Amendment to "Performance Analysis of the V-BLAST Algorithm: An Analytical Approach." [1]

TL;DR

This paper revises and extends an analytical approach for V-BLAST performance analysis, demonstrating that previous approximations are valid and providing new BER results for systems with more than two receive antennas.

Contribution

It shows the previous analysis holds without approximations and extends BER results to BPSK-modulated V-BLAST with multiple receive antennas.

Findings

Previous approximations are valid with minor modifications.

Extended BER analysis to BPSK with more than two receive antennas.

Block error rate is dominated by first step BER at high SNR.

Abstract

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).