A Design Method of Criteria for Detecting the Number of Signals

This paper proposes a novel design method of criteria for detecting the number of signals superimposed in multichannel time-series. Based on probabilistic properties of difference in maximum log likelihood at infinite SNR, penalty functions in information theoretic criteria are designed by giving specific upper bounds of error probabilities. The proposed design method uses an approximation of probability distribution functions of the difference in maximum log likelihood. Finally, simulation results are shown to demonstrate flexible criteria for detecting the number of signals can be designed in the case that the number of available samples of observation vectors is small and also large.