Detection diversity of spatio-temporal data using Pitman's efficiency for low SNR regimes

In this work, we use Pitman's efficiency to characterize the diversity of a spatio-temporal distributed detection system. Pitman's efficiency directly measures the detection ability of the data at low signal to noise ratios (SNRs). We study how the statistics of spatio-temporal distributed data affect the diversity of the system. We derive the diversity measure for the optimal likelihood ratio test (LRT) statistic for slow fading channels. Moreover, we capture the heterogeneity of channel gains and channel noise variances in our diversity expressions. Then, we compare our diversity measure with another one that was also proposed for low SNRs.