Large-system performance analysis of blind and group-blind multiuser receivers

Abstract

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain , the number of users , and the number of received signal samples all go to infinity, while keeping the ratios and fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the function.

Multiuser detectors for large CDMA random access systems over Rayleigh fading channels

“…Since the original SIR expressions for decorrelator and MMSE detectors given by (8) and (30) are functions of spreading sequences, when the number of users is large, the exact SIR computation results are difficult to be obtained. However, because the asymptotic SIR results for decorrelator and MMSE detectors presented in (17) and (32) are merely functions of SNR, transmission probability θ and demanded traffic α, and independent of the number of users, the SIR results can be obtained when the system is large.…”

“…The exact and asymptotic SIR results are depicted in Figures 1--3 to show the accuracy of the deduced SIR expressions (17) and (32), in which, the solid curves represent the asymptotic results and the dashed curves represent the exact results, and the number of users K is assumed to be 16, 32, and 64. While for the decorrelator, the asymptotic and exact SIR results are obtained through (17) and (8), the asymptotic and exact SIR results for the MMSE detector are obtained through (32) and (30). Figure 1 describes the average SIR performance of decorrelator and MMSE detectors versus SNR with α = 1 and θ = 0.8, from which, it can be seen clearly that the MMSE detector can achieve larger average SIR value than decorrelator detector, especially in low SNR region.…”

“…Obviously, the spectral radius of (I − AĨA * ) is bounded in K. According to Theorem A.2 in Ref. [17], we have…”

“…However, since all users interfere with each other, it would be difficult to determine the distribution of β 1 (n). Encouragingly, recent results [10,17] on the large CDMA systems show that the interference can be decoupled and the analysis of β 1 (n) is feasible. Therefore, following theorem is proposed to analyze β 1 (n).…”