Consistent CFAR detection of a linear signal based on partially consistent observations

This letter addresses the problem of consistent constant false-alarm rate (CFAR) detection based on partially consistent observations. The term "partially consistent observations" refers to the fact that the number of unknown parameters increases with the number of samples, and therefore, the number of observed samples is insufficient for consistent estimation of all parameters. Specifically, the problem of detecting a deterministic signal with unknown linear parameters in nonstationary white Gaussian noise is addressed. Two families of CFAR detectors are proposed; their consistency is discussed; and their performance is examined.