Exact post-scheduling SINR analysis for orthogonal random beamforming systems

Abstract

Derived are the exact cumulative distribution functions (CDFs) of each user's feedback signal-to-interference-plus-noise ratio (SINR), and the post-scheduling SINR in orthogonal random beamforming systems with M transmit antennas and K single-antenna users considering both user feedback and scheduling. A key contribution is to derive the exact CDF of the post-scheduling SINR by direct integration, and it is verified by Monte-Carlo simulations. It is also shown that the existing approximate CDF is different from the exact distribution for SINR smaller than 0 dB. Introduction: Since orthogonal random beamforming (ORBF) was first proposed in [1], it has been considered a practical scheme for a Gaussian broadcast channel with M transmit antennas and K single-antenna users. To analyse the performance of ORBF systems such as sum-rate, throughput, and average BER, it is necessary to know the statistical distribution of the scheduled user's signal-to-interference-plus-noise ratio (SINR). In the literature [1-5], however, performance analysis has been done with an approximate cumulative distribution function (CDF) of the post-scheduling SINR, which assumes an unrealistic feedback scheme.This Letter studies the exact statistical distribution of the post-scheduling SINR in the orthogonal random beamforming system with M transmit antennas and K single-antenna users considering both user feedback and scheduling. The probability distributions of each user's feedback SINR and the post-scheduling SINR are derived rigorously by direct integration and multinomial distribution. It is also shown that the derived CDF of the post-scheduling SINR happens to be the same as the the existing approximate CDF for SINR higher than 0 dB.