Adaptive array detection of uncertain rank one waveforms

Adaptive array detection of known (within a complex scaling) rank one space time waveforms in unknown spatial noise has received considerable attention. The two published solutions are the adaptive matched filter, and the GLRT. We expand on this work to consider the case of rank one waveforms that are uncertain, i.e., only partially known. More precisely, we model the space time steering vector as the Kronecker product of two vectors, each of which is unknown but is known to lie in a known subspace. Applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication. Using the principle of invariance, we construct detectors based on the maximal invariant. We show that the SNR required to achieve a given detection probability (for a given false alarm rate) is only weakly impacted by waveform uncertainty. Thus, our detector approaches the performance of earlier detectors, which entail known waveforms.