Theoretical analysis of non-linear quantization of broadband channels

Multi-user multi-antenna wireless communications require the knowledge of channel state information (CSI) in order to cancel or mitigate interference between users. The knowledge of this quantization error due to the channel quantization is of extreme importance to theoretically evaluate and improve the performance of limited feedback communications. In this paper we present theoretical expressions for the statistical characterization of the quantization error obtained when a broadband multicarrier channel is quantized in the frequency domain, taking advantage of Gaussian channel behavior for multipath channels. The derived expression is valid for any type of non-linear quantization, and it is validated through Monte Carlo simulations for an interpolated uniform and non-uniform quantization strategies, under different scenarios.