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

In this paper, 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.