[Paper Review] Dual-Functional Radar-Communication Waveform Design: A Symbol-Level Precoding Approach

Rang Liu, Ming Li+2 more|arXiv (Cornell University)|Aug 11, 2021

Radar Systems and Signal ProcessingEngineering44 references153 citations

TL;DR

This paper proposes a symbol-level precoding approach for MIMO dual-functional radar-communication (DFRC) systems to simultaneously optimize radar beampattern accuracy and multi-user communication quality. By exploiting symbol-specific waveform design, it achieves superior instantaneous beampatterns and lower SER compared to block-level precoding, with two efficient algorithms—PDD-MM-BCD and ALM-RBFGS—offering trade-offs between performance and computational complexity.

ABSTRACT

Dual-functional radar-communication (DFRC) systems can simultaneously perform both radar and communication functionalities using the same hardware platform and spectrum resource. In this paper, we consider multi-input multi-output (MIMO) DFRC systems and focus on transmit beamforming designs to provide both radar sensing and multi-user communications. Unlike conventional block-level precoding techniques, we propose to use the recently emerged symbol-level precoding approach in DFRC systems, which provides additional degrees of freedom (DoFs) that guarantee preferable instantaneous transmit beampatterns for radar sensing and achieve better communication performance. In particular, the squared error between the designed and desired beampatterns is minimized subject to the quality-of-service (QoS) requirements of the communication users and the constant-modulus power constraint. Two efficient algorithms are developed to solve this non-convex problem on both the Euclidean and Riemannian spaces. The first algorithm employs penalty dual decomposition (PDD), majorization-minimization (MM), and block coordinate descent (BCD) methods to convert the original optimization problem into two solvable sub-problems, and iteratively solves them using efficient algorithms. The second algorithm provides a much faster solution at the price of a slight performance loss, first transforming the original problem into Riemannian space, and then utilizing the augmented Lagrangian method (ALM) to obtain an unconstrained problem that is subsequently solved via a Riemannian Broyden-Fletcher-Goldfarb-Shanno (RBFGS) algorithm. Extensive simulations verify the distinct advantages of the proposed symbol-level precoding designs in both radar sensing and multi-user communications.

Motivation & Objective

• To address the limited degrees of freedom (DoFs) and poor instantaneous beampattern performance in conventional block-level precoding for DFRC systems.
• To enable simultaneous high-rate communication and accurate radar sensing using a shared MIMO hardware platform.
• To design a transmit waveform that minimizes beampattern error while satisfying user QoS and constant-modulus constraints.
• To develop efficient algorithms for solving the non-convex optimization problem arising from symbol-level precoding.

Proposed method

• Formulates a non-convex optimization problem minimizing squared beampattern error under QoS and constant-modulus constraints.
• Proposes the PDD-MM-BCD algorithm using penalty dual decomposition, majorization-minimization, and block coordinate descent to iteratively solve sub-problems.
• Develops the ALM-RBFGS algorithm by transforming the problem into Riemannian space and solving via augmented Lagrangian and Riemannian BFGS.
• Employs symbol-level precoding to make the transmit vector dependent on instantaneous symbols, enabling constructive interference exploitation in communications.
• Uses a constant-modulus constraint to ensure power amplifier efficiency and hardware compatibility.
• Applies Riemannian optimization techniques to handle the non-convex manifold constraint in the ALM-RBFGS approach.

Experimental results

Research questions

• RQ1 Can symbol-level precoding improve instantaneous radar beampattern accuracy compared to block-level precoding in DFRC systems?
• RQ2 How does symbol-level precoding enhance communication performance in terms of SER while maintaining radar sensing quality?
• RQ3 What are the trade-offs between performance and computational complexity in symbol-level DFRC waveform design?
• RQ4 Can Riemannian optimization techniques effectively solve the non-convex symbol-level precoding problem in DFRC systems?
• RQ5 How do the proposed algorithms compare in convergence speed and execution time under varying user counts?

Key findings

• The PDD-MM-BCD algorithm achieves monotonically converging objective values with rapid outer-loop convergence, reaching constraint feasibility within 4 iterations.
• The ALM-RBFGS algorithm reduces execution time to approximately 2% of PDD-MM-BCD, with average execution times of 0.233 seconds for 6 users.
• Both proposed algorithms achieve significantly higher detection probability (e.g., 0.85 at 10−5 false alarm rate) than block-level methods, especially with limited signal samples.
• The SER performance of symbol-level precoding is lower than block-level methods, with ALM-RBFGS showing slightly worse SER due to minor constraint violations but still outperforming block-level approaches.
• The ALM-RBFGS algorithm requires orders of magnitude fewer iterations than PDD-MM-BCD for solving the augmented Lagrangian problem, due to direct quartic objective minimization.
• Extensive simulations confirm that symbol-level precoding enables better angle estimation and target detection with limited signal samples, demonstrating its superiority in instantaneous performance.