Passive Multi-Channel Detection: A General First-Order Statistical Theory

In this article a general first-order statistical framework is established for passive multi-channel detection and localization of an unknown radiated signal. This radiated signal is written in terms of a finite basis expansion, and the map between these basis coefficients and the measured data on a sensor is a channel that might be known, partially known, or unknown except for the dimension of the signal subspace. The noise at each sensor is assumed to be Gaussian and white; the noise variances at each sensor may be known, unknown and equal, or unknown and possibly unequal. This article develops detectors for all nine of these cases. These detectors are each generalized likelihood ratios, and typically decompose into locally computed detector statistics plus pairwise coherence, or cross-validation, statistics. Of particular note are the scale-invariant detectors that preserve a constant false alarm rate (CFAR) property with respect to noise power.