Performance analysis of the V-BLAST algorithm: an analytical approach

A geometrically based analytical approach to the performance analysis of the V-BLAST algorithm is presented in this paper, which is based on the analytical model of the Gramm-Schmidt process. This approach presents a new geometrical view of the V-BLAST and explains some of its properties in a complete and rigorous form, including a statistical analysis of postprocessing signal-to-noise ratios for a 2×n system (where n is the number of receive antennas). Closed-form analytical expressions of the vector signal at ith processing step and its power are presented. A rigorous proof that the diversity order at ith step (without optimal ordering) is (n-m+i) is given (where m is the number of transmit antennas). It is shown that the optimal ordering is based on the least correlation criterion and that the after-processing signal power is determined by the channel correlation matrices in a fashion similar to the channel capacity. Closed-form analytical expressions are derived for outage probabilities and average BER of a 2×n system. The effect of the optimal ordering is shown to be to increase the first step SNR by 3 dB (rather than to increase the diversity order as one might intuitively expect based on the selection combining argument) and to increase the second step outage probability twice.