V-BLAST Without Optimal Ordering: Analytical Performance Evaluation for Rayleigh Fading Channels

Abstract

Abstract-The Bell Labs layered space-time (BLAST) algorithm is simple, and hence, a popular choice for a multiple-input multiple-output (MIMO) receiver. Its bit-error rate (BER) performance has been studied mainly using numerical (Monte Carlo) techniques, since exact analytical evaluation presents serious difficulties. Close examination of the problem of BLAST BER performance analysis reveals that the major difficulty for analytical evaluation 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 evaluation is possible for arbitrary number of transmit and receive antennas in an independent, identically distributed Rayleigh fading channel, which provides deep insight and understanding that cannot be gained using the Monte Carlo approach alone. A result on the maximum ratio combining weights, which is used at each detection step, is derived to obtain a number of results: independence of noise, distribution of signal-to-noise ratio (SNR), and block-or bit-error rates. We present a detailed analysis and expressions for uncoded error rates at each detection step, which hold true for any modulation format and take simple closed form in some cases. Asymptotic form of these expressions for large SNRs is particularly simple. Extensive Monte Carlo simulations validate the analytical results and conclusions.Index Terms-Bit-error rate (BER), Bell Labs layered space-time (BLAST), error propagation, multiantenna systems, multiple-input multiple-output (MIMO), performance analysis.

Performance Analysis of V-BLAST with Optimum Power Allocation

“…In the optimized system, i α are chosen to minimize the total BER or the BLER, either average or instantaneous. Since we rely on the BLAST error rate performance analysis in [5], [7]- [9], we also adopt the same basic assumptions.…”

“…Closed-from expressions for the BLER and TBER of the unordered V-BLAST can be found in [5], [7]- [10]. For the sake of simplicity and completeness, we give below their high-SNR approximations only.…”

“…The optimal ordering procedure is computationallydemanding, which is a limitation for some applications. Since the successive interference cancellation is used, lower detection steps have on average a smaller SNR and thus produce more errors, which further propagate to higher steps [5]- [7] so that the overall error performance may be not satisfactory, especially if no coding is used.…”

“…for given channel realization) total error rate (TBER) 1 of the V-BLAST, with or without the optimal ordering [3] [4]. The approximate solutions for the 1 The TBER is defined as the error rate at the output stream to which all the individual sub-streams are merged after the detection (see [7] for more details). Thus, it takes into account the actual number of errors at the transmitted symbol vector.…”

“…Thus, it takes into account the actual number of errors at the transmitted symbol vector. The block error rate (BLER) is defined as the probability to have at least one error at the detected Tx symbol vector [7]. It does not take into account the actual number of errors, but only the fact of their presence.…”