Likelihood ratio test-based interval estimate of the number of signals present in a measurement

A multi-step procedure is proposed to construct a confidence interval for the number of signals present and a comparative analysis of our procedure with other existing procedures is conducted. The proposed procedure uses likelihood ratio statistics and its simulated percentiles sequentially to determine the upper and lower limits for the confidence interval. A preference zone in the parameter space of the population eigenvalues is denned and it is used to separate the signals and the noise. The least favourable configuration (LFC) is derived asymptotically under the preference zone. Under the LFC, the procedure parameters necessary to attain the required confidence level are determined. A comparative analysis with other procedures is presented in tables.