MMSE-based MDL method for robust estimation of number of sources without eigendecomposition

It is well known that the conventional eigenvalue-based minimum description length (MDL) approach for source number estimation suffers from high computational load and performs optimally only in the presence of spatially and temporally white noise. To improve the robustness of the MDL methodology, we propose to utilize the minimum mean square error (MMSE) of the multistage Wiener filter to calculate the required description length for encoding the observed data, instead of relying on the eigenvalues of the data covariance matrix. As there is no need to calculate the covariance matrix and its eigenvalue decomposition, our derived MMSE-based MDL (mMDL) method is also more computationally efficient than the traditional counterparts. Numerical examples are included to demonstrate the robustness of the mMDL detector in nonuniform noise.