Performance of natural frequency-based target detection in frequency domain

We consider the performance analysis of the natural frequency-based radar target detection in the frequency domain. Two cases of the detection are considered: one is for known residues, called the likelihood ratio test (LRT), and the other is for unknown residues, called the generalized likelihood ratio test (GLRT). In time-domain detection scheme [Mooney JE, Ding Z, Riggs L. Performance analysis of a GLRT in late-time radar target detection. Prog. Electromagn. Res. 1999; 24: 77-96], the authors showed that the decision statistic for the LRT and the decision statistic for the GLRT are Gaussian distributed and chi-square distributed, respectively. Note that the formulation in [Mooney JE, Ding Z, Riggs L. Performance analysis of a GLRT in late-time radar target detection. Prog. Electromagn. Res. 1999; 24: 77-96] is for the time-domain late time response and that the formulation proposed in this paper is for the frequency response. In this paper, we consider the detection problem in the frequency domain. The scheme is validated by comparing the detection performance using the analytical method with that using the Monte-Carlo simulation.