Dynamic Joint Communications and Sensing Precoding Design: A Lyapunov Approach

This letter proposes a dynamic joint communications and sensing (JCAS) framework to adaptively design dedicated sensing and communications precoders. We first formulate a stochastic control problem to maximize the long-term average signal-to-noise ratio for sensing, subject to a minimum average communications signal-to-interference-plus-noise ratio requirement and a power budget. Using Lyapunov optimization, specifically the drift-plus-penalty method, we cast the problem into a sequence of per-slot non-convex problems. To solve these problems, we develop a successive convex approximation method. Additionally, we derive a closed-form solution to the per-slot problems based on the notion of zero-forcing. Numerical evaluations demonstrate the efficacy of the proposed methods and highlight their superiority compared to a baseline method based on conventional design.

Optimal ISAC Beamforming Structure and Efficient Algorithms for Sum Rate and CRLB Balancing

Integrated sensing and communications (ISAC) has emerged as a promising paradigm to unify wireless communications and radar sensing, enabling efficient spectrum and hardware utilization. A core challenge with realizing the gains of ISAC stems from the unique challenges of dual purpose beamforming design due to the highly non-convex nature of key performance metrics such as sum rate for communications and the Cramer-Rao lower bound (CRLB) for sensing. In this paper, we propose a low-complexity structured approach to ISAC beamforming optimization to simultaneously enhance spectral efficiency and estimation accuracy. Specifically, we develop a successive convex approximation (SCA) based algorithm which transforms the original non-convex problem into a sequence of convex subproblems ensuring convergence to a locally optimal solution. Furthermore, leveraging the proposed SCA framework and the Lagrange duality, we derive the optimal beamforming structure for CRLB optimization in ISAC systems. Our findings characterize the reduction in radar streams one can employ without affecting performance. This enables a dimensionality reduction that enhances computational efficiency. Numerical simulations validate that our approach achieves comparable or superior performance to the considered benchmarks while requiring much lower computational costs.

Adaptive and Self-Tuning SBL with Total Variation Priors for Block-Sparse Signal Recovery

This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the hyper-parameter space of the sparse signal. The main contributions are two-fold. 1) We extend the TV penalty beyond the immediate neighbor, thus enabling better capture of the signal structure. 2) A dynamic framework is provided to learn the penalty parameter for regularization. It is based on the statistical dependencies between the entries of tentative blocks, thus eliminating the need for fine-tuning. The superior performance of the proposed method is empirically demonstrated by extensive computer simulations with the state-of-art benchmarks. The proposed solution exhibits both excellent performance and robustness against sparsity model mismatch.

Low-Complexity Cramér-Rao Lower Bound and Sum Rate Optimization in ISAC Systems

While Cram\'er-Rao lower bound is an important metric in sensing functions in integrated sensing and communications (ISAC) designs, its optimization usually involves a computationally expensive solution such as semidefinite relaxation. In this paper, we aim to develop a low-complexity yet efficient algorithm for CRLB optimization. We focus on a beamforming design that maximizes the weighted sum between the communications sum rate and the sensing CRLB, subject to a transmit power constraint. Given the non-convexity of this problem, we propose a novel method that combines successive convex approximation (SCA) with a shifted generalized power iteration (SGPI) approach, termed SCA-SGPI. The SCA technique is utilized to approximate the non-convex objective function with convex surrogates, while the SGPI efficiently solves the resulting quadratic subproblems. Simulation results demonstrate that the proposed SCA-SGPI algorithm not only achieves superior tradeoff performance compared to existing method but also significantly reduces computational time, making it a promising solution for practical ISAC applications.

Deep Unfolding-Empowered MmWave Massive MIMO Joint Communications and Sensing

In this paper, we propose a low-complexity and fast hybrid beamforming design for joint communications and sensing (JCAS) based on deep unfolding. We first derive closed-form expressions for the gradients of the communications sum rate and sensing beampattern error with respect to the analog and digital precoders. Building on this, we develop a deep neural network as an unfolded version of the projected gradient ascent algorithm, which we refer to as UPGANet. This approach efficiently optimizes the communication-sensing performance tradeoff with fast convergence, enabled by the learned step sizes. UPGANet preserves the interpretability and flexibility of the conventional PGA optimizer while enhancing performance through data training. Our simulations show that UPGANet achieves up to a 33.5% higher communications sum rate and 2.5 dB lower beampattern error compared to conventional designs based on successive convex approximation and Riemannian manifold optimization. Additionally, it reduces runtime and computational complexity by up to 65% compared to PGA without unfolding.

Performance Analysis and Power Allocation for Massive MIMO ISAC Systems

Integrated sensing and communications (ISAC) is envisioned as a key feature in future wireless communications networks. Its integration with massive multiple-input-multiple-output (MIMO) techniques promises to leverage substantial spatial beamforming gains for both functionalities. In this work, we consider a massive MIMO-ISAC system employing a uniform planar array with zero-forcing and maximum-ratio downlink transmission schemes combined with monostatic radar-type sensing. Our focus lies on deriving closed-form expressions for the achievable communications rate and the Cram\'er--Rao lower bound (CRLB), which serve as performance metrics for communications and sensing operations, respectively. The expressions enable us to investigate important operational characteristics of massive MIMO-ISAC, including the mutual effects of communications and sensing as well as the advantages stemming from using a very large antenna array for each functionality. Furthermore, we devise a power allocation strategy based on successive convex approximation to maximize the communications rate while guaranteeing the CRLB constraints and transmit power budget. Extensive numerical results are presented to validate our theoretical analyses and demonstrate the efficiency of the proposed power allocation approach.

Multi-Static Cell-Free Massive MIMO ISAC: Performance Analysis and Power Allocation

In this work, we consider a cell-free massive multiple-input multiple-output (MIMO) integarted sensing and communications (ISAC) system with maximum-ratio transmission schemes combined with multistatic radar-type sensing. Our focus lies on deriving closed-form expressions for the achievable communications rate and the Cram\'er-Rao lower bound (CRLB), which serve as performance metrics for communications and sensing operations, respectively. The expressions enable us to investigate important operational characteristics of multistatic cell-free massive MIMO-ISAC, including the mutual effects of communications and sensing as well as the advantages stemming from using numerous distributed antenna arrays for each functionality. Furthermore, we optimize the power allocation among the access points to maximize the communications rate while guaranteeing the CRLB constraints and total transmit power budget. Extensive numerical results are presented to validate our theoretical findings and demonstrate the efficiency of the proposed power allocation approach.

Coverage Analysis for 3D Indoor Terahertz Communication System Over Fluctuating Two-Ray Fading Channels

In this paper, we develop a novel analytical framework for a three-dimensional (3D) indoor terahertz (THz) communication system. Our proposed model incorporates more accurate modeling of wall blockages via Manhattan line processes and precise modeling of THz fading channels via a fluctuating two-ray (FTR) channel model. We also account for traditional unique features of THz, such as molecular absorption loss, user blockages, and 3D directional antenna beams. Moreover, we model locations of access points (APs) using a Poisson point process and adopt the nearest line-of-sight AP association strategy. Due to the high penetration loss caused by wall blockages, we consider that a user equipment (UE) and its associated AP and interfering APs are all in the same rectangular area, i.e., a room. Based on the proposed rectangular area model, we evaluate the impact of the UE's location on the distance to its associated AP. We then develop a tractable method to derive a new expression for the coverage probability by examining the interference from interfering APs and considering the FTR fading experienced by THz communications. Aided by simulation results, we validate our analysis and demonstrate that the UE's location has a pronounced impact on its coverage probability. Additionally, we find that the optimal AP density is determined by both the UE's location and the room size, which provides valuable insights for meeting the coverage requirements of future THz communication system deployment.

Digital and Hybrid Precoding Designs in Massive MIMO with Low-Resolution ADCs

Low-resolution analog-to-digital converters (ADCs) have emerged as an efficient solution for massive multiple-input multiple-output (MIMO) systems to reap high data rates with reasonable power consumption and hardware complexity. In this paper, we study precoding designs for digital, fully connected (FC) hybrid, and partially connected (PC) hybrid beamforming architectures in massive MIMO systems with low-resolution ADCs at the receiver. We aim to maximize the spectral efficiency (SE) subject to a transmit power budget and hardware constraints on the analog components. The resulting problems are nonconvex and the quantization distortion introduces additional challenges. To address them, we first derive a tight lower bound for the SE, based on which we optimize the precoders for the three beamforming architectures under the majorization-minorization framework. Numerical results validate the superiority of the proposed precoding designs over their state-of-the-art counterparts in systems with low-resolution ADCs, particularly those with 1-bit resolution. The results show that the PC hybrid precoding design can achieve an SE close to those of the digital and FC hybrid precoding designs in 1-bit systems, highlighting the potential of the PC hybrid beamforming architectures.

Model-Based Machine Learning for Max-Min Fairness Beamforming Design in JCAS Systems

Joint communications and sensing (JCAS) is expected to be a crucial technology for future wireless systems. This paper investigates beamforming design for a multi-user multi-target JCAS system to ensure fairness and balance between communications and sensing performance. We jointly optimize the transmit and receive beamformers to maximize the weighted sum of the minimum communications rate and sensing mutual information. The formulated problem is highly challenging due to its non-smooth and non-convex nature. To overcome the challenges, we reformulate the problem into an equivalent but more tractable form. We first solve this problem by alternating optimization (AO) and then propose a machine learning algorithm based on the AO approach. Numerical results show that our algorithm scales effectively with the number of the communications users and provides better performance with shorter run time compared to conventional optimization approaches.