Weighted MMSE Precoding for Constructive Interference Region

Abstract

In this paper, we propose a symbol-level precoding (SLP) design that aims to minimize the weighted mean square error between the received signal and the constellation point located in the constructive interference region (CIR). Unlike most existing SLP schemes that rely on channel state information (CSI) only, the proposed scheme exploits both CSI and the distribution information of the noise to achieve improved performance. We firstly propose a simple generic description of CIR that facilitates the subsequent SLP design. Such an objective can further be formulated as a nonnegative least squares (NNLS) problem, which can be solved efficiently by the active-set algorithm. Furthermore, the weighted minimum mean square error (WMMSE) precoding and the existing SLP can be easily verified as special cases of the proposed scheme. Finally, simulation results show that the proposed precoding outperforms the state-of-the-art SLP schemes in full signal-to-noise ratio ranges in both uncoded and coded systems without additional complexity over conventional SLP.

Multi-User Symbol-Level Precoding for Downlink Reconfigurable MIMO Communication Systems

“…CI is defined as the interference that moves the received signal further away from the decision boundaries to enhance the demodulation performance, and CIR is the region where the signal is located with CI [5], [14], [29]. Fig.…”

“…1 shows the typical CIR (green areas) for 8PSK, where the dotted lines are the decision boundaries of s k , µ k , and ν k are boundary parameters of CIR corresponding to s k . The typical CIR of s k can be expressed as [29]…”

“…According to the CIR description in [29], the problem of SINR balancing ( 13) can be reformulated as…”

“…The PM problem minimized the transmit power given the SINR requirement [8]- [13], [15], [16], [28], and its optimal solution could be scaled to that of the SINR balancing problem [28], which targeted to maximize the minimum SINR while satisfying the transmit power constraint [5], [9], [14], [16], [26], [27]. Moreover, [29] investigated the MMSE problem that minimizes the mean square error (MSE) between the received signal and the expected signal located in CIR, based on which an SLP scheme was proposed to achieve significant performance with low complexity. Furthermore, the SINR balancing and MMSEbased SLP schemes have been proven to be the generalizations of ZF precoding and MMSE precoding [5], [14], [29], respectively.…”

“…Moreover, [29] investigated the MMSE problem that minimizes the mean square error (MSE) between the received signal and the expected signal located in CIR, based on which an SLP scheme was proposed to achieve significant performance with low complexity. Furthermore, the SINR balancing and MMSEbased SLP schemes have been proven to be the generalizations of ZF precoding and MMSE precoding [5], [14], [29], respectively.…”