Asymptotic Performance of Lp-Norm MIMO Detection

Full search L1-norm (FS-L1) and sphere decoding Linfty-norm (SD-Linfty) 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-Lp 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-Lp 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-Lp 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 Linfty detectors may result in large performance gains or degradations compared to L2 detectors depending on the type of noise.