Analytical characterization of CSI quantization effects on broadband multipath channels

The knowledge of channel state information (CSI) at transmitter is crucial in precoding techniques to efficiently explore wireless multiuser multi-antenna capabilities namely to mitigate the interference and/or to separate spatial streams. For frequency division duplex systems, the CSI available is a quantized version fed back from the receivers, and the nonlinear effects associated to CSI quantization can lead to significant performance degradation. The knowledge of the statistical characteristics of those nonlinear distortion effects is important for performance evaluation purposes, as well as to design robust precoding techniques. In this paper we consider a general broadband multipath channel sampled in the frequency domain and obtain the analytical statistical characterization of the nonlinear distortion effects associated to CSI quantization. Our analytical approach is valid for non-uniform quantizers, and it also includes quantizer saturation and channel oversampling effects. It provides a detailed statistical characterization in time and frequency domains, associated to the channel impulse and frequency responses, respectively. The derived theoretical statistical characterization of quantization distortion is validated by simulation, showing its high accuracy. As an application, we consider a multicarrier transmission employing a precoding technique with reduced feedback techniques employing a small number of quantization bits per channel sample.