MU-MIMO Symbol-Level Precoding for QAM Constellations with Maximum Likelihood Receivers

In this paper, we investigate symbol-level precoding (SLP) and efficient decoding techniques for downlink transmission, where we focus on scenarios where the base station (BS) transmits multiple quadrature amplitude modulation (QAM) constellation streams to users equipped with multiple receive antennas. We begin by formulating a symbol-level joint design scheme aimed at collaboratively optimizing the transmit precoding and receive combining matrices. This coupled problem is addressed by employing the alternating optimization (AO) method, and closed-form solutions are derived by analyzing the obtained two subproblems. Furthermore, to address the dependence of the receive combining matrix on the transmit signals, we switch to maximum likelihood detection (MLD) method for decoding. Notably, we have demonstrated that the smallest singular value of the precoding matrix significantly impacts the performance of MLD method. Specifically, a lower value of the smallest singular value results in degraded detection performance. Additionally, we show that the traditional SLP matrix is rank-one, making it infeasible to directly apply MLD at the receiver end. To circumvent this limitation, we propose a novel symbol-level smallest singular value maximization problem, termed SSVMP, to enable SLP in systems where users employ the MLD decoding approach. Moreover, to reduce the number of variables to be optimized, we further derive a more generic semidefinite programming (SDP)-based optimization problem. Numerical results validate the effectiveness of our proposed schemes and demonstrate that they significantly outperform the traditional block diagonalization (BD)-based method.