Capacity Analysis of Multiple Antenna Systems with Mismatched Channel Quantization Schemes

We consider in this paper the analysis of transmit beamforming methods in multiple antenna systems with finite-rate feedback of the channel state information. We focus our attention on providing capacity analysis of a quantized MISO system over correlated fading channels with sub-optimal and mismatched channel quantizers. Two types of mismatched quantizers are investigated, which include: 1) quantizers designed with simple suboptimal criterion, and 2) quantizers whose codebooks are designed with a mismatched channel covariance matrix. We approach this problem from a source coding perspective by formulating the quantized MISO system as a general vector quantization problem with encoder side information, constrained quantization space and non-mean-squared distortion function. By utilizing the high-resolution distortion analysis of the generalized quantizer, we obtain tight lower bounds of the capacity loss of a quantized MISO system with both optimal and mismatched channel quantizers. Theoretical as well as empirical results reveal significant performance degradation of the mismatched quantizers when compared to the optimal channel quantizers. This elucidates the importance of choosing proper codebook design criterion and using correct source statistical distributions