WaveMax: Radar Waveform Design via Convex Maximization of FrFT Phase Retrieval

The ambiguity function (AF) is a critical tool in radar waveform design, representing the two-dimensional correlation between a transmitted signal and its time-delayed, frequency-shifted version. Obtaining a radar signal to match a specified AF magnitude is a bi-variate variant of the well-known phase retrieval problem. Prior approaches to this problem were either limited to a few classes of waveforms or lacked a computable procedure to estimate the signal. Our recent work provided a framework for solving this problem for both band- and time-limited signals using non-convex optimization. In this paper, we introduce a novel approach WaveMax that formulates waveform recovery as a convex optimization problem by relying on the fractional Fourier transform (FrFT)-based AF. We exploit the fact that AF of the FrFT of the original signal is equivalent to a rotation of the original AF. In particular, we reconstruct the radar signal by solving a low-rank minimization problem, which approximates the waveform using the leading eigenvector of a matrix derived from the AF. Our theoretical analysis shows that unique waveform reconstruction is achievable with a sample size no more than three times the signal frequencies or time samples. Numerical experiments validate the efficacy of WaveMax in recovering signals from noiseless and noisy AF, including scenarios with randomly and uniformly sampled sparse data.

Deep Learning Model-Based Channel Estimation for THz Band Massive MIMO with RF Impairments

THz band enabled large scale massive MIMO (M-MIMO) is considered as a key enabler for the 6G technology, given its enormous bandwidth and for its low latency connectivity. In the large-scale M-MIMO configuration, enlarged array aperture and small wavelengths of THz results in an amalgamation of both far field and near field paths, which makes tasks such as channel estimation for THz M-MIMO highly challenging. Moreover, at the THz transceiver, radio frequency (RF) impairments such as phase noise (PN) of the analog devices also leads to degradation in channel estimation performance. Classical estimators as well as traditional deep learning (DL) based algorithms struggle to maintain their robustness when performing for large scale antenna arrays i.e., M-MIMO, and when RF impairments are considered for practical usage. To effectively address this issue, it is crucial to utilize a neural network (NN) that has the ability to study the behaviors of the channel and RF impairment correlations, such as a recurrent neural network (RNN). The RF impairments act as sequential noise data which is subsequently incorporated with the channel data, leading to choose a specific type of RNN known as bidirectional long short-term memory (BiLSTM) which is followed by gated recurrent units (GRU) to process the sequential data. Simulation results demonstrate that our proposed model outperforms other benchmark approaches at various signal-to-noise ratio (SNR) levels.

Near-Field Signal Processing: Unleashing the Power of Proximity

After nearly a century of specialized applications in optics, remote sensing, and acoustics, the near-field (NF) electromagnetic propagation zone is experiencing a resurgence in research interest. This renewed attention is fueled by the emergence of promising applications in various fields such as wireless communications, holography, medical imaging, and quantum-inspired systems. Signal processing within NF sensing and wireless communications environments entails addressing issues related to extended scatterers, range-dependent beampatterns, spherical wavefronts, mutual coupling effects, and the presence of both reactive and radiative fields. Recent investigations have focused on these aspects in the context of extremely large arrays and wide bandwidths, giving rise to novel challenges in channel estimation, beamforming, beam training, sensing, and localization. While NF optics has a longstanding history, advancements in NF phase retrieval techniques and their applications have lately garnered significant research attention. Similarly, utilizing NF localization with acoustic arrays represents a contemporary extension of established principles in NF acoustic array signal processing. This article aims to provide an overview of state-of-the-art signal processing techniques within the NF domain, offering a comprehensive perspective on recent advances in diverse applications.

CoFAR Clutter Estimation using Covariance-Free Bayesian Learning

A cognitive fully adaptive radar (CoFAR) adapts its behavior on its own within a short period of time in response to changes in the target environment. For the CoFAR to function properly, it is critical to understand its operating environment through estimation of the clutter channel impulse response (CCIR). In general, CCIR is sparse but prior works either ignore it or estimate the CCIR by imposing sparsity as an explicit constraint in their optimization problem. In this paper, contrary to these studies, we develop covariance-free Bayesian learning (CoFBL) techniques for estimating sparse CCIR in a CoFAR system. In particular, we consider a multiple measurement vector scenario and estimate a simultaneously sparse (row sparse) CCIR matrix. Our CoFBL framework reduces the complexity of conventional sparse Bayesian learning through the use of the diagonal element estimation rule and conjugate gradient descent algorithm. We show that the framework is applicable to various forms of CCIR sparsity models: group, joint, and joint-cum-group. We evaluate our method through numerical experiments on a data set generated using RFView, a high-fidelity modeling and simulation tool. We derive Bayesian Cram\'{e}r-Rao bounds for the various considered scenarios to benchmark the performance of our algorithms. Our results demonstrate that the proposed CoFBL-based approaches perform better than the existing popular approaches such as multiple focal underdetermined system solver and simultaneous orthogonal matching pursuit.

Inverse Particle and Ensemble Kalman Filters

In cognitive systems, recent emphasis has been placed on studying cognitive processes of the subject whose behavior was the primary focus of the system's cognitive response. This approach, known as inverse cognition, arises in counter-adversarial applications and has motivated the development of inverse Bayesian filters. In this context, a cognitive adversary, such as a radar, uses a forward Bayesian filter to track its target of interest. An inverse filter is then employed to infer adversary's estimate of target's or defender's state. Previous studies have addressed this inverse filtering problem by introducing methods like inverse Kalman filter (I-KF), inverse extended KF (I-EKF), and inverse unscented KF (I-UKF). However, these inverse filters assume additive Gaussian noises and/or rely on local approximations of non-linear dynamics at the state estimates, limiting their practical application. Contrarily, this paper adopts a global filtering approach and develops an inverse particle filter (I-PF). The particle filter framework employs Monte Carlo (MC) methods to approximate arbitrary posterior distributions. Moreover, under mild system-level conditions, the proposed I-PF demonstrates convergence to the optimal inverse filter. Additionally, we explore MC techniques to approximate Gaussian posteriors and introduce inverse Gaussian PF (I-GPF) and inverse ensemble KF (I-EnKF). Our I-GPF and I-EnKF can efficiently handle non-Gaussian noises with suitable modifications. Additionally, we propose the differentiable I-PF, differentiable I-EnKF, and reproducing kernel Hilbert space-based EnKF (RKHS-EnKF) methods to address scenarios where system information is unknown to defender. Using recursive Cram\'er-Rao lower bound and non-credibility index (NCI), our numerical experiments for different applications demonstrate the estimation performance and time complexity of the proposed filters.

CoSTAP: Clutter Suppression in Co-Pulsing FDA-STAP

Range-dependent clutter suppression poses significant challenges in airborne frequency diverse array (FDA) radar, where resolving range ambiguity is particularly difficult. Traditional space-time adaptive processing (STAP) techniques used for clutter mitigation in FDA radars operate in the physical domain defined by first-order statistics. In this paper, unlike conventional airborne uniform FDA, we introduce a space-time-range adaptive processing (STRAP) method to exploit second-order statistics for clutter suppression in the newly proposed co-pulsing FDA radar. This approach utilizes co-prime frequency offsets (FOs) across the elements of a co-prime array, with each element transmitting at a non-uniform co-prime pulse repetition interval (C-Cube). By incorporating second-order statistics from the co-array domain, the co-pulsing STRAP or CoSTAP benefits from increased degrees of freedom (DoFs) and low computational cost while maintaining strong clutter suppression capabilities. However, this approach also introduces significant computational burdens in the coarray domain. To address this, we propose an approximate method for three-dimensional (3-D) clutter subspace estimation using discrete prolate spheroidal sequences (DPSS) to balance clutter suppression performance and computational cost. We first develop a 3-D clutter rank evaluation criterion to exploit the geometry of 3-D clutter in a general scenario. Following this, we present a clutter subspace rejection method to mitigate the effects of interference such as jammer. Compared to existing FDA-STAP algorithms, our proposed CoSTAP method offers superior clutter suppression performance, lower computational complexity, and enhanced robustness to interference. Numerical experiments validate the effectiveness and advantages of our method.

The Curse of Beam-Squint in ISAC: Causes, Implications, and Mitigation Strategies

Integrated sensing and communications (ISAC) has emerged as a means to efficiently utilize spectrum and thereby save cost and power. At the higher end of the spectrum, ISAC systems operate at wideband using large antenna arrays to meet the stringent demands for high-resolution sensing and enhanced communications capacity. However, the wideband implementation entails beam-squint, that is, deviations in the generated beam directions because of the narrowband assumption in the analog components. This causes significant degradation in the communications capacity, target detection, and parameter estimation. This article presents the design challenges caused by beam-squint and its mitigation in ISAC systems. In this context, we also discuss several ISAC design perspectives including far-/near-field beamforming, channel/direction estimation, sparse array design, and index modulation. There are also several research opportunities in waveform design, beam training, and array processing to adequately address beam-squint in ISAC.

Co-Designing Statistical MIMO Radar and In-band Full-Duplex Multi-User MIMO Communications -- Part II: Joint Precoder, Radar Code, and Receive Filters Design

We address the challenge of spectral sharing between a statistical multiple-input multiple-output (MIMO) radar and an in-band full-duplex (IBFD) multi-user MIMO (MU-MIMO) communications system operating simultaneously in the same frequency band. Existing research on joint MIMO-radar-MIMO-communications (MRMC) systems has limitations, such as focusing on colocated MIMO radars, half-duplex MIMO communications, single-user scenarios, neglecting practical constraints, or employing separate transmit/receive units for MRMC coexistence. This paper, along with companion papers (Part I and III), proposes a comprehensive MRMC framework that addresses all these challenges. In the previous companion paper (Part I), we presented signal processing techniques for a distributed IBFD MRMC system. In this paper, we introduce joint design of statistical MIMO radar codes, uplink/downlink precoders, and corresponding receive filters using a novel metric called compounded-and-weighted sum mutual information. To solve the resulting highly non-convex problem, we employ a combination of block coordinate descent (BCD) and alternating projection methods. Numerical experiments show convergence of our algorithm, mitigation of uplink interference, and stable data rates under varying noise levels, channel estimate imperfections, and self-interference. The subsequent companion paper (Part III) extends the discussion to multiple targets and evaluates the tracking performance of our MRMC system.

Co-Designing Statistical MIMO Radar and In-band Full-Duplex Multi-User MIMO Communications -- Part III: Multi-Target Tracking

As a next-generation wireless technology, the in-band full-duplex (IBFD) transmission enables simultaneous transmission and reception of signals over the same frequency, thereby doubling spectral efficiency. Further, a continuous up-scaling of wireless network carrier frequencies arising from ever-increasing data traffic is driving research on integrated sensing and communications (ISAC) systems. In this context, we study the co-design of common waveforms, precoders, and filters for an IBFD multi-user (MU) multiple-input multiple-output (MIMO) communications with a distributed MIMO radar. This paper, along with companion papers (Part I and II), proposes a comprehensive MRMC framework that addresses all these challenges. In the companion papers, we developed signal processing and joint design algorithms for this distributed system. In this paper, we tackle multi-target detection, localization, and tracking. This co-design problem that includes practical MU-MIMO constraints on power and quality-of-service is highly non-convex. We propose a low-complexity procedure based on Barzilai-Borwein gradient algorithm to obtain the design parameters and mixed-integer linear program for distributed target localization. Numerical experiments demonstrate the feasibility and accuracy of multi-target sensing of the distributed FD ISAC system. Finally, we localize and track multiple targets by adapting the joint probabilistic data association and extended Kalman filter for this system.

Beyond Diagonal RIS: Key to Next-Generation Integrated Sensing and Communications?

Reconfigurable intelligent surface (RIS) have introduced unprecedented flexibility and adaptability toward smart wireless channels. Recent research on integrated sensing and communication (ISAC) systems has demonstrated that RIS platforms enable enhanced signal quality, coverage, and link capacity. In this paper, we explore the application of fully-connected beyond diagonal RIS (BD-RIS) to ISAC systems. BD-RIS introduces additional degrees of freedom by allowing non-zero off-diagonal elements for the scattering matrix, potentially enabling further functionalities and performance enhancements. In particular, we consider the joint design objective of maximizing the weighted sum of the signal-to-noise ratio (SNR) at the radar receiver and communication users by leveraging the extra degrees-of-freedom offered in the BD-RIS setting. These degrees-of-freedom are unleashed by formulating an alternating optimization process over known and auxiliary (latent) variables of such systems. Our numerical results reveal the advantages of deploying BD-RIS in the context of ISAC and the effectiveness of the proposed algorithm by improving the SNR values for both radar and communication users by several orders of magnitude.