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 postscheduling 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.