On BER analysis of the BLAST without optimal ordering over Rayleigh fading channel

The BLAST algorithm is a simple and, hence, popular solution for signal processing at the MIMO receiver. Its BER performance has been studied mainly using numerical (Monte-Carlo) techniques since exact analytical analysis presents serious difficulties. Close examination of the problem of BLAST BER performance analysis reveals that the major difficulty for analytical analysis is due to the optimal ordering procedure. Hence, we analyze the algorithm performance without optimal ordering. While this is a disadvantage of the analysis, there are certain advantages as well. Exact closed-form analytical analysis is possible in the general case of m×n system for the iid (independent and identically distributed) Rayleigh channel, which provides deep insight and understanding that cannot be gained using the Monte-Carlo approach alone. We present closed-form expressions for instantaneous and average BER at each detection step, which hold true for any modulation format and take the simple form in some cases (i.e. BPSK, QPSK, BFSK, etc.). Asymptotic form (for large SNR) of these expressions is especially simple. As expected, the first-step BER dominates the total BER and D-BLAST provides some improvement over V-BLAST in terms of the "worst" BER, which, however, disappears asymptotically. We stress that these conclusions hold true for any modulation. Comparison to the V-BLAST with optimal ordering allows to better understand the advantages provided by the optimal ordering procedure.