Determining the number of sources in signal processing

The problem of detection in signal processing is often referred to determine the number of signal sources in a noisy environment. It has many engineering applications, ranging from military surveillance to mobile communications. The detection is also important in other areas of signal processing, such as the estimation of certain parameters: frequency spectrum and direction of arrival. The spectral peaks obtained from the Fourier transform of the data were used in early time to estimate these parameters, but the spectral resolutions are generally poor due to the practical limitations such as the time length of data record. Model-based parameter estimation has been an area of active research. Many high-resolution approaches have been developed, but they require certain prior knowledge, among them the number of signal sources is often most crucial. It is thus clear that signal detection plays an important role in parameter estimation, system modeling and identification, and stochastic realization. The detection problems are generally classified into two categories: determination of number of signals, each having different frequencies; and determination of signals, each coming from different locations