Decision Statistics for Noncoherent Signal Detection in Multi-Element Antenna Arrays

This article gives a detailed analysis of the characteristics of the exact statistic for the optimal noncoherent signal detection in multi-element antenna arrays. This task is important for reliable initial detection of User Equipment (UE) signals coming from an unknown direction in LTE random access procedure. It is shown that application of the exact statistic is complex because the thresholds of the Neyman-Pearson (NP) criterion depend on the SNR. A detailed comparison of the exact and various approximate decision statistics has been carried out. The results show that the choice of the statistic can make noticeable impact on the probability of missed detection for multi-element antenna array. A new combined decision statistic has been proposed, whose characteristics are close to the exact statistic.