar case. To meet real-time processing requirements, we further propose low-complexity closed-form solutions based on the reverse alignment/cancellation and minimum mean-square error (MMSE) criteria for the single-radar and multi-radar cases, respectively. Additionally, we propose practical low-complexity estimation schemes at the target to acquire angle-of-arrival (AoA) and/or path gain information via a small number of receive sensing devices. Simulation results validate the performance advantages of our proposed IRS-aided electromagnetic stealth system with the proposed IRS reflection designs.

Current spectral compressed sensing methods via Hankel matrix completion employ symmetric factorization to demonstrate the low-rank property of the Hankel matrix. However, previous non-convex gradient methods only utilize asymmetric factorization to achieve spectral compressed sensing. In this paper, we propose a novel nonconvex projected gradient descent method for spectral compressed sensing via symmetric factorization named Symmetric Hankel Projected Gradient Descent (SHGD), which updates only one matrix and avoids a balancing regularization term. SHGD reduces about half of the computation and storage costs compared to the prior gradient method based on asymmetric factorization. Besides, the symmetric factorization employed in our work is completely novel to the prior low-rank factorization model, introducing a new factorization ambiguity under complex orthogonal transformation. Novel distance metrics are designed for our factorization method and a linear convergence guarantee to the desired signal is established with $O(r^{2}\log(n))$ observations. Numerical simulations demonstrate the superior performance of the proposed SHGD method in phase transitions and computation efficiency compared to state-of-the-art methods.

The $L_{1}/L_{2}$ norm ratio arose as a sparseness measure and attracted a considerable amount of attention due to three merits: (i) sharper approximations of $L_{0}$ compared to the $L_{1}$; (ii) parameter-free and scale-invariant; (iii) more attractive than $L_{1}$ under highly-coherent matrices. In this paper, we first establish the partly smooth property of $L_{1}$ over $L_{2}$ minimization relative to an active manifold ${\cal M}$ and also demonstrate its prox-regularity property. Second, we reveal that ADMM${}_{p}$ (or ADMM${}^{+}_{p}$) can identify the active manifold within a finite iterations. This discovery contributes to a deeper understanding of the optimization landscape associated with $L_{1}$ over $L_{2}$ minimization. Third, we propose a novel heuristic algorithm framework that combines ADMM${}_{p}$ (or ADMM${}^{+}_{p}$) with a globalized semismooth Newton method tailored for the active manifold ${\cal M}$. This hybrid approach leverages the strengths of both methods to enhance convergence. Finally, through extensive numerical simulations, we showcase the superiority of our heuristic algorithm over existing state-of-the-art methods for sparse recovery.

This paper considers the problem of locating a target in 2D from range measurements containing outliers. Assuming the number of outliers is known, we formulate the problem of minimizing inlier losses while ignoring outliers. This leads to a combinatorial, non-convex, non-smooth problem involving the percentile function. Using the framework of risk analysis from Rockafellar et al., we start by interpreting this formulation as a Value-at-Risk (VaR) problem from portfolio optimization. To the best of our knowledge, this is the first time that a localization problem was formulated using risk analysis theory. To solve the VaR formulation, we start by constructing a majorizer set that contains any solution of a general percentile problem. This construction is useful because, when applied to a localization scenario in 2D, it allows to majorize the solution set in terms of singletons, circumferences, ellipses and hyperbolas. Using known parametrizations of these curves, we propose a grid method for the original non-convex problem. So we reduce the task of optimizing the VaR objective to that of efficiently sampling the proposed majorizer set. We compare our algorithm with several benchmarks in target localization. Numerical simulations show that our method is fast while, on average, improving the accuracy of the best benchmarks by at least $100$ m in a $1$ Km${}^{2}$ area. Furthermore, our approach is shown to be robust when the number of outliers is over-estimated and the position of the anchors is either fixed or sampled uniformly in the $1$ Km${}^{2}$ area.

Visible light communication (VLC) is envisioned as an important technique for short-range communications, but its potential for user device (UD) localization is not fully exploited, which is challenging due to diffuse-scattering interference and random fading. In this paper, we focus on the 6 degree-of-freedom (DoF) UD state estimation (i.e., 3D location and 3D pose angles) based on VLC. Specifically, a novel successive convex approximation (SCA)-based optimization algorithm is proposed, where UD location, pose angles and channel state are simultaneously estimated. Thus, the disturbance of random fading and diffuse-scattering interference for UD localization is alleviated via VLC-assisted channel equalization, and hence our SCA-based 6-DoF state detection solution outperforms state-of-the-art baselines. In addition, a unified performance analysis framework is established for VLC-based 6-DoF state detection, and structured information models are exploited for tractable performance quantification. A closed-form Cramer-Rao lower bound on UD localization error and pose angle estimate error is established respectively, and the impact of measurement noise, scattering interference, bandwidth, the quantities of photodiodes and light-emitting-diodes, etc, on the VLC-based UD state detection performance is analysed. Our closed-form analysis cannot only shed lights on the performance limits of VLC-based 6D state detection, but also gain insights into the impact of system configuration and fading environments.

When a narrow-band source travels over a receiver, the observed signal will experience a Doppler frequency shift that can be exploited to determine its location. The Doppler shift is not constant even if the motion is linear with constant velocity and it has a rate of change. This work explores the Doppler derivatives (DDs) in addition to the Doppler-shifted frequencies (DSFs) encountered by a number of static receivers to locate the source in position and velocity, for the cases where the emitting frequency is known and not known. The algorithms from the literature are sub-optimum and require a one-dimensional grid search if the emitting frequency is not known. We first analyze the benefit of incorporating DD for DSF localization in terms of complexity lessening, performance improvement, and blind geometry reduction. The paper continues to develop localization algorithms for the known and unknown emitted frequency cases, in which one is the closed-form solution that is computationally attractive and the other is the semidefinite programming (SDP) solution that is noise resilient. The closed-form estimator is shown by theory to be optimum under small Gaussian noise. Both algorithms do not require grid search and their computational complexities are analyzed. Simulations support the promising performance of the proposed algorithms.

In this paper we propose a framework to leverage Lie group symmetries on arbitrary spaces exploiting algebraic signal processing (ASP). We show that traditional group convolutions are one particular instantiation of a more general Lie group algebra homomorphism associated to an algebraic signal model rooted in the Lie group algebra $L^{1}(G)$ for given Lie group $G$. Exploiting this fact, we decouple the discretization of the Lie group convolution elucidating two separate sampling instances: the filter and the signal. To discretize the filters, we exploit the exponential map that links a Lie group with its associated Lie algebra. We show that the discrete Lie group filter learned from the data determines a unique filter in $L^{1}(G)$, and we show how this uniqueness of representation is defined by the bandwidth of the filter given a spectral representation. We also derive error bounds for the approximations of the filters in $L^{1}(G)$ with respect to its learned discrete representations. The proposed framework allows the processing of signals on spaces of arbitrary dimension and where the actions of some elements of the group are not necessarily well defined. Finally, we show that multigraph convolutional signal models come as the natural discrete realization of Lie group signal processing models, and we use this connection to establish stability results for Lie group algebra filters. To evaluate numerically our results, we build neural networks with these filters and we apply them in multiple datasets, including a knot classification problem.

This paper presents a statistical signal processing-based algorithmic approach to enhance the compute signal-to-noise ratio (compute SNR) of 6T SRAM-based analog in-memory computing (IMC) architectures which have recently emerged as an attractive alternative to mainstream digital accelerators for machine learning workloads due to their superior energy efficiency and compute densities. However, today, the compute SNR of analog IMCs is limited by device parameter variations and noise. To overcome this limitation, we propose a maximum likelihood (ML)-based statistical error compensation (MLEC) technique to improve the accuracy of binary dot-products (DPs) realized in 6T (six transistor) SRAM-based analog IMC architectures. The MLEC method involves exploiting the symmetric nature of the 6T SRAM bitcell to extract multiple observations efficiently and employ them for detection purposes. MLEC methods involving two (MLEC-2) and four (MLEC-4) observations are proposed along with efficient architectures to realize them in hardware, e.g., distribution-aware and energy-aware approximations of MLEC-4. Simulations in a commercial $\mathbf{28} \mathrm{\mathbf{nm}}$ CMOS process demonstrate that the proposed methods increase the compute SNR for the commonly used 144-dimensional DP by $\mathbf{5} \mathrm{\mathbf{dB}}$-to-$\mathbf{12} \mathrm{\mathbf{dB}}$. This improvement in the bank-level compute SNR leads to a network-level accuracy improvement of up to $\mathbf{11} \boldsymbol{\mathbf{\%}}$ when a ResNet-20 (CIFAR-10 dataset) network is implemented on the IMC. Employing energy models of the IMC, the energy overhead of MLEC is estimated to lie between $\mathbf{3} \boldsymbol{\mathbf{\%}}$-to-$\mathbf{10} \boldsymbol{\mathbf{\%}}$ resulting in up to $\mathbf{45.6} \boldsymbol{\mathbf{\%}}$ and $\mathbf{18}\%$ increase in energy efficiency (1b-TOPS/W) for a target SNR of $\mathbf{20} \mathrm{\mathbf{dB}}$ and ResNet-20 accuracy of $\mathbf{90} \boldsymbol{\mathbf{\%}}$ on the CIFAR-10 dataset, respectively, compared to a conventional (uncompensated) 6T SRAM-based IMC.

The constrained composite-convex parameter estimation problem on the networked system, where the composite-convex function consists of a sum of node-specific smooth loss functions and a nonsmooth regularizer, is investigated in this paper. To reduce the communication burden, the event-triggered mechanism is introduced and the novel event-triggered proximal online gradient descent algorithm (EPOGDA) is proposed. The analysis shows that if the event-triggered threshold converges to zero as time tends to infinity and the cumulative difference between consecutive optimal values is sublinear, the dynamic regret of EPOGDA is sublinear. Further, we extend the proposed EPOGDA to the gradient-free scenarios, where the gradients are estimated using the Gaussian smoothed gradient estimator (GSGE). The GSGE-EPOGDA is presented and analyzed, which does not lead to performance degradation as compared to EPOGDA. Finally, the advantages of EPOGDA and GSGE-EPOGDA are verified on a distributed multi-sensor network.

We consider the problem of tracking the velocity profile of a target or phenomenon, which is distributed across its range, such as atmospheric wind velocity across altitudes from radar measurements. Typical pulsed radars apply spectral techniques on the matched filtered samples collected from the return echoes at each range bin. Both the true signal as well as the false targets can lead to prominent peaks in the spectral domain, and the recovery algorithms should identify the true profile across range bins. When the measurements in adjacent range bins are correlated, a dynamic program-based data association turns out to be highly suitable. This algorithm is popularly known as the Viterbi Data Association (VDA). While VDA has good performance when the true signal is present along with a small number of competing false spectral peaks in each range bin, poor SNRs from high altitude reflections may trigger several false peaks, considerably deteriorating the performance of the VDA. The main contribution of the current paper is in incorporating frequency domain subspace methods (in particular, Frequency selective ESPRIT) to iteratively refine the measurements such that the VDA can further improve the best-identified track so far. When data from multiple sensors are available, the proposed Iterative VDA (IVDA) algorithm can be further reinforced using multi-sensor fusion techniques, which we call the Reinforced IVDA. Both of the proposed algorithms demonstrate significant performance improvements in estimating target velocity at altitudes with low SNRs. In addition to simulations, the proposed algorithms are validated on field data collected from a Mesosphere Stratosphere Troposphere (MST) wind profiling radar.

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy, researchers introduce extra constraints to the measuring procedure by including a random aperture mask in the optical path that randomly modulates the light projected on the target object and gives the coded diffraction patterns (CDP). It is known that random masks are non-bandlimited and can lead to considerable high-frequency components in the Fourier intensity measurements. These high-frequency components can be beyond the Nyquist frequency of the optical system and are thus ignored by the phase retrieval optimization algorithms, resulting in degraded reconstruction performances. Recently, our team developed a binary green noise masking scheme that can significantly reduce the high-frequency components in the measurement. However, the scheme cannot be extended to generate multiple-level aperture masks. This paper proposes a two-stage optimization algorithm to generate multi-level random masks named OptMask that can also significantly reduce high-frequency components in the measurements but achieve higher accuracy than the binary masking scheme. Extensive experiments on a practical optical platform were conducted. The results demonstrate the superiority and practicality of the proposed OptMask over the existing masking schemes for CDP phase retrieval.

Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive ‘adversary’ tracks its target of interest via a stochastic framework such as a Kalman filter (KF). The target or ‘defender’ then employs another inverse stochastic filter to infer the forward filter estimates of the defender computed by the adversary. For linear systems, the inverse Kalman filter (I-KF) has been recently shown to be effective in these counter-adversarial applications. In the paper, contrary to prior works, we focus on non-linear system dynamics and formulate the inverse unscented KF (I-UKF) to estimate the defender's state based on the unscented transform, or equivalently, statistical linearization technique. We then generalize this framework to unknown systems by proposing reproducing kernel Hilbert space-based UKF (RKHS-UKF) to learn the system dynamics and estimate the state based on its observations. Our theoretical analyses to guarantee the stochastic stability of I-UKF and RKHS-UKF in the mean-squared sense show that, provided the forward filters are stable, the inverse filters are also stable under mild system-level conditions. We show that, despite being a suboptimal filter, our proposed I-UKF is a conservative estimator, i.e., I-UKF's estimated error covariance upper-bounds its true value. Our numerical experiments for several different applications demonstrate the estimation performance of the proposed filters using recursive Cramér-Rao lower bound and non-credibility index (NCI).

The dual objective of this paper is to first characterize the probability distribution of the random variable (RV), $U$, equivalent to the sum of multiple products of two independent circularly symmetric complex normal (CN) RVs, in order to then evaluate the fundamental limit of multi-input multi-output (MIMO)-reconfigurable intelligent surface (RIS) communication systems in terms of channel/signal-to-noise ratio (SNR) gain. First, we derive simple closed-form expressions of the joint moment generating function and probability density function (pdf) of the real and imaginary parts of $U$, as well as the pdf and mean value of $|U|$, and validate their accuracy via numerical simulations. Second, we provide a rigorous analysis of how MIMO-RIS improves channel propagation by relying on our probabilistic characterization of $U$. More specifically, we obtain a simple upper bound of the MIMO-RIS capacity, expressed as a function of its channel gain, for a large number of RIS elements. We then derive closed-form expressions of this channel gain, as well as the MIMO-RIS to MIMO SNR gain, and validate their accuracy via numerical simulations. Our analysis leads to the following insights: 1) RIS improvement in channel propagation accounts for a “baseline”/intrinsic improvement due to the amplitude response of each RIS phase-shifter element and a directionality improvement due to the optimization of the RIS phase-shifters used for steering the incident radiation towards its intended direction. 2) The intrinsic improvement is larger than the directionality improvement, and the latter is only significant when the number of RIS elements is very large in comparison with the square root of the product between the number of transmit and receive antennas.

This paper considers a binary sequential joint detection and estimation problem, which aims to find an optimal scheme to minimize the average stopping time under the constraints on the detection error probabilities and the estimation errors. The scheme consists of a randomized stopping rule, a randomized detector and two estimators under two different decisions. To obtain the optimal scheme, we need to solve a non-convex minimization problem defined on a complicated Banach space. First, this non-convex problem is equivalently transformed into a concave maximization problem defined on a finite-dimensional Hilbert space, which however involves an objective function without closed-form expression. Then, by exploiting Danskin's theorem, the subdifferential of the objective function can be computed. Next, we propose a globally convergent algorithm based on the projected subgradient method to obtain the globally optimal solution of the convex problem. Last, by utilizing the solution of the convex problem, we provide a method to efficiently construct a solution of the original non-convex problem, i.e., the optimal randomized stopping rule, randomized detector and estimators. The numerical simulation results show the verifications of our methods.

When parameters of mobile telecommunication channels change rapidly, classical adaptive filters, such as exponentially weighted least squares algorithms or gradient algorithms, fail to estimate them with sufficient accuracy. In cases like this, one can use identification methods based on explicit models of parameter changes such as the method of basis functions (BF). When prior knowledge about parameter changes is available the BF approach can be optimized. The paper presents and compares three locally optimized BF algorithms differing in computational requirements. It also demonstrates how the performance of the proposed algorithms can be enhanced in cases where prior knowledge depends on unknown and/or time-varying environmental factors.

One-bit compressed sensing has found broad applications. Due to the constraint on the unit sphere, the classic $\ell_{1}$ minimization frequently returns a signal which is not sparse enough. In this paper, $\ell_{1}-\ell_{q} (1<q\leq 2)$ nonconvex minimization method is developed for one-bit compressed sensing. We demonstrate that $\ell_{1}-\ell_{q}$ minimization does return a much sparser signal than $\ell_{1}$ minimization. Furthermore, we establish $\ell_{1}-\ell_{q}$ optimization iterative algorithm inspired by difference-of-convex algorithm (DCA), and prove the convergence of the new algorithm. Theoretical proofs show that $\ell_{1}-\ell_{q}$ minimization method performs better when $q$ is closer to $1$, and our algorithm converges in finite steps in normal cases. Numerical experiments display the advantage of this new algorithm compared to the existing ones.

Joint blind source separation (JBSS) is a powerful methodology for analyzing multiple related datasets, able to jointly extract sources that describe statistical dependencies across the datasets. However, JBSS can be computationally prohibitive with high-dimensional data, thus there exists a key need for more efficient JBSS algorithms. JBSS algorithms typically rely on numerical solutions, which may be expensive due to their iterative nature. In contrast, analytic solutions follow consistent procedures that are often less expensive. In this paper, we introduce an efficient analytic solution for JBSS. Denoting a set of sources dependent across the datasets as a “source component vector” (SCV), our solution minimizes correlation among separate SCVs by minimizing distance of the SCV cross-covariance’s eigenvector matrix from a block diagonal matrix. Under the orthogonality constraint, this leads to a system of linear equations wherein each subproblem has an analytic solution. We derive identifiability conditions of our solution’s estimator, and demonstrate estimation performance and time efficiency in comparison with other JBSS algorithms that exploit source correlation across datasets. Results demonstrate that our solution achieves the lowest asymptotic computational complexity among JBSS algorithms, and is capable of superior estimation performance compared with algorithms of similar complexity.

This paper proposes a multi-dimensional resource management (MRM) scheme for multifunctional radar systems that aims to improve multiple target tracking accuracy under dynamic jamming environments. The proposed scheme constructs an optimization model to coordinate the radar's power and frequency resources. To combat dynamic jammers, we present a Reinforcement Learning based active anti-jamming Markov Decision Process model. The resulting signal to interference plus noise ratio and the Bayesian Cramer-Rao lower bound under jamming environments are calculated, and a multiple target tracking performance optimization model is built for the MRM scheme. We show that the MRM problem can be decoupled as two subproblems, one for combating dynamic jammer and the other for resource allocation. A two-step solution technique is developed to solve the resulting optimization subproblem based on decoupling analysis, and the obtained solution is proven to maximize target tracking performance. Simulation results indicate that the proposed method can evidently beat the dynamic jamming and improve the target tracking accuracy within a given power budget.

In radar and communication systems, there exist a large class of signals with constant modulus property, including BPSK, QPSK, LFM, and phase-coded signals. In this paper, we focus on the problem of joint constant modulus waveform estimation and interference suppression from signals received at an antenna array. Instead of seeking a compromise between interference suppression and output noise power reduction by the Capon method or utilizing the interference direction (ID) prior to place perfect nulls at the IDs and subsequently minimize output noise power by the linearly constrained minimum variance (LCMV) beamformer, we devise a novel power ratio criterion, namely, interference-plus-noise-to-noise ratio (INNR) in the beamformer output to attain perfect interference nulling and minimal output noise power as in LCMV yet under the unknown ID case. A two-stage fractional program-based method is developed to jointly suppress the interferences and estimate the constant modulus waveform. In the first stage, we formulate an optimization model with a fractional objective function to minimize the INNR. Then, in the second stage, another fraction-constrained optimization problem is established to refine the weight vector from the solution space constrained by the INNR bound, to achieve approximately perfect nulls and minimum output noise power. Moreover, the solution is further extended to tackle the case with steering vector errors. Numerical results demonstrate the excellent performance of our methods.

This paper studies the relationship between a graph neural network (GNN) and a manifold neural network (MNN) when the graph is constructed from a set of points sampled from the manifold, thus encoding geometric information. We consider convolutional MNNs and GNNs where the manifold and the graph convolutions are respectively defined in terms of the Laplace-Beltrami operator and the graph Laplacian. Using the appropriate kernels, we analyze both dense and moderately sparse graphs. We prove non-asymptotic error bounds showing that convolutional filters and neural networks on these graphs converge to convolutional filters and neural networks on the continuous manifold. As a byproduct of this analysis, we observe an important trade-off between the discriminability of graph filters and their ability to approximate the desired behavior of manifold filters. We then discuss how this trade-off is ameliorated in neural networks due to the frequency mixing property of nonlinearities. We further derive a transferability corollary for geometric graphs sampled from the same manifold. We validate our results numerically on a navigation control problem and a point cloud classification task.

The problem of robustly reconstructing an integer vector from its erroneous remainders appears in many applications in the field of multidimensional (MD) signal processing. To address this problem, a robust MD Chinese remainder theorem (CRT) was recently proposed for a special class of moduli, where the remaining integer matrices left-divided by a greatest common left divisor (gcld) of all the moduli are pairwise commutative and coprime. The strict constraint on the moduli limits the usefulness of the robust MD-CRT in practice. In this paper, we investigate the robust MD-CRT for a general set of moduli. We first introduce a necessary and sufficient condition on the difference between paired remainder errors, followed by a simple sufficient condition on the remainder error bound, for the robust MD-CRT for general moduli, where the conditions are associated with (the minimum distances of) these lattices generated by gcld's of paired moduli, and a closed-form reconstruction algorithm is presented. We then generalize the above results of the robust MD-CRT from integer vectors/matrices to real ones. Finally, we validate the robust MD-CRT for general moduli by employing numerical simulations, and apply it to MD sinusoidal frequency estimation based on multiple sub-Nyquist samplers.

Recent literature shows a growing interest in the integration of federated learning (FL) and multilevel stochastic compositional optimization (MSCO), which arises in meta-learning and reinforcement learning. It is known that a bottleneck in FL is communication efficiency, when compared to non-distributed methods. Yet, it remains unclear whether communication-efficient algorithms exist for MSCO in distributed settings. Single-loop optimizations, used in recent methods, structurally require communications per fixed samples generated, resulting in communication complexity being no less than sample complexity, hence lower bounded by $\mathcal{O}(1/\epsilon)$, for reaching an $\epsilon$-accurate solution. This paper studies distributed MSCO of a smooth and strongly convex objective with smooth gradients. Based on a double-loop strategy, we proposed Federated Stochastic Compositional Gradient Extrapolation (FedSCGE), a federated MSCO method that attains an optimal $\mathcal{O}(\log\frac{1}{\epsilon})$ communication complexity while maintaining an (almost) optimal $\tilde{\mathcal{O}}(1/\epsilon)$ sample complexity, both of which independent of client number, making the approach scalable. Our analysis leverages the random gradient extrapolation method (RGEM) in [19] and generalizes it by overcoming the biased gradients of MSCO. To the best of our knowledge, our work is the first to show the simultaneous attainability of both complexity bounds for distributed MSCO.

In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising an appropriate kernel, we show that this problem has a solution that can be evaluated in a distributed way. We interpret the problem and solution using both deterministic and Bayesian perspectives and link them to existing graph signal processing and GGSP frameworks. We then provide an online implementation via random Fourier features. Under the Bayesian framework, we investigate the statistical performance under the asymptotic sampling scheme. Finally, we validate our theory and methods on real-world datasets.

In this paper, we introduce a novel resource allocation approach for integrated sensing-communication (ISAC) using the Kullback–Leibler divergence (KLD) metric. Specifically, we consider a base-station with limited power and antenna resources serving a number of communication users and detecting multiple targets simultaneously. First, we analyse the KLD for two possible antenna deployments, which are the separated and shared deployments, then use the results to optimise the resources of the base-station through minimising the average KLD for the network while satisfying a minimum predefined KLD requirement for each user equipment (UE) and target. To this end, the optimisation is formulated and presented as a mixed integer non-linear programming (MINLP) problem and then solved using two approaches. In the first approach, we employ a genetic algorithm, which offers remarkable performance but demands substantial computational resources; and in the second approach, we propose a rounding-based interior-point method (RIPM) that provides a more computationally-efficient alternative solution at a negligible performance loss. The results demonstrate that the KLD metric can be an effective means for optimising ISAC networks, and that both optimisation solutions presented offer superior performance compared to uniform power and antenna allocation.

Passive monitoring of acoustic or radio sources has important applications in modern convenience, public safety, and surveillance. A key task in passive monitoring is multiobject tracking (MOT). This paper presents a Bayesian method for multisensor MOT for challenging tracking problems where the object states are high-dimensional, and the measurements follow a nonlinear model. Our method is developed in the framework of factor graphs and the sum-product algorithm (SPA) and implemented using random samples or “particles”. The multimodal probability density functions provided by the SPA are effectively represented by a Gaussian mixture model (GMM). To perform the operations of the SPA with improved sample efficiency, we make use of particle flow (PFL). Here, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. This makes it possible to obtain good object detection and tracking performance even in challenging multisensor MOT scenarios with single sensor measurements that have a lower dimension than the object positions. We perform a numerical evaluation in a passive acoustic monitoring scenario where multiple sources are tracked in 3-D from 1-D time-difference-of-arrival (TDOA) measurements provided by pairs of hydrophones. Our numerical results, obtained by processing synthetic and real data, demonstrate favorable detection and estimation accuracy compared to state-of-the-art reference techniques.

This paper proposes a scalable distributed policy gradient method and proves its convergence to near-optimal solution in multi-agent linear quadratic networked systems. The agents engage within a specified network under local communication constraints, implying that each agent can only exchange information with a limited number of neighboring agents. On the underlying graph of the network, each agent implements its control input depending on its nearby neighbors’ states in the linear quadratic control setting. We show that it is possible to approximate the exact gradient only using local information. Compared with the centralized optimal controller, the performance gap decreases to zero exponentially as the communication and control ranges increase. We also demonstrate how increasing the communication range enhances system stability in the gradient descent process, thereby elucidating a critical trade-off. The simulation results verify our theoretical findings.

In machine learning applications, data are often high-dimensional and intricately related. It is often of interest to find the underlying structure and Granger causal relationships among the data and represent these relationships with directed graphs. In this paper, we study multivariate time series, where each series is associated with a node of a graph, and where the objective is to estimate the topology of a sparse graph that reflects how the nodes of the graph affect each other, if at all. We propose a novel fully Bayesian approach that employs a sparsity-encouraging prior on the hyperparameters. The proposed method allows for nonlinear and multiple lag relationships among the time series. The method is based on Gaussian processes, and it treats the entries of the graph adjacency matrix as hyperparameters. It utilizes a modified automatic relevance determination (ARD) kernel and allows for learning the mapping function from selected past data to current data as edges of a graph. We show that the resulting adjacency matrix provides the intrinsic structure of the graph and answers causality-related questions. Numerical tests show that the proposed method has comparable or better performance than state-of-the-art methods.

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the set defined by one of the constraints, our algorithm only requires projecting onto a half-space approximation of the set, which significantly reduces the computational cost as it admits a closed-form formula. Second, to exploit the structure that the objective is a sum, variance reduction is incorporated into our algorithm to further improve the performance. As theoretical contributions, under a novel error bound condition and other standard assumptions, we prove that the proposed RPM converges to an optimal solution and that both optimality and feasibility gaps vanish at a sublinear rate. In particular, via a new analysis framework, we show that our RPM attains a faster convergence rate in optimality gap than existing RPMs when the objective function has a Lipschitz continuous gradient, capitalizing the benefit of the variance reduction. We also provide sufficient conditions for the error bound condition to hold. Experiments on a beamforming problem and a robust classification problem are presented to demonstrate the superiority of our RPM over existing ones.

Colocated multiple-input multiple-output (MIMO) technology has been widely used in automotive radars as it provides accurate angular estimation of the objects with a relatively small number of transmitting and receiving antennas. Since the Direction Of Departure (DOD) and the Direction Of Arrival (DOA) of line-of-sight targets coincide, MIMO signal processing allows for the formation of a larger virtual array for angle finding. However, multiple paths impinging the receiver is a major limiting factor, in that radar signals may bounce off obstacles, creating echoes for which the DOD does not equal the DOA. Thus, in complex scenarios with multiple scatterers, the direct paths of the intended targets may be corrupted by indirect paths from other objects, which leads to inaccurate angle estimation or ghost targets. In this paper, we focus on detecting the presence of ghosts due to multipath by regarding it as the problem of deciding between a composite hypothesis, ${\cal H}_{0}$ say, that the observations only contain an unknown number of direct paths sharing the same (unknown) DOD's and DOA's, and a composite alternative, ${\cal H}_{1}$ say, that the observations also contain an unknown number of indirect paths, for which DOD's and DOA's do not coincide. We exploit the Generalized Likelihood Ratio Test (GLRT) philosophy to determine the detector structure, offering closed-form expressions for theoretical detection performance, and a convex waveform optimization approach to improve detection performance. In practical scenarios, the unknown parameters of GLRT philosophy are replaced by carefully designed estimators. The angles of both the active direct paths and of the multi-paths are indeed estimated through a sparsity-enforced Compressed Sensing (CS) approach with Levenberg-Marquardt (LM) optimization to estimate the angular parameters in the continuous domain. Simulation and experimental results are finally offered in order to validate the proposed solution.

In the rapidly advancing landscape of 6G, characterized by ultra-high-speed wideband transmission in millimeter-wave and terahertz bands, our paper addresses the pivotal task of enhancing physical layer security (PLS) within near-field wideband communications. We introduce true-time delayer (TTD)-incorporated analog beamfocusing techniques designed to address the interplay between near-field propagation and wideband beamsplit, an uncharted domain in existing literature. Our approach to maximizing secrecy rates involves formulating an optimization problem for joint power allocation and analog beamformer design, employing a two-stage process encompassing a semi-digital solution and analog approximation. This problem is efficiently solved through a combination of alternating optimization, fractional programming, and block successive upper-bound minimization techniques. Additionally, we present a low-complexity beamsplit-aware beamfocusing strategy, capitalizing on geometric insights from near-field wideband propagation, which can also serve as a robust initial value for the optimization-based approach. Numerical results substantiate the efficacy of the proposed methods, clearly demonstrating their superiority over TTD-free approaches in fortifying wideband PLS, as well as the advantageous secrecy energy efficiency achieved by leveraging low-cost analog devices.

Message passing algorithms on graphical models offer a low-complexity and distributed paradigm for performing marginalization from a high-dimensional distribution. However, the convergence behaviors of message passing algorithms can be heavily affected by the adopted message update schedule. In this paper, we focus on the variational message passing (VMP) applied to Gaussian graphical models and its convergence under different schedules is analyzed. In particular, based on the update equations of VMP under the mean-field assumption, we prove that the mean vectors obtained from VMP are the exact marginal mean vectors under any valid message passing schedule, giving the legitimacy of using VMP in Gaussian graphical models. Furthermore, three categories of valid message passing schedules, namely serial schedule, parallel schedule and randomized schedule are considered for VMP update. In the basic serial schedule, VMP unconditionally converges, but could be slow in large-scale distributed networks. To speed up the serial schedule, a group serial schedule is proposed while guaranteeing the VMP convergence. On the other hand, parallel schedule and its damped variant are applied to accelerate VMP, where the necessary and sufficient convergence conditions are derived. To allow nodes with different local computation resources to compute messages more flexibly and efficiently, a randomized schedule is proposed for VMP update, and the probabilistic necessary and sufficient convergence conditions are presented. Finally, numerical results and applications are presented to illustrate the trade-offs in the ease and speed of convergence.

This paper addresses the Sensor Network Localization (SNL) problem using received signal strength. The SNL is formulated as an Euclidean Distance Matrix Completion (EDMC) problem under the unit ball sample model. Using the Burer-Monteiro factorization type cost function, the EDMC is solved by Riemannian conjugate gradient with Hager-Zhang line search method on a quotient manifold. A “rank reduction” pre-process is proposed for proper initialization and to achieve global convergence with high probability. Simulations on a synthetic scene show that our approach attains better localization accuracy and is computationally efficient compared to several baseline methods. Characterization of a small local basin of attraction around the global optima of the s-stress function under Bernoulli sampling rule and incoherence matrix completion framework is conducted for the first time. Theoretical result conjectures that the Euclidean distance problem with a structure-less sample mask can be effectively handled using spectral initialization followed by vanilla first-order methods. This preliminary analysis, along with the aforementioned numerical accomplishments, provides insights into revealing the landscape of the s-stress function and may stimulate the design of simpler algorithms to tackle the non-convex formulation of general EDMC problems.

This paper focuses on minimizing the decentralized finite-sum optimization over a network, where each pair of neighboring agents is associated with a nonlinear proximity constraint. Additionally, each agent possesses a private convex cost that can be decomposed into an average of multiple constituent functions. The goal of the network is to collectively minimize the sum of individual costs while satisfying all constraints. Due to their fast convergence and low computational burden, stochastic variance reduction methods have primarily been studied for finite-sum minimization problems. However, these algorithms did not consider the constrained optimization problems. To bridge this gap, we propose a decentralized stochastic algorithmic framework called VQ-VR. This framework extends the virtual-queue-based algorithm introduced in [1] to stochastic settings for constrained optimization instead of using the classical saddle point method. VQ-VR operates between stochastic variance-reduced gradient descent steps and virtual queue updates. Furthermore, we describe and analyze two specific instantiations of this framework, namely VQ-SVRG and VQ-SAGA. Our convex analysis relies on the drift of a novel quadratic Lyapunov function. We prove that VQ-SVRG and VQ-SAGA both achieve the sublinear convergence rate of $\mathcal{O}(1/K)$ in terms of expected cost suboptimality and constraint violations for smooth and general convex problems, where $K$ is the number of iterations. To the best of our knowledge, VQ-VR is the first stochastic algorithm capable of solving decentralized nonlinear constrained optimization problems with a convergence rate of $\mathcal{O}(1/K)$. Additionally, we present numerical results on two specific applications: decentralized QCQP and decentralized logistic regression. These results verify the theoretical results and demonstrate that, on a per-gradient-evaluation basis, our algorithms achieve a relative cost gap improvement of more than 7dB compared to existing methods.

The continuously growing size of deep neural networks (DNNs) has sparked a surge in research on model compression techniques. Among these techniques, multi-resolution model compression has emerged as a promising approach which can generate multiple DNN models with shared weights and different computational complexity (resolution) through a single training. However, in most existing multi-resolution compression methods, the model structures for different resolutions are either predefined or uniformly controlled. This can lead to performance degradation as they fail to implement systematic compression to achieve the optimal model for each resolution. In this paper, we propose to perform multi-resolution compression from a Bayesian perspective. We design a resolution-aware likelihood and a two-layer prior for the channel masks, which allow joint optimization of the shared weights and the model structure of each resolution. To solve the resulted Bayesian inference problem, we develop a low complexity partial update block variational Bayesian inference (PUB-VBI) algorithm. Furthermore, we extend our proposed method into the arbitrary resolution case by proposing an auxiliary neural network (NN) to learn the mapping from the input resolution to the corresponding channel masks. Simulation results show that our proposed method can outperform the baselines on various NN models and datasets.

An autonomous underwater vehicle (AUV) can be employed to estimate an underwater target's position using the Doppler shift measurement extracted from received signals. Conventionally, the received signals have to be divided into several short frames so that the Doppler shift is constant in each one. When the AUV is far away from the target, the signal to noise ratio (SNR) is quite low. An intuitive solution is to increase the frame length to suppress noise and boost SNR. However, it is worth noting that the Doppler shift is actually changing over time, and the prolonged frame length will inevitably induce modeling error. This is a fundamental dilemma in the Doppler-shift-based underwater localization. In this paper, we reveal that the assumption of constant Doppler shift comes from the zero-th order Taylor expansion of the real-time model. To increase the frame length without jeopardizing the model accuracy, we modify the model by taking the first-order Taylor expansion. By doing so, the frame length can be prolonged by one order of magnitude without introducing non-negligible modeling error. What this new model says is that when the target broadcasts a single-tone signal, the AUV will receive a linear frequency modulated (LFM) signal parameterized by a Doppler shift and a corresponding changing rate, i.e., Doppler rate. Although the Doppler rate is very small, it helps us improve the estimation accuracy of Doppler shift. Besides, the Doppler rate also contains target's position information. Thus, a two-phase localization algorithm is proposed by jointly using the Doppler shift and the Doppler rate measurements. Intuitively, the Doppler rate is only loosely related to the target's position and should not significantly contribute to the localization accuracy, but the Cramér-Rao lower bound (CRLB) analysis says differently. This can be explained by showing that the Doppler rate complements the vanishing degree of freedom (DoF) in the position information for far-field localization, i.e., the information fusion. The theoretical results are verified through extensive simulations.

Federated learning (FL) is an emerging machine learning paradigm for training models across multiple edge devices holding local data sets, without explicitly exchanging the data. Recently, over-the-air (OTA) FL has been suggested to reduce the bandwidth and energy consumption, by allowing the users to transmit their data simultaneously over a Multiple Access Channel (MAC). However, this approach results in channel noise directly affecting the optimization procedure, which may degrade the accuracy of the trained model. In this paper we jointly exploit the prior distribution of local weights and the channel distribution, and develop an OTA FL algorithm based on a Bayesian approach for signal aggregation. Our proposed technique, dubbed Bayesian Air Aggregation Federated learning (BAAF), is shown to effectively mitigate noise and fading effects induced by the channel. To handle statistical heterogeneity of users data, which is a second major challenge in FL, we extend BAAF to allow for appropriate local updates by the users and develop the Controlled Bayesian Air Aggregation Federated-learning (COBAAF) algorithm. In addition to using a Bayesian approach to average the channel output, COBAAF controls the drift in local updates using a judicious design of correction terms. We analyze the convergence of the learned global model using BAAF and COBAAF in noisy and heterogeneous environments, showing their ability to achieve a convergence rate similar to that achieved over error-free channels. Simulation results demonstrate the improved convergence of BAAF and COBAAF over existing methods in machine learning tasks.

Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random variables with a fixed and known number of vector elements, while certain applications rely on random finite sets (RFSs) with an unknown number of vector elements. In this paper, we develop BP rules for factor graphs defined on sequences of RFSs where each RFS has an unknown number of elements, with the intention of deriving novel inference methods for RFSs. Furthermore, we show that vector-type BP is a special case of set-type BP, where each RFS follows the Bernoulli process. To demonstrate the validity of developed set-type BP, we apply it to the Poisson multi-Bernoulli (PMB) filter for simultaneous localization and mapping (SLAM), which naturally leads to a set-type BP PMB-SLAM method, which is analogous to a vector type SLAM method, subject to minor modifications.

Part I of this two-part paper focused on the formulation of percentile problems, complexity analysis, and development of power control algorithms via the quadratic fractional transform (QFT) and logarithmic fractional transform (LFT) for sum-least-$q^{\mathrm{th}}$-percentile (SLqP) rate maximization problems. In this second part, we first tackle the significantly more challenging problems of optimizing SLqP rate via beamforming in a multiuser, multiple-input multiple-output (MU-MIMO) network to maximize cell-edge throughput. To this end, we first propose an adaptation of the QFT algorithm presented in Part I that enables optimization of the complex-valued multidimensional beamforming weights for the SLqP rate utility function. We also introduce a new class of problems which we term as sum-greatest-$q^{\mathrm{th}}$-percentile weighted mean squared error (SGqP-WMSE) minimization. We show that this class subsumes the well-known sum-weighted mean squared error (WMMSE) minimization and max-WMSE minimization problems. We demonstrate an equivalence between this class of problems and the SLqP rate maximization problems, and show that this correspondence can be exploited to obtain stationary-point solutions for the aforementioned beamforming problem. Next, we develop extensions for the QFT and LFT algorithms from Part I to optimize ergodic long-term average or ergodic SLqP utility. Finally, we also consider related problems which can be solved using the proposed techniques, including hybrid utility functions targeting optimization at specific subsets of users within cellular networks.