On the Asymptotic BER of MMSE Detector in Massive MIMO Systems

The minimum-mean-square-error (MMSE) detector is widely used in multiple-input multiple-output (MIMO) systems, since it is considered as the best linear detector. However, obtaining a tight bit error rate (BER) expression is not a straightforward task. In massive MIMO (M-MIMO) systems, due to the asymptotically orthogonal channel matrix property, the BER evaluation is less complex by using the random matrix theory. In this article, two closed-form BER expressions are derived for the MMSE detector in M-MIMO systems. The first one is an asymptotic result by using the Marchenko-Pastur distribution, and the second one is an accurate result by using an approximation of the ZF detector performance.