Multichannel Detection of an Unknown Rank-N Signal Using Uncalibrated Receivers

This letter addresses the problem of detecting an unknown rank-N signal using multiple receivers that are uncalibrated in the sense that each applies an unknown scaling to the received signal and the (possibly unequal) receiver noise powers are unknown. This problem has been addressed for the case in which the signal can be modeled as a linear combination of N Gaussian random vectors. We consider the alternative approach of modeling the signal as a deterministic unknown. We derive an approximate generalized likelihood ratio test (GLRT) for low signal-to-noise ratios (SNRs). The resulting detector is invariant to relative scalings of the data, and is therefore constant false alarm rate (CFAR) with respect to the unknown noise powers. Numerical examples show this low-SNR GLRT performs well at all SNRs and can outperform other CFAR detectors when N = 1. However, CFAR detectors derived assuming unknown Gaussian signals appear to perform better for N > 1.