An exact outage analysis of zero-forcing V-BLAST with greedy ordering

In this paper, an outage probability analysis is carried out on zero-forcing (ZF) vertical Bell Labs Layered Space-Time (V-BLAST) algorithm based on a greedy selection of decoding order, which is optimal in diversity-multiplexing tradeoff sense. We provide a mathematical framework to make the analysis tractable and derive the probability density function expressions of the squared substream gains. Especially, we obtain a compact expression on the joint pdf of squared substream gains for any number of transmit and receive antennas. Moreover, using the analytical results, we illustrate the optimum cutoff value under optimal power allocation that minimizes the total consumed power for a given target total rate. Finally, we provide numerical results and verify our analysis by means of simulations.