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Kumar Vijay Mishra

Publications and source records attributed to Kumar Vijay Mishra.

At least 55 records · Page 3Linked to original sources
arXiv2023

Information Geometry for the Working Information Theorist

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient statistics, and efficient estimators. Today, information geometry has emerged as an interdisciplinary field that finds applications in diverse areas such as radar sensing, array signal processing, quantum physics, deep learning, and optimal transport. This article presents an overview of essential information geometry to initiate an information theorist, who may be unfamiliar with this exciting area of research. We explain the concepts of divergences on statistical manifolds, generalized notions of distances, orthogonality, and geodesics, thereby paving the way for concrete applications and novel theoretical investigations. We also highlight some recent information-geometric developments, which are of interest to the broader information theory community.

cs.IT↗
arXiv2023

Index-Modulated Metasurface Transceiver Design using Reconfigurable Intelligent Surfaces for 6G Wireless Networks

Higher spectral and energy efficiencies are the envisioned defining characteristics of high data-rate sixth-generation (6G) wireless networks. One of the enabling technologies to meet these requirements is index modulation (IM), which transmits information through permutations of indices of spatial, frequency, or temporal media. In this paper, we propose novel electromagnetics-compliant designs of reconfigurable intelligent surface (RIS) apertures for realizing IM in 6G transceivers. We consider RIS modeling and implementation of spatial and subcarrier IMs, including beam steering, spatial multiplexing, and phase modulation capabilities. Numerical experiments for our proposed implementations show that the bit error rates obtained via RIS-aided IM outperform traditional implementations. We further establish the programmability of these transceivers to vary the reflection phase and generate frequency harmonics for IM through full-wave electromagnetic analyses of a specific reflect-array metasurface implementation.

eess.SP↗
arXiv2023

Terahertz-Band Direction Finding With Beam-Split and Mutual Coupling Calibration

Terahertz (THz) band is currently envisioned as the key building block to achieving the future sixth generation (6G) wireless systems. The ultra-wide bandwidth and very narrow beamwidth of THz systems offer the next order of magnitude in user densities and multi-functional behavior. However, wide bandwidth results in a frequency-dependent beampattern causing the beams generated at different subcarriers split and point to different directions. Furthermore, mutual coupling degrades the system's performance. This paper studies the compensation of both beam-split and mutual coupling for direction-of-arrival (DoA) estimation by modeling the beam-split and mutual coupling as an array imperfection. We propose a subspace-based approach using multiple signal classification with CalibRated for bEAam-split and Mutual coupling (CREAM-MUSIC) algorithm for this purpose. Via numerical simulations, we show the proposed CREAM-MUSIC approach accurately estimates the DoAs in the presence of beam-split and mutual coupling.

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arXiv2023

Widely Separated MIMO Radar Using Matrix Completion

We present a low-complexity widely separated multiple-input-multiple-output (WS-MIMO) radar that samples the signals at each of its multiple receivers at reduced rates. We process the low-rate samples of all transmit-receive chains at each receiver as data matrices. We demonstrate that each of these matrices is low rank as long as the target moves slowly within a coherent processing interval. We leverage matrix completion (MC) to recover the missing samples of each receiver signal matrix at the common fusion center. Subsequently, we estimate the targets' positions and Doppler velocities via the maximum likelihood method. Our MC-WS-MIMO approach recovers missing samples and thereafter target parameters at reduced rates without discretization. Our analysis using ambiguity functions shows that antenna geometry affects the performance of MC-WS-MIMO. Numerical experiments demonstrate reasonably accurate target localization at SNR of 20 dB and sampling rate reduction to 20%.

eess.SP↗
arXiv2023

Inverse Extended Kalman Filter -- Part I: Fundamentals

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the purpose of predicting the adversary's future steps has led to recent formulations of inverse Kalman filter (I-KF). In this context of inverse filtering, we address the key challenges of non-linear process dynamics and unknown input to the forward filter by proposing an inverse extended Kalman filter (I-EKF). The purpose of this paper and the companion paper (Part II) is to develop the theory of I-EKF in detail. In this paper, we assume perfect system model information and derive I-EKF with and without an unknown input when both forward and inverse state-space models are non-linear. In the process, I-KF-with-unknown-input is also obtained. We then provide theoretical stability guarantees using both bounded non-linearity and unknown matrix approaches and prove the I-EKF's consistency. Numerical experiments validate our methods for various proposed inverse filters using the recursive Cramér-Rao lower bound as a benchmark. In the companion paper (Part II), we further generalize these formulations to highly non-linear models and propose reproducing kernel Hilbert space-based EKF to handle incomplete system model information.

math.OC↗
arXiv2023

Multi-IRS-Aided Doppler-Tolerant Wideband DFRC System

Intelligent reflecting surface (IRS) is recognized as an enabler of future dual-function radar-communications (DFRC) by improving spectral efficiency, coverage, parameter estimation, and interference suppression. Prior studies on IRS-aided DFRC focus either on narrowband processing, single-IRS deployment, static targets, non-clutter scenario, or on the under-utilized line-of-sight (LoS) and non-line-of-sight (NLoS) paths. In this paper, we address the aforementioned shortcomings by optimizing a wideband DFRC system comprising multiple IRSs and a dual-function base station that jointly processes the LoS and NLoS wideband multi-carrier signals to improve both the communications SINR and the radar SINR in the presence of a moving target and clutter. We formulate the transmit, {receive} and IRS beamformer design as the maximization of the worst-case radar signal-to-interference-plus-noise ratio (SINR) subject to transmit power and communications SINR. We tackle this nonconvex problem under the alternating optimization framework, where the subproblems are solved by a combination of Dinkelbach algorithm, consensus alternating direction method of multipliers, and Riemannian steepest decent. Our numerical experiments show that the proposed multi-IRS-aided wideband DFRC provides over $4$ dB radar SINR and $31.7$\% improvement in target detection over a single-IRS system.

cs.IT↗
arXiv2023

Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. To address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cramér-Rao lower bound as a benchmark.

math.OC↗
arXiv2023

Sparse Array Design for Direction Finding using Deep Learning

In the past few years, deep learning (DL) techniques have been introduced for designing sparse arrays. These methods offer the advantages of feature engineering and low prediction-stage complexity, which is helpful in tackling the combinatorial search inherent to finding a sparse array. In this chapter, we provide a synopsis of several direction finding applications of DL-based sparse arrays. We begin by examining supervised and transfer learning techniques that have applications in selecting sparse arrays for a cognitive radar application. Here, we also discuss the use of meta-heuristic learning algorithms such as simulated annealing for the case of designing two-dimensional sparse arrays. Next, we consider DL-based antenna selection for wireless communications, wherein sparse array problem may also be combined with channel estimation, beamforming, or localization. Finally, we provide an example of deep sparse array technique for integrated sensing and communications (ISAC) application, wherein a trade-off of radar and communications performance makes ISAC sparse array problem very challenging. For each setting, we illustrate the performance of model-based optimization and DL techniques through several numerical experiments. We discuss additional considerations required to ensure robustness of DL-based algorithms against various imperfections in array data.

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arXiv2023

Constant Curvature Curve Tube Codes for Low-Latency Analog Error Correction

Recent research in ultra-reliable and low latency communications (URLLC) for future wireless systems has spurred interest in short block-length codes. In this context, we analyze arbitrary harmonic bandwidth (BW) expansions for a class of high-dimension constant curvature curve codes for analog error correction of independent continuous-alphabet uniform sources. In particular, we employ the circumradius function from knot theory to prescribe insulating tubes about the centerline of constant curvature curves. We then use tube packing density within a hypersphere to optimize the curve parameters. The resulting constant curvature curve tube (C3T) codes possess the smallest possible latency, i.e., block-length is unity under BW expansion mapping. Further, the codes perform within $5$ dB signal-to-distortion ratio of the optimal performance theoretically achievable at a signal-to-noise ratio (SNR) $< -5$ dB for BW expansion factor $n \leq 10$. Furthermore, we propose a neural-network-based method to decode C3T codes. We show that, at low SNR, the neural-network-based C3T decoder outperforms the maximum likelihood and minimum mean-squared error decoders for all $n$. The best possible digital codes require two to three orders of magnitude higher latency compared to C3T codes, thereby demonstrating the latter's utility for URLLC.

cs.IT↗
arXiv2023

Dual-Blind Deconvolution for Overlaid Radar-Communications Systems

The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-time and Doppler velocities of multiple transmission paths and multiple targets. We exploit the sparsity of both channels to solve the highly ill-posed DBD problem by casting it into a sum of multivariate atomic norms (SoMAN) minimization. We devise a semidefinite program to estimate the unknown target and communications parameters using the theories of positive-hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples required for near-perfect recovery is dependent on the logarithm of the maximum of number of radar targets and communications paths rather than their sum. We show that our SoMAN method and PhTP formulations are also applicable to more general scenarios such as unsynchronized transmission, the presence of noise, and multiple emitters. Numerical experiments demonstrate great performance enhancements during parameter recovery under different scenarios.

cs.IT↗
arXiv2023

Unique Bispectrum Inversion for Signals with Finite Spectral/Temporal Support

Retrieving a signal from its triple correlation spectrum, also called bispectrum, arises in a wide range of signal processing problems. Conventional methods do not provide an accurate inversion of bispectrum to the underlying signal. In this paper, we present an approach that uniquely recovers signals with finite spectral support (band-limited signals) from at least $3B$ measurements of its bispectrum function (BF), where $B$ is the signal's bandwidth. Our approach also extends to time-limited signals. We propose a two-step trust region algorithm that minimizes a non-convex objective function. First, we approximate the signal by a spectral algorithm and then refine the attained initialization based on a sequence of gradient iterations. Numerical experiments suggest that our proposed algorithm is able to estimate band-/time-limited signals from its BF for both complete and undersampled observations.

eess.SP↗
arXiv2023

Quantized Phase-Shift Design of Active IRS for Integrated Sensing and Communications

Integrated sensing and communications (ISAC) is a spectrum-sharing paradigm that allows different users to jointly utilize and access the crowded electromagnetic spectrum. In this context, intelligent reflecting surfaces (IRSs) have lately emerged as an enabler for non-line-of-sight (NLoS) ISAC. Prior IRS-aided ISAC studies assume passive surfaces and rely on the continuous-valued phase-shift model. In practice, the phase-shifts are quantized. Moreover, recent research has shown substantial performance benefits with active IRS. In this paper, we include these characteristics in our IRS-aided ISAC model to maximize the receive radar and communications signal-to-noise ratios (SNR) subjected to a unimodular IRS phase-shift vector and power budget. The resulting optimization is a highly non-convex unimodular quartic optimization problem. We tackle this problem via a bi-quadratic transformation to split the design into two quadratic sub-problems that are solved using the power iteration method. The proposed approach employs the M-ary unimodular sequence design via relaxed power method-like iteration (MaRLI) to design the quantized phase-shifts. Numerical experiments employ continuous-valued phase shifts as a benchmark and demonstrate that our active-IRS-aided ISAC design with MaRLI converges to a higher value of SNR with an increase in the number of IRS quantization bits.

cs.IT↗
arXiv2023

RIS-Aided Wideband Holographic DFRC

To enable non-line-of-sight (NLoS) sensing and communications, dual-function radar-communications (DFRC) systems have recently proposed employing reconfigurable intelligent surface (RIS) as a reflector in wireless media. However, in the dense environment and higher frequencies, severe propagation and attenuation losses are a hindrance for RIS-aided DFRC systems to utilize wideband processing. To this end, we propose equipping the transceivers with the reconfigurable holographic surface (RHS) that, different from RIS, is a metasurface with an embedded connected feed deployed at the transceiver for greater control of the radiation amplitude. This surface is crucial for designing compact low-cost wideband wireless systems, wherein ultra-massive antenna arrays are required to compensate for the losses incurred by severe attenuation and diffraction. We consider a novel wideband DFRC system equipped with an RHS at the transceiver and a RIS reflector in the channel. We jointly design the digital, holographic, and passive beamformers to maximize the radar signal-to-interference-plus-noise ratio (SINR) while ensuring the communications SINR among all users. The resulting nonconvex optimization problem involves maximin objective, constant modulus, and difference of convex constraints. We develop an alternating maximization method to decouple and iteratively solve these subproblems. Numerical experiments demonstrate that the proposed method achieves better radar performance than non-RIS, random-RHS, and randomly configured RIS-aided DFRC systems.

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arXiv2023

Counter-Adversarial Learning with Inverse Unscented Kalman Filter

In counter-adversarial systems, to infer the strategy of an intelligent adversarial agent, the defender agent needs to cognitively sense the information that the adversary has gathered about the latter. Prior works on the problem employ linear Gaussian state-space models and solve this inverse cognition problem by designing inverse stochastic filters. However, in practice, counter-adversarial systems are generally highly nonlinear. In this paper, we address this scenario by formulating inverse cognition as a nonlinear Gaussian state-space model, wherein the adversary employs an unscented Kalman filter (UKF) to estimate the defender's state with reduced linearization errors. To estimate the adversary's estimate of the defender, we propose and develop an inverse UKF (IUKF) system. We then derive theoretical guarantees for the stochastic stability of IUKF in the mean-squared boundedness sense. Numerical experiments for multiple practical applications show that the estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.

math.OC↗
arXiv2023

Moving Target Detection via Multi-IRS-Aided OFDM Radar

An intelligent reflecting surface (IRS) consists of passive reflective elements capable of altering impinging waveforms. The IRS-aided radar systems have recently been shown to improve detection and estimation performance by exploiting the target information collected via non-line-of-sight paths. However, the waveform design problem for an IRS-aided radar has remained relatively unexplored. In this paper, we consider a multi-IRS-aided orthogonal frequency-division multiplexing (OFDM) radar and study the theoretically achievable accuracy of target detection. In addition, we jointly design the OFDM signal and IRS phase-shifts to optimize the target detection performance via an alternating optimization approach. To this end, we formulate the IRS phase-shift design problem as a unimodular bi-quadratic program which is tackled by a computationally cost-effective approach based on power-method-like iterations. Numerical experiments illustrate that our proposed joint design of IRS phase-shifts and the OFDM code improves the detection performance in comparison with conventional OFDM radar.

eess.SP↗
arXiv2023

Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques

Beamforming is a signal processing technique to steer, shape, and focus an electromagnetic wave using an array of sensors toward a desired direction. It has been used in several engineering applications such as radar, sonar, acoustics, astronomy, seismology, medical imaging, and communications. With the advances in multi-antenna technologies largely for radar and communications, there has been a great interest on beamformer design mostly relying on convex/nonconvex optimization. Recently, machine learning is being leveraged for obtaining attractive solutions to more complex beamforming problems. This article captures the evolution of beamforming in the last twenty-five years from convex-to-nonconvex optimization and optimization-to-learning approaches. It provides a glimpse of this important signal processing technique into a variety of transmit-receive architectures, propagation zones, paths, and conventional/emerging applications.

eess.SP↗
arXiv2023

An Overview of Advances in Signal Processing Techniques for Classical and Quantum Wideband Synthetic Apertures

Rapid developments in synthetic aperture (SA) systems, which generate a larger aperture with greater angular resolution than is inherently possible from the physical dimensions of a single sensor alone, are leading to novel research avenues in several signal processing applications. The SAs may either use a mechanical positioner to move an antenna through space or deploy a distributed network of sensors. With the advent of new hardware technologies, the SAs tend to be denser nowadays. The recent opening of higher frequency bands has led to wide SA bandwidths. In general, new techniques and setups are required to harness the potential of wide SAs in space and bandwidth. Herein, we provide a brief overview of emerging signal processing trends in such spatially and spectrally wideband SA systems. This guide is intended to aid newcomers in navigating the most critical issues in SA analysis and further supports the development of new theories in the field. In particular, we cover the theoretical framework and practical underpinnings of wideband SA radar, channel sounding, sonar, radiometry, and optical applications. Apart from the classical SA applications, we also discuss the quantum electric-field-sensing probes in SAs that are currently undergoing active research but remain at nascent stages of development.

eess.SP↗
arXiv2023

Joint Waveform and Passive Beamformer Design in Multi-IRS-Aided Radar

Intelligent reflecting surface (IRS) technology has recently attracted a significant interest in non-light-of-sight radar remote sensing. Prior works have largely focused on designing single IRS beamformers for this problem. For the first time in the literature, this paper considers multi-IRS-aided multiple-input multiple-output (MIMO) radar and jointly designs the transmit unimodular waveforms and optimal IRS beamformers. To this end, we derive the Cramer-Rao lower bound (CRLB) of target direction-of-arrival (DoA) as a performance metric. Unimodular transmit sequences are the preferred waveforms from a hardware perspective. We show that, through suitable transformations, the joint design problem can be reformulated as two unimodular quadratic programs (UQP). To deal with the NP-hard nature of both UQPs, we propose unimodular waveform and beamforming design for multi-IRS radar (UBeR) algorithm that takes advantage of the low-cost power method-like iterations. Numerical experiments illustrate that the MIMO waveforms and phase shifts obtained from our UBeR algorithm are effective in improving the CRLB of DoA estimation.

cs.IT↗