On interval estimation for the number of signals

We propose a multi-step procedure for constructing a confi-dence interval for the number of signals present. The pro-posed procedure uses the ratios of a sample eigenvalue and the sum of different sample eigenvalues sequentially to de-termine the upper and lower limits for the confidence inter-val. A preference zone in the parameter space of the popula-tion 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) asymp-totically under the preference zone. Some important proce-dure 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.