Asymptotic Performance of Lp-Norm MIMO Detection

Full search L₁-norm (FS-L₁) and sphere decoding L_∞-norm (SD-L_∞) detectors have been previously proposed for multiple-input multiple-output (MIMO) systems as they entail a lower receiver complexity than the optimal L₂-norm detector. However, the performance loss caused by application of these suboptimal detectors in additive white Gaussian noise (AWGN) has not been well investigated yet. In this paper, we analyze the asymptotic bit error rate of general FS-L_p and SD-Lp detectors in independent identically distributed Rayleigh fading channels. Our results are valid for all types of noise with finite moments including AWGN. We show that both FS-L_p and SD-Lp detectors achieve a diversity gain equal to the number of receive antennas independent of the metric parameter p and the type of noise. However, except for the conventional L₂ case, the performances of FS-L_p and SD-Lp detectors are not identical and the performance differences may be several dB for large numbers of receive antennas. Also, our results show that p=2 is not optimal in non-Gaussian noise and L₁ and L_∞ detectors may result in large performance gains or degradations compared to L₂ detectors depending on the type of noise.