Distributed Quantization of Order Statistics with Applications to CSI Feedback

Feedback of channel state information (CSI) in wireless systems is essential in order to exploit multi-user diversity and achieve the highest possible performance. When each spatially distributed user in the wireless system is assumed to have i.i.d. scalar CSI values, the optimal fixed-rate and entropy-constrained point density functions are established in the high-resolution regime for the quantization of the CSI feedback to a centralized scheduler under the mean square error (MSE) criterion. The spatially distributed nature of the users leads to a distributed functional scalar quantization approach for the optimal high resolution point densities of the CSI feedback. Under a mild absolute moment criterion, it is shown that with a greedy scheduling algorithm at the centralized scheduler, the optimal fixed-rate point density for each user corresponds to a point density associated with the maximal order statistic distribution. This result is generalized to monotonic functions of arbitrary order statistics. Optimal point densities under entropy-constrained quantization for the CSI are established under mild conditions on the distribution function of the CSI metric.