Analysis of MIMO Systems with Finite-Rate Channel State Information Feedback: A Source Coding Perspective

This paper employs a source coding approach to study the effects of finite-rate quantization of the channel state information on the performance of MIMO systems over flat fading channels. In our previous work, the finite-rate feedback-based communication system was formulated as a general fixed-rate vector quantization problem for the purposes of analysis. In this paper, the analysis is extended to deal with complex variables further facilitating its use for communication systems with feedback. As an extended application of the general distortion analysis, tight lower bounds on the capacity loss of MIMO systems due to the finite-rate channel quantization are provided in this paper. Based on the obtained analytical results, it is shown that the system capacity loss decreases exponentially with the ratio of the quantization rate to the total degrees of freedom of the source variable. Interestingly, it is also shown that when the number of beams used by the transmit pre-coder equals to half of the transmit antennas (but not the minimal number of transmit and receive antennas), the system has the maximum number of free parameters to quantize. Finally, numerical and simulation results are presented which further confirm the tightness of theoretical distortion bounds.