In this paper, we study the mean square error (MSE) and the bit error rate (BER) performance of the box-relaxation decoder in massive multiple-input-multiple-output (MIMO) systems under the assumptions of imperfect channel state information (CSI) and receive-side channel correlation. Our analysis assumes that the number of transmit and receive antennas ($n$,and $m$) grow simultaneously large while their ratio remains fixed. For simplicity of the analysis, we consider binary phase shift keying (BPSK) modulated signals. The asymptotic approximations of the MSE and BER enable us to derive the optimal power allocation scheme under MSE/BER minimization. Numerical simulations suggest that the asymptotic approximations are accurate even for small $n$ and $m$. They also show the important role of the box constraint in mitigating the so called double descent phenomenon.

翻译：在本文中,我们研究了在不完善的频道状态信息(CSI)和接收端频道相关性的假设下,在大规模多投入-多产出(MIMO)系统中的箱式放松解密系统的平均平方差(MSE)和比特差率(BER)的性能。我们的分析假设,传输和接收天线的数量($和$)同时增长,而天线的比例保持不变。为了简化分析,我们认为二进制的转换键(BPSK)调制信号(BPSK)是二进制的。MSE和BER的无症状近似使我们能够在MSE/BER最小化条件下获得最佳的电力分配计划。数字模拟表明,即使小美元和美元,无源近似也是准确的。它们也显示了框限制在缓解所谓的双生现象方面的重要作用。