Accurate Analytical BER Performance for ZF Receivers Under Imperfect Channel in Low-SNR Region for Large Receiving Antennas

Most analytical work for zero-forcing (ZF) receivers are conducted for small-scale multiple-input multiple-output (MIMO) systems in large signal-to-noise ratio (SNR) region and under small channel estimation error conditions. Using large receiving antennas, systems are expected to work in the low-SNR region and under large channel estimation error. In these conditions, we observe an obvious mismatch between the existing analytical results and the simulations. In this letter, we derive an accurate analytical bit error rate (BER) expression for ZF receivers under imperfect channel estimation. We show that our results match nicely with the simulations in small-scale and large-scale MIMO systems, even when large channel estimation error presents.