Detection diversity of multiantenna spectrum sensors

In the context of spectrum sensing, we investigate the performance of detectors equipped with M antennas (co-located or distributed) under Rayleigh fading, in terms of detection diversity. Rather than the high-SNR concept of diversity order common in the communications literature, we adopt the notion recently advocated by Daher and Adve in the radar community: the slope of the average probability of detection (P̅_D) vs. SNR curve at P̅_D = 0.5. This definition is well suited to spectrum sensing, which invariably deals with low SNR levels. It is shown that the diversity order grows as M for an optimal centralized detector having access to all observations, whereas for the two distributed schemes considered (the multiantenna energy detector and the OR detector) it grows no faster than √M.