Study on consistent CFAR detection of a linear signal with unknown parameters

The problem of consistent constant false-alarm rate (CFAR) detection based on partially consistent observations is addressed. The term "partially consistent observation" means 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 discussed. Two families of CFAR detectors are proposed with their consistency and performance being studied.