arXiv subjects

Kumar Vijay Mishra

Publications and source records attributed to Kumar Vijay Mishra.

At least 19 recordsLinked to original sources

arXiv2026

Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework

While stochastic geometry provides a powerful framework for the analysis of cellular networks, standard Monte Carlo simulations often suffer from slow convergence due to the stochasticity of the infinite far-field. This work introduces the \textit{Rao-Blackwellized Hybrid Estimator} (RBHE), which enhances simulation efficiency by analytically marginalizing the residual far-field interference via the conditional Laplace functional. By partitioning the interference field into $K$ dominant interferers and an infinite tail, we derive an estimator that combines exact spatial sampling with a rigorous analytical representation. We prove that the RBHE is an unbiased estimator for any finite truncation, while its systematic bias relative to the infinite-plane benchmark decays at a rate of $\mathcal{O}(K^{1-η/2})$. Numerical results demonstrate significant sample parsimony; in the high-reliability regime ($T = -10$ dB) with $K=2$, the RBHE yields a variance reduction gain of $90.75\times$, enabling a $98.90\%$ reduction in the spatial realizations required to reach a target precision. This framework effectively bridges the gap between tractable analytical models and high-fidelity simulations.

cs.IT↗

arXiv2026

Hypercomplex Phase Retrieval

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of the phase retrieval (PR) problem, wheren a complex-valued signal is recovered from intensity-only measurements, have attracted growing interest. Hypercomplex phase retrieval (HPR) naturally arises in a range of optical imaging and computational sensing applications, where signals are often modeled using quaternion- or octonion-valued representations. Similar to classical PR, HPR problems may involve measurements obtained via complex, hypercomplex, Fourier, or other structured sensing operators. These formulations open new avenues for the development of advanced HSP-based algorithms and theoretical frameworks. This chapter surveys emerging methodologies and applications of HPR, with particular emphasis on optical imaging systems.

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arXiv2026

IEEE 802.11ad-Aided 5-D Sensing with a UAV Swarm in Urban Environment

Aerial base stations mounted on unmanned aerial vehicles (UAVs) support next-generation wireless networks in challenging environments such as urban areas, disaster zones, and remote locations. Further, UAV swarms overcome the challenges of limited battery life and other operational constraints of a single UAV. However, tracking mobile users on the ground by each UAV and the corresponding synchronization between the UAVs is a significant issue that must be addressed before this framework can be deployed in reality. Incorporating additional sensing capabilities to facilitate this additional requirement would introduce significant overhead in terms of hardware, cost, and power to each UAV. Instead, we propose an integrated sensing and communications-enabled swarm UAV system, based on the millimeter-wave IEEE 802.11ad protocol. Further, we show that our proposed system is capable of five-dimensional (5-D) ground target sensing (range, Doppler velocity, azimuth, elevation, and polarization) in an urban environment. Numerical experiments using realistic models demonstrate and validate the performance of 5-D sensing using our proposed 802-11ad-aided UAV system.

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arXiv2025

Fundamental Limits for Near-Field Sensing -- Part I: Narrow-Band Systems

Extremely large-scale antenna arrays (ELAAs) envisioned for 6G enable high-resolution sensing. However, the ELAAs worked in extremely high frequency will push operation into the near-field region, where spherical wavefronts invalidate classical far-field models and alter fundamental estimation limits. The purpose of this and the companion paper (Part II) is to develop the theory of fundamental limits for near-field sensing systems in detail. In this paper (Part I), we develop a unified narrow-band near-field signal model for joint parameter sensing of moving targets using the ELAAs. Leveraging the Slepian--Bangs formulation, we derive closed-form Cram'er--Rao bounds (CRBs) for joint estimation of target position, velocity, and radar cross-section (RCS) under the slow-time sampling model. To obtain interpretable insights, we further establish explicit far-field and near-field approximations that reveal how the bounds scale with array aperture, target range, carrier wavelength, and coherent integration length. The resulting expressions expose the roles of self-information terms and their cross terms, clarifying when Fresnel corrections become non-negligible and providing beamformer and algorithm design guidelines for near-field sensing with ELAAs. Simulation results validate the derived CRBs and their far-field and near-field approximations, demonstrating accurate agreement with the analytical scaling laws across representative array sizes and target ranges.

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arXiv2025

Fundamental Limits for Near-Field Sensing -- Part II: Wide-Band Systems

Near-field sensing with extremely large-scale antenna arrays (ELAAs) in practical 6G systems is expected to operate over broad bandwidths, where delay, Doppler, and spatial effects become tightly coupled across frequency. The purpose of this and the companion paper (Part I) is to develop the unified Cram'er--Rao bounds (CRBs) for sensing systems spanning from far-field to near-field, and narrow-band to wide-band. This paper (Part II) derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval. We establish an exact near-field wide-band signal model that captures frequency-dependent propagation, spherical-wave geometry, and the intrinsic coupling between target location and motion parameters across subcarriers and slow time. Similar as Part I using the Slepian--Bangs formulation, we derive the wide-band Fisher information matrix and the CRBs for joint estimation of target position, velocity, and radar cross-section, and we show how wide-band information aggregates across orthogonal subcarriers. We further develop tractable far-field and near-field approximations which provide design-level insights into the roles of bandwidth, coherent integration length, and array aperture, and clarify when wide-band effects. Simulation results validate the derived CRBs and its approximations, demonstrating close agreement with the analytical scaling laws across representative ranges, bandwidths, and array configurations.

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arXiv2025

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.

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arXiv2025

A Survey of Deep Learning Architectures for Intelligent Reflecting Surfaces

Intelligent reflecting surfaces (IRSs) have recently received significant attention for 6G wireless communications as they enable the control of the wireless propagation environment. The use of IRS also provides reducing the hardware complexity, physical size, weight as well as cost of conventional large antenna arrays. However, deployment of the IRS entails dealing with multiple channel links between the base station (BS) and the users. Further, the BS and IRS beamformers require a joint design, wherein the IRS elements must be rapidly reconfigured. Data-driven techniques, such as deep learning (DL), are critical in addressing these challenges. The lower computation time and model-free nature of DL make it robust against data imperfections and environmental changes. At the physical layer, DL has been shown to be effective for IRS signal detection, channel estimation, and active/passive beamforming using architectures such as supervised, unsupervised, and reinforcement learning. This article provides a synopsis of these techniques for designing DL-based IRS-assisted wireless systems.

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arXiv2025

Twisting Signals for Joint Radar-Communications: An OAM Vortex Beam Approach

Orbital angular momentum (OAM) technology has attracted much research interest in recent years because of its characteristic helical phase front twisting around the propagation axis and natural orthogonality among different OAM states to encode more degrees of freedom than classical planar beams. Leveraging upon these features, OAM technique has been applied to wireless communication systems to enhance spectral efficiency and radar systems to distinguish spatial targets without beam scanning. Leveraging upon these unique properties, we propose an OAM-based millimeter-wave joint radar-communications (JRC) system comprising a bi-static automotive radar and vehicle-to-vehicle (V2V) communications. Different from existing uniform circular array (UCA) based OAM systems where each element is an isotropic antenna, an OAM spatial modulation scheme utilizing a uniform linear array (ULA) is adopted with each element being a traveling-wave antenna, producing multiple Laguerre-Gaussian (LG) vortex beams simultaneously. Specifically, we first build a novel bi-static automotive OAM-JRC model that embeds communication messages in a radar signal, following which a target position and velocity parameters estimation algorithm is designed with only radar frames. Then, an OAM-based mode-division multiplexing (MDM) strategy between radar and JRC frames is presented to ensure the JRC parameters identifiability and recovery. Furthermore, we analyze the performance of the JRC system through deriving recovery guarantees and Cramér-Rao lower bound (CRLB) of radar target parameters and evaluating the bit error rate (BER) of communication, respectively. Our numerical experiments validate the effectiveness of the proposed OAM-based JRC system and parameter estimation method.

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arXiv2025

Structure-Preserving Medical Image Generation from a Latent Graph Representation

Supervised learning techniques have proven their efficacy in many applications with abundant data. However, applying these methods to medical imaging is challenging due to the scarcity of data, given the high acquisition costs and intricate data characteristics of those images, thereby limiting the full potential of deep neural networks. To address the lack of data, augmentation techniques leverage geometry, color, and the synthesis ability of generative models (GMs). Despite previous efforts, gaps in the generation process limit the impact of data augmentation to improve understanding of medical images, e.g., the highly structured nature of some domains, such as X-ray images, is ignored. Current GMs rely solely on the network's capacity to blindly synthesize augmentations that preserve semantic relationships of chest X-ray images, such as anatomical restrictions, representative structures, or structural similarities consistent across datasets. In this paper, we introduce a novel GM that leverages the structural resemblance of medical images by learning a latent graph representation (LGR). We design an end-to-end model to learn (i) a LGR that captures the intrinsic structure of X-ray images and (ii) a graph convolutional network (GCN) that reconstructs the X-ray image from the LGR. We employ adversarial training to guide the generator and discriminator models in learning the distribution of the learned LGR. Using the learned GCN, our approach generates structure-preserving synthetic images by mapping generated LGRs to X-ray. Additionally, we evaluate the learned graph representation for other tasks, such as X-ray image classification and segmentation. Numerical experiments demonstrate the efficacy of our approach, increasing performance up to $3\%$ and $2\%$ for classification and segmentation, respectively.

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arXiv2025

Diffusion model for gradient preconditioning in hyperspectral imaging inverse problems

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints. A common workaround is to partition measurements and estimate local statistics-such as the covariance matrix-using only partial observations. However, this strategy introduces noise in the optimization gradients, especially when each partition contains few samples. In this work, we reinterpret this accumulation of gradient noise as a diffusion process, where successive partitions inject increasing uncertainty into the learning signal. Building on this insight, we propose a novel framework that leverages denoising diffusion models to learn a reverse process in gradient space. The model is trained to map noisy gradient estimates toward clean, well-conditioned updates, effectively preconditioning the optimization. Our approach bridges generative modeling and inverse problem solving, improving convergence and reconstruction quality under aggressive sampling regimes. We validate our method on hyperspectral recovery tasks, demonstrating significant gains in accuracy and stability over traditional optimization pipelines.

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arXiv2025

Coherent Source Enumeration with Compact ULAs

Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent sources in small uniform linear arrays, where ambiguities arise in the spatial spectrum. We address this by decomposing the forward-backward smoothed covariance matrix into a sum of a rank-constrained Toeplitz matrix and a diagonal matrix with non-negative entries representing the signal and noise subspaces, respectively. The resulting non-convex optimization problem is solved by proposing Toeplitz approach for rank-based target estimation (TARgEt) that employs the alternating direction method of multipliers. Numerical results on both synthetic and real-world datasets demonstrate the effectiveness and robustness of TARgEt over the state-of-the-art.

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arXiv2025

Inverse Particle Filter

In cognitive systems, recent emphasis has been placed on studying the 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 the adversary's estimate of the target's or defender's state. Previous studies have addressed this inverse filtering problem by introducing methods like the inverse Kalman filter (KF), inverse extended KF, and inverse unscented KF. However, these filters typically assume additive Gaussian noise models and/or rely on local approximations of non-linear dynamics at the state estimates, limiting their practical application. In contrast, this paper adopts a global filtering approach and presents the development of 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 propose the differentiable I-PF to address scenarios where system information is unknown to the defender. Using the recursive Cramer-Rao lower bound and non-credibility index (NCI), our numerical experiments for different systems demonstrate the estimation performance and time complexity of the proposed filter.

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arXiv2025

CLuP-Based Dual-Deconvolution in Automotive ISAC Scenarios

Accurate target parameter estimation of range, velocity, and angle is essential for vehicle safety in advanced driver assistance systems (ADAS) and autonomous vehicles. To enable spectrum sharing, ADAS may employ integrated sensing and communications (ISAC). This paper examines a dual-deconvolution automotive ISAC scenario where the radar waveform is known but the propagation channel is not, while in the communications domain, the channel is known but the transmitted message is not. Conventional maximum likelihood (ML) estimation for automotive target parameters is computationally demanding. To address this, we propose a low-complexity approach using the controlled loosening-up (CLuP) algorithm, which employs iterative refinement for efficient separation and estimation of radar targets. We achieve this through a nuclear norm restriction that stabilizes the problem. Numerical experiments demonstrate the robustness of this approach under high-mobility and noisy automotive environments, highlighting CLuP's potential as a scalable, real-time solution for ISAC in future vehicular networks.

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arXiv2025

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.

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arXiv2024

Terahertz-Band Integrated Sensing and Communications: Challenges and Opportunities

The sixth generation (6G) wireless networks aim to achieve ultra-high data transmission rates, very low latency and enhanced energy-efficiency. To this end, terahertz (THz) band is one of the key enablers of 6G to meet such requirements. The THz-band systems are also quickly emerging as high-resolution sensing devices because of their ultra-wide bandwidth and very narrow beamwidth. As a means to efficiently utilize spectrum and thereby save cost and power, THz integrated sensing and communications (ISAC) paradigm envisages a single integrated hardware platform with a common signaling mechanism. However, ISAC at THz-band entails several design challenges such as beam split, range-dependent bandwidth, near-field beamforming, and distinct channel model. This article examines the technologies that have the potential to bring forth ISAC and THz transmission together. In particular, it provides an overview of antenna and array design, hybrid beamforming, integration with reflecting surfaces and data-driven techniques such as machine learning. These systems also provide research opportunities in developing novel methodologies for channel estimation, near-field beam split, waveform design, and beam misalignment.

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arXiv2024

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.

cs.IT↗

arXiv2024

Spatial Path Index Modulation in mmWave/THz-Band Integrated Sensing and Communications

As the demand for wireless connectivity continues to soar, the fifth generation and beyond wireless networks are exploring new ways to efficiently utilize the wireless spectrum and reduce hardware costs. One such approach is the integration of sensing and communications (ISAC) paradigms to jointly access the spectrum. Recent ISAC studies have focused on upper millimeter-wave and low terahertz bands to exploit ultrawide bandwidths. At these frequencies, hybrid beamformers that employ fewer radio-frequency chains are employed to offset expensive hardware but at the cost of lower multiplexing gains. Wideband hybrid beamforming also suffers from the beam-split effect arising from the subcarrier-independent (SI) analog beamformers. To overcome these limitations, this paper introduces a spatial path index modulation (SPIM) ISAC architecture, which transmits additional information bits via modulating the spatial paths between the base station and communications users. We design the SPIM-ISAC beamformers by first estimating both radar and communications parameters by developing beam-split-aware algorithms. Then, we propose to employ a family of hybrid beamforming techniques such as hybrid, SI, and subcarrier-dependent analog-only, and beam-split-aware beamformers. Numerical experiments demonstrate that the proposed SPIM-ISAC approach exhibits significantly improved spectral efficiency performance in the presence of beam-split than that of even fully digital non-SPIM beamformers.

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arXiv2024

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 Cramér-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.

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