Effect of CSI quantization on the average rate in MU-MIMO WLANs

In Multi-User Multiple Input Multiple Output (MU-MIMO) Wireless Local Area Networks (WLANs), the optimal-solution such as Dirty Paper Coding (DPC) or the sub-optimal solution Zeroforcing Beamforming (ZFB) with perfect Channel State Information (CSI), is practically limited due to the complexity and the non-availability of perfect CSI at the Access Points (APs)/transmitters. In such a context, ZFB based on channel quantization available at the APs (ZFQ) is the obvious choice for the Multi-User transmission strategy. However, since the quantized CSI is used instead of the perfect CSI at the APs, the quantization error and its impact on the average rate for ZFQ have to be quantified in MU-MIMO WLAN settings. In this paper, we derive a closed-form expression for the upper bound of the channel quantization error and the average rate reduction due to the quantization error with respect to the perfect CSI at the APs. In MU-MIMO WLAN settings, our analytical and numerical studies show that, with an increasing number of antennas at the clients, both the quantization error bound and the average rate reduction increase for ZFQ, in comparison to the ZFB with the perfect CSI.