Detection of a bandlimited signal with unknown parameters

In this paper, we investigate the detection of a band-limited signal with unknown central frequency, exact bandwidth and the spectrum in white Gaussian noise with unknown variance. We propose a practically implementable Generalized Likelihood Ratio (GLR) detector with these unknown parameters and verify its performance through some simulation examples. Furthermore, in order to evaluate the performance of this detector, we derive a Most Powerful Invariant (MPI) detector in the case of known partial Signal to Noise Ratios (SNRs), i.e., where the SNR of the different Discrete Fourier Transform components of the signal are known. Our results show the close performance of the GLR detector and this MPI detector. In addition, we propose a locally MPI detector in small SNRs, that performs slightly better than GLR in these SNRs.