  An analytical technique for the outage and BER analysis of the nx2 V-BLAST
algorithm with the optimal ordering has been presented in [1], including
closed-form exact expressions for average BER and outage probabilities, and
simple high-SNR approximations. The analysis in [1] is based on the following
essential approximations: 1. The SNR was defined in terms of total
after-projection signal and noise powers, and the BER was analyzed based on
their ratio. This corresponds to a non-coherent (power-wise) equal-gain
combining of both the signal and the noise, and it is not optimum since it does
not provide the maximum output SNR. 2. The definition of the total
after-projection noise power at each step ignored the fact that the
after-projection noise vector had correlated components. 3. The after-combining
noises at different steps (and hence the errors) were implicitly assumed to be
independent of each other. Under non-coherent equal-gain combining, that is not
the case. It turns out that the results in [1] hold also true without these
approximations, subject to minor modifications only. The purpose of this note
is to show this and also to extend the average BER results in [1] to the case
of BPSK-modulated V-BLAST with more than two Rx antennas (eq. 18-20).
Additionally, we emphasize that the block error rate is dominated by the first
step BER at the high-SNR mode (eq. 14 and 21).
