Matched and adaptive subspace detectors when interference dominates noise

In much of modern radar, sonar and wireless communication it seems more reasonable to model measurements as signal-plus-subspace interference-plus-broadband noise, than as signal-plus-colored noise. This observation leads naturally to a variety of detection and estimation problems in the linear statistical model. To solve these problems, one requires oblique pseudo-inverses, oblique projections, and zero-forcing orthogonal projections. The problem is that these operators depend on knowledge of signal and interference subspaces, and this information is often not at hand. More typically the signal subspace is known, but the interference subspace is unknown. In this paper we prove a theorem which allows these operators to be estimated directly from experimental data, without knowledge of the interference subspace. As a by-product, the theorem shows how signal subspace covariance and power may be estimated. The results of this paper form the foundation for the rapid adaptation of receivers which are then used for detection and estimation. They may be applied to detection and estimation in radar and sonar and to data decoding in multiuser communication receivers.