Building a confidence interval for the number of signals in noise using likelihood ratio test statistics

We propose a multi-step procedure for constructing a confidence interval for the number of signals present in noise. The proposed procedure uses likelihood ratio statistics and their simulated percentiles in a sequential manner to estimate the upper and lower limits for the confidence interval. A preference zone in the parameter space of the population eigenvalues is defined and used to separate signals from noise. We derive the least favorable configuration asymptotically under the preference zone and use it to determine the procedure parameters for the required confidence level. We applied our procedure to computer simulated radar data and the MCARM measured data set.