On the Performance of Independent Processing of Independent Data Sets for Distributed Detection

We consider a distributed detection problem where sensors are deployed to obtain information about a common source of interest. The centralized processing takes advantage of all sensor information, but requires more resources for data transmission and computation. On the other hand, independent processing requires less resources at a cost of some performance loss. In this letter, we analyze the performance of the generalized likelihood ratio test (GLRT) and the independent GLRT (IGLRT), and quantify the performance loss of the IGLRT. It is shown that the performance loss is due to an extra noise-like term with a chi-squared distribution which only depends on the dimensionality of the unknown parameters p and the number of sensors M. The result is extended to a special scenario when sensors can communicate freely within the same group. Simulation results are provided to verify our analysis.