Reduced Feedback Schemes Using Random Beamforming in MIMO Broadcast Channels

A random beamforming scheme for the Gaussian MIMO broadcast channel with channel quality feedback is investigated and extended. Considering the case where the receivers each have receive antennas, the effects of feeding back various amounts of signal-to-interference-plus-noise ratio (SINR) information are analyzed. Using the results from order statistics of the ratio of a linear combination of exponential random variables, the distribution function of the maximum order statistic of the SINR observed at the receiver is found. The analysis from viewing each antenna as an individual user is extended to allow combining at the receivers, where it is known that the linear MMSE combiner is the optimal linear receiver and the CDF for the SINR after optimal combining is derived. Analytically, using the Delta Method, the asymptotic distribution of the maximum order statistic of the SINR with and without combining is shown to be, in the nomenclature of extreme order statistics, of type 3. The throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users. Finally, to further reduce the amount of feedback, a hard threshold is applied to the SINR feedback. The amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded.