Quantifying information rate losses with zero-forcing and maximum-likelihood detectors

MIMO systems have caught a lot of attentions mainly because of the boost of the information rate. However, so far the existing results only consider continuous signals at the receiver side. The effect of detectors on the mutual information has not been addressed. In this paper, we study the mutual information between the transmitted discrete signal and the quantized signal given by maximum-likelihood or zero-forcing detectors over MIMO channels. To differentiate from the mutual information without quantization step, we refer the one here as post-detection mutual information (PMI). The approximations for PMI with MLD or ZFD and the closed form of the PMI with ZFD are derived. We show that the reliable data rates that can be transmitted through the MIMO channels with MLD or ZFD is actually reduced by the presence of quantization. The approximations proposed in the paper match well with the simulation results in the mid to high SNR region.