Multichannel detection of an unknown rank-one signal with uncalibrated receivers

This paper addresses the problem of detecting an unknown rank-one signal using multiple receivers that are uncalibrated in the sense that they each apply an unknown scaling to the received signal, and their respective noise powers are unknown. This problem has been addressed for the case in which the unknown signal can be modeled as a Gaussian random vector. However, that assumption is not applicable to some signal types, such as the constant modulus signals found in radar and communications. For these problems, the signal can be modeled as a deterministic unknown, which is the approach taken here. We derive a generalized likelihood ratio test for this problem under a low signal-to-noise ratio (SNR) assumption. The resulting detector is invariant to relative scalings of the data, and therefore possesses the constant false alarm rate (CFAR) property with respect to the unknown noise powers. Numerical examples show the proposed detector can outperform CFAR detectors derived under the Gaussian assumption.