Dependent Randomization in Parallel Binary Decision Fusion

We consider a parallel decentralized detection system employing a bank of local detectors (LDs) to access a commonly-observed phenomenon. The system makes a binary decision about the phenomenon, accepting one of two hypotheses ($H_0$ (“absent”) or $H_1$ (“present”)). The $k{{\rm{th}}}$ LD uses a local decision rule to compress its local observations $y_k$ into a binary local decision $u_k$; $u_k=0$ if the $k{{\rm{th}}}$ LD accepts $H_0$ and $u_k=1$ if it accepts $H_1$. The $k{{\rm{th}}}$ LD sends its decision $u_k$ over a noiseless dedicated channel to a Data Fusion Center (DFC). The DFC combines the local decisions it receives from $n$ LDs ($u_1, u_2,\ldots, u_n$) into a single binary global decision $u_0$ ($u_0=0$ for accepting $H_0$ or $u_0=1$ for accepting $H_1$). If each LD uses a single deterministic local decision rule (calculating $u_k$ from the local observations $y_k$) and the DFC uses a single deterministic global decision rule (calculating $u_0$ from the $n$ local decisions), the team receiver operating characteristic (ROC) curve is in general non-concave. The system’s performance under a Neyman-Pearson criterion may then be suboptimal in the sense that a mixed strategy may yield a higher probability of detection when the probability of false alarm is constrained not to exceed a certain value, $\alpha>0$. Specifically, a “dependent randomization” detection scheme can be applied in certain circumstances to improve the system’s performance by making the ROC curve concave. This scheme requires a coordinated and synchronized action between the DFC and the LDs. In this study, we specify when dependent randomization is needed, and discuss the proper response of the detection system if synchronization between the LDs and the DFC is temporarily lost.