Estimating the number of signals with unknown parameters under Gaussian noises

Model order selection is an important stage in many technical areas. Estimating the number of signals with unknown parameters is a special case of the model order selection problem. We describe a class of signal parameters for which we show that the widely used maximum likelihood method is useless for estimating the number of signals. It is established, that the amplitude parameters belong to this class. Therefore, we study the estimation problem for the number of signals with unknown amplitudes in discrete time. Five algorithms for estimating the number of signals are described, including the new one. Finally, we provide a performance analysis of these algorithms, comparing them using both analytical and numerical approaches.