In multi-user multiple input multiple output (MU-MIMO) uplink, the bit error rate (BER) of linear detection schemes, namely, zero forcing (ZF) and minimum mean square error (MMSE) under correlated Rayleigh fading channel deteriorates with increase in spatial correlation and load factor due to the increase in the condition number of the channel matrix. Moreover, the performance gap between ZF and MMSE increases with increase in the antenna number for large load factors. To address this issue, in this paper, truncated singular value decomposition (TSVD), which is a popular method for solving ill-posed problem, is used in the ZF detection process through proper selection of hard threshold. However, the pseudo-inverse computed using TSVD is an approximate inverse, which results in interference at the output of the detection process. Therefore, a mathematical expression for the post-processing signal-to-interference-plus-noise ratio (SINR) of the substream is derived and subsequently BER is evaluated. Further, the analytical BER is analyzed with respect to the parameters namely, average signal-to-noise ratio (SNR) ( ), correlation coefficient ( ), load factor ( ), and number of singular values considered to compute the hard threshold ( ) and also validated by Monte Carlo trails. From the simulation results, it is observed that for higher order MU-MIMO systems and at lower values of , the performance of TSVD-based scheme is comparable with that of MMSE by decreasing the truncation parameter ( ). Moreover, as the complexity of TSVD-based ZF using randomized schemes is ), therefore, the complexity of detection significantly decreases with decrease in .

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相关瑞利衰落信道下基于截断SVD的MU-MIMO ZF检测方案的误码率分析

在多用户多输入多输出（MU-MIMO）上行链路中，线性检测方案的误码率（BER），即相关瑞利衰落信道下的迫零（ZF）和最小均方误差（MMSE）随着增加而恶化由于信道矩阵条件数的增加，空间相关性和负载因子的变化。此外，对于大负载因子，ZF 和 MMSE 之间的性能差距随着天线数量的增加而增加。为了解决这个问题，在本文中，通过正确选择硬阈值，在ZF检测过程中使用截断的奇异值分解（TSVD），这是解决缺乏问题的流行方法。但是，使用 TSVD 计算的伪逆是近似逆，这会导致检测过程的输出产生干扰。所以，导出子流的后处理信号与干扰加噪声比 (SINR) 的数学表达式，然后评估 BER。此外，分析误码率是针对参数进行分析的，即平均信噪比 (SNR) ( )、相关系数 ( )、负载因子 ( ) 以及计算硬阈值 ( ) 时考虑的奇异值数量， 并且还通过蒙特卡罗轨迹进行了验证。从仿真结果可以看出，对于更高阶的 MU-MIMO 系统，在较低的 值下，通过降低截断参数 ( ) ，基于 TSVD 的方案的性能与 MMSE 的性能相当 。此外，由于使用随机方案的基于 TSVD 的 ZF 的复杂度为)，因此，检测的复杂度随着 的减小而显着降低。