Automatic Regularization for Linear MMSE Filters

In this work, we consider the problem of regularization in minimum mean-squared error (MMSE) linear filters. Exploiting the relationship with statistical machine learning methods, the regularization parameter is found from the observed signals in a simple and automatic manner. The proposed approach is illustrated through system identification examples, where the automatic regularization yields near-optimal results. Minimum mean-squared error (MMSE) linear filters are ubiquitous in many signal processing applications such as channel equalization [1, Ch. 5.4], system identification [2], antenna beamforming [1, Ch. 6.5], and many others. The core idea is to use a linear transformation of the input signal that approximates the desired signal with the smallest average squared error.