Theoretical performance analysis and simulation of a GLRT tonal detector

The performance analysis for an optimal tonal detector is described . The detector is based on the generalized likelihood ratio test (GLRT) by using the statistical properties of the power spectrum observations. Unlike the conventional average power processor (AVGPR), which performs simple integration by averaging, the tonal detector is developed by optimally integrating the power spectrum observations and exploits the statistical characteristics of the power spectrum. The exact performance of the proposed detector is difficult to be evaluated, since the probability distribution of the log likelihood ratio cannot be obtained easily. Also, there is no general result for the GLRT detector. Here we adopt two methods to solve the problem. One is Van Trees' (1968) method and the other is the central limit theorem method. Using the second method, we derive the approximate probability density functions (PDF) of the detector under both hypotheses. They approach the Gaussian distribution with shifted mean for large data records. The Monte Carlo simulations support our conclusion about the PDF. On the basis of that, we derive the receiver operating characteristics (ROC) of the optimal detector. Then we compare it with the AVGPR, the performance of which is also studied. The simulation results show that the performance of our detector is better than the conventional AVGPR.