Capacity Analysis of Correlated Multiple Antenna Systems With Finite Rate Feedback

We consider in this paper the analysis of transmit beamforming methods in multiple antenna systems over correlated fading channels and with finite rate feedback of the channel state information. The problem is formulated as a general vector quantization problem with encoder side information, constrained quantization space and non-mean-square distortion function. By utilizing the high-resolution distortion analysis of the generalized quantizer, which is applicable to a wide range of scenarios, we obtain a tight lower bound on the capacity loss of the finite rate quantized MISO system over correlated fading channels. The lower bound of the capacity loss of correlated MISO channels is a generalization of existing results available for i.i.d. channels. The bound, in addition to providing insight into the exact nature of dependence of the quantization loss on the channel correlation matrix, indicates that the loss is less than that of the i.i.d. channels but with the same exponential decaying factor w.r.t. the feedback rate. The generality of the framework is further demonstrated by considering its application to the analysis of suboptimal mismatched channel quantizers, i.e. quantizers designed with an incorrect channel covariance matrix, and comparing it to systems with optimal quantizers. Finally, numerical and simulation results of the finite rate quantized MISO beamforming system with codebook designed by the Lloyd algorithm are presented that confirm the accuracy of the obtained analytical results.