Global MDL Minimization-based Method for Detection of the Number of Sources in Presence of Unknown Nonuniform Noise

The classical Minimum Description Length (MDL) approach for detection of the number of sources fails in the presence of unknown nonuniform noise. In order to solve this problem, we propose to detect the number of sources by the global minimization of a newly built MDL criteria, named as the GM-MDL method. The proposed GM-MDL method first builds a new MDL objective function, which is a function of the number of sources and a whitening vector. Afterwards, the genetic algorithm (GA) is employed to find the global minimum solution of the newly built MDL objective function, which gives the estimates of the number of sources and the whitening vector. Simulation results demonstrate that the proposed GM-MDL method can estimate the number of sources correctly in the scenarios of unknown nonuniform and uniform noise. In addition, compared with the existing methods, the proposed GM-MDL method has significant improvement when the Worst Noise Power Ratio (WNPR) is large and/or the signal-to-noise ratio (SNR) is low. Furthermore, it also demonstrates a good performance in few snapshots.