Optimal Precoding Design for Monostatic ISAC Systems: MSE Lower Bound and DoF Completion

TL;DR

This paper analyzes the MSE lower bound for target sensing in monostatic ISAC systems and proposes a waveform augmentation and precoder design strategy to optimize parameter estimation performance, achieving theoretical bounds.

Contribution

It introduces a DoF completion method for waveform augmentation and a globally optimal precoder design via SDR, improving sensing performance in ISAC systems.

Findings

The proposed waveform augmentation achieves the MSE lower bound.

The precoder design effectively minimizes MSE under SINR constraints.

Simulation results confirm the approach's effectiveness.

Abstract

In this letter, we study the parameter estimation performance for monostatic downlink integrated sensing and communications (ISAC) systems. In particular, we analyze the mean squared error (MSE) lower bound for target sensing in the downlink ISAC system that reveals the suboptimality in re-using the conventional communication waveform for sensing. To realize a practical dual-functional waveform, we propose a waveform augmentation strategy that imposes an extra signal structure, namely the degrees-of-freedom (DoF) completion method. The proposed approach is capable of improving the parameter estimation performance of the ISAC system and achieving the derived MSE lower bound. To improve the performance of the proposed strategy, we formulate an MSE minimization problem to design the ISAC precoder, subject to the communication users' signal-interference-plus-noise-ratio (SINR) constraints. Despite the non-convexity of the waveform design problem, we obtain its globally optimal solution via semi-definite relaxation (SDR) and the proposed constructive method. Simulation results validate the proposed DoF completion technology could achieve the derived MSE lower bound and the effectiveness of the MSE-based ISAC waveform design.