SINR and Throughput Analysis for Random Beamforming Systems with Adaptive Modulation

In this paper, we derive the exact probability distribution of post-scheduling signal-to-interference-plus-noise ratio (SINR) considering both user feedback and scheduling. We also develop an optimized adaptive modulation scheme in orthogonal random beamforming systems with M transmit antennas and K single-antenna users. The exact probability distributions of each user's feedback SINR and the exact post-scheduling SINR are derived rigorously by direct integration and multinomial distribution. It is also shown that the derived cumulative distribution function (CDF) of the post-scheduling SINR happens to be identical to the the existing approximate CDF for SINR higher than 0 dB. The closed form expressions of system performance, such as average spectral efficiency (ASE) and average bit error ratio (A-BER), are derived using the CDF of the post-scheduling SINR. The optimal SINR thresholds that maximize the ASE with a target A-BER constraint are solved using the derived closed form CDF and a Lagrange multiplier. Key contributions of this paper include the derivation of the exact CDF of post-scheduling SINR by direct integration, and its application to an optimized adaptive modulation based on a Lagrange multiplier. Simulations show the correspondence between theoretical and empirical CDF's, and the performance improvement of the proposed adaptive modulation method in terms of ASE.