In this work, we explore symbol-level precoding (SLP) and efficient decoding strategies for downlink transmission in multi-user multiple-input multiple-output (MU-MIMO) systems. We specifically study scenarios where the base station (BS) sends multiple multi-level modulated data streams to users for decoding. We formulate an optimization problem for joint symbollevel transmit precoding and receive combining. However, the receive combining matrix is dependent on the transmit symbols in the joint design scheme, thus, we employ maximum likelihood detection (MLD) method at the receiver side. we demonstrate that the smallest singular value of the precoding matrix significantly affects the MLD performance, while traditional SLP scheme returns a rank-one precoding matrix, which results in inferior error-rate performance to users. To overcome this challenge, we propose a novel channel state information (CSI)-Free SLP scheme that employs semidefinite programming (SDP) method to enable SLP technique in systems utilizing MLD decoding, where the design of the precoding matrix depends only on the modulated data symbols. Numerical simulations confirm that our proposed scheme substantially outperforms the traditional block diagonalization methods.

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.

This paper addresses the design of the receive combining matrix in a multiuser multiple-input multiple-output (MU-MIMO) downlink system, where the base station (BS) employs symbol-level precoding (SLP) to transmit multiple data streams to multiple users with multiple antennas. Unlike in the single-antenna user scenario, the design of the receive combining matrix becomes crucial in this context. To overcome the challenge of the receive combining matrix's dependency on the transmit signals, we propose a practical scheme utilizing the interference rejection combiner (IRC) for signal decoding. However, directly applying the IRC receiver to the considered MU-MIMO system presents challenges due to the rank-one transmit precoding matrix. To address this issue, we propose a new regularized IRC (RIRC) receiver. The problem is tackled by using the alternating optimization (AO) method, enabling the derivation of an optimal solution structure for the transmit precoding matrix. Numerical results demonstrate the substantial performance gain of the practical SLP scheme with the RIRC receiver over conventional Block Diagonalization (BD) based approach.

Consider a multiuser multiple-input multiple-output (MU-MIMO) downlink system in which the base station (BS) sends multiple data streams to multi-antenna users via symbol-level precoding (SLP), where the optimization of receive combining matrix becomes crucial, unlike in the single-antenna user scenario. We begin by introducing a joint optimization problem on the symbol-level transmit precoder and receive combiner. The problem is solved using the alternating optimization (AO) method, and the optimal solution structures for transmit precoding and receive combining matrices are derived by using Lagrangian and Karush-Kuhn-Tucker (KKT) conditions, based on which, the original problem is transformed into an equivalent quadratic programming problem, enabling more efficient solutions. To address the challenge that the above joint design is difficult to implement, we propose a more practical scheme where the receive combining optimization is replaced by the interference rejection combiner (IRC), which is however difficult to directly use because of the rank-one transmit precoding matrix. Therefore, we introduce a new regularized IRC (RIRC) receiver to circumvent the above issue. Numerical results demonstrate that the practical SLP-RIRC method enjoys only a slight communication performance loss compared to the joint transmit precoding and receive combining design, both offering substantial performance gains over the conventional BD-based approaches.