Error Exponents for Target-Class Detection with Nuisance Parameters

We study the target class detection performance of a sensor network having a structured topology. The target is in the far-field of the network, located at a distance gamma and angle thetas, and produces a random signal field that is sampled by sensors. It is assumed that samples have a correlation structure and power level that depend on gamma, thetas and the target´s class i, i isin {0,1}. We study the Neyman-Pearson miss probability error exponent for this scenario using large deviations theory. When (gamma, thetas) is known, we characterize the properties of the error exponent as a function of signal and design parameters. When (gamma, thetas) has at least one unknown component, we use the theory of adaptive tests to prove that there exists a test that achieves the same error exponent as if (gamma, thetas) were known in some scenarios, but that there exists no such test in others.