On interval estimation for the number of signals

We propose a multi-step procedure for constructing a confidence interval for the number of signals present. The proposed procedure uses the ratios of a sample eigenvalue and the sum of different sample eigenvalues sequentially to determine the upper and lower limits for the confidence interval. A preference zone in the parameter space of the population eigenvalues is defined to separate the signals and the noise. We derive the probability of a correct estimation, P(CE), and the least favorable configuration (LFC) asymptotically under the preference zone. Some important procedure properties are shown. Under the asymptotic LFC, the P(CE) attains its minimum over the preference zone in the parameter space of all eigenvalues. Therefore a minimum sample size can be determined in order to implement our procedure with a guaranteed probability requirement.