BER analysis of truncated SVD‐based MU‐MIMO ZF detection scheme under correlated Rayleigh fading channel

Abstract

SummaryIn 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 .