Capacity Analysis of MIMO Systems Using Limited Feedback Transmit Precoding Schemes

This paper employs a high resolution quantization framework to study the effects of finite-rate feedback of the channel state information (CSI) on the performance of multiple-input-multiple-output (MIMO) systems over independently and identically distributed (i.i.d.) Rayleigh flat fading channels. The contributions of this paper are twofold. First, we extend the general distortion analysis of vector quantizers to deal with complex source variables. Necessary and sufficient conditions that guarantee a concise high-resolution distortion analysis in the complex domain is presented. Second, as an application of the proposed complex distortion analysis, tight lower bounds on the capacity loss due to the finite-rate channel quantization are provided for MIMO systems employing a fixed number of equal power spatial beams. Based on the obtained closed-form analytical results, it is shown that the system capacity loss decreases exponentially as the ratio of the quantization rate to the total degrees of freedom of the channel state information to be quantized. Moreover, MIMO CSI-quantizers using mismatched codebooks that are only optimized for high-signal-to-noise ratio (SNR) and low-SNR regimes are also investigated to quantify the penalties incurred by the use of mismatched codebooks. In addition, the analysis is extended to deal with MIMO systems using multi-mode spatial multiplexing transmission schemes with finite-rate CSI feedback. Finally, numerical and simulation results are presented which confirm the tightness of the derived theoretical distortion bounds.