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Sketching the interference wall: A linear programming approach

In this paper, we study the fundamental performance for detecting a signal in the presence of interference and noise. A Gaussian noise model with zero mean and fixed variance is assumed, where the probability distribution of the interference exhibits uncertainty. Among our interests are the “regions of detection performance” (RODP) due to the presence of interference. The RODP represents a set of possible PMD (PFA) values under various interference power levels and a fixed noise power level. We adopt the linear programming (LP) approach to obtain tight bounds on probability of missed detection (PMD) and probability of false alarm (PFA) per node and at the fusion site. Although classical moment-bound theory delivers identical results for the basic problem setup (e.g. one node), our interpretation based on LP appears to be more succinct and may be generalized to different scenarios. Within certain interference level, the fusion-based detection system yields concave upper boundary and convex lower boundary of RODP, both are tight bounds and functions of interference power. Our results may applicable in hierarchical fusion or other detection-driven scenarios.