Exploiting Symmetric Non-Convexity for Multi-Objective Symbol-Level DFRC Signal Design

Symbol-level precoding (SLP) is a promising solution for addressing the inherent interference problem in dual-functional radar-communication (DFRC) signal designs. This paper considers an SLP-DFRC signal design problem which optimizes the radar performance under communication performance constraints. We show that a common phase modulation applied to the transmit signals from an antenna array does not affect the performance of different radar sensing metrics, including beampattern similarity, signal-to-interference-plus-noise ratio (SINR), and Cram\'er-Rao lower bound (CRLB). We refer to this as symmetric-rotation invariance, upon which we develop low-complexity yet efficient DFRC signal design algorithms. More specifically, we propose a symmetric non-convexity (SNC)-based DFRC algorithm that relies on the non-convexity of the radar sensing metrics to identify a set of radar-only solutions. Based on these solutions, we further exploit the symmetry property of the radar sensing metrics to efficiently design the DFRC signal. We show that the proposed SNC-based algorithm is versatile in the sense that it can be applied to the DFRC signal optimization of all three sensing metrics mentioned above (beampattern, SINR, and CRLB). In addition, since the radar sensing metrics are independent of the communication channel and data symbols, the set of radar-only solutions can be constructed offline, thereby reducing the computational complexity. We also develop an accelerated SNC-based algorithm that further reduces the complexity. Finally, we numerically demonstrate the superiority of the proposed algorithms compared to existing methods in terms of sensing and communication performance as well as computational requirements.

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.

Comprehensive Review of Deep Unfolding Techniques for Next-Generation Wireless Communication Systems

The application of machine learning in wireless communications has been extensively explored, with deep unfolding emerging as a powerful model-based technique. Deep unfolding enhances interpretability by transforming complex iterative algorithms into structured layers of deep neural networks (DNNs). This approach seamlessly integrates domain knowledge with deep learning (DL), leveraging the strengths of both methods to simplify complex signal processing tasks in communication systems. To provide a solid foundation, we first present a brief overview of DL and deep unfolding. We then explore the applications of deep unfolding in key areas, including signal detection, channel estimation, beamforming design, decoding for error-correcting codes, sensing and communication, power allocation, and security. Each section focuses on a specific task, highlighting its significance in emerging 6G technologies and reviewing recent advancements in deep unfolding-based solutions. Finally, we discuss the challenges associated with developing deep unfolding techniques and propose potential improvements to enhance their applicability across diverse wireless communication scenarios.

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.

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.

Beamforming Design for Max-Min Fairness Performance Balancing in ISAC Systems

Integrated sensing and communications (ISAC) is envisioned as a key technology for future wireless communications. In this paper, we consider a downlink monostatic ISAC system wherein the base station serves multiple communications users and sensing targets at the same time in the presence of clutter. We aim at both guaranteeing fairness among the communications users while simultaneously balancing the performances of communications and sensing functionalities. Therefore, we optimize the transmit and receive beamformers to maximize the weighted minimum signal-to-interference and clutter-plus-noise ratios. The design problem is highly challenging due to the non-smooth and non-convex objective function and strongly coupled variables. We propose two efficient methods to solve the problem. First, we rely on fractional programming and transform the original problem into convex sub-problems, which can be solved with standard convex optimization tools. To further reduce the complexity and dependence on numerical tools, we develop a novel approach to address the inherent non-smoothness of the formulated problem. Finally, the efficiencies of the proposed designs are demonstrated by numerical results.