Factor Graph Based LMMSE Filtering for Colored Gaussian Processes

We propose a reduced complexity, graph based linear minimum mean square error (LMMSE) filter in which the non-white statistics of a random noise process are taken into account. Our method corresponds to block LMMSE filtering, and has the advantage of complexity linearly increasing with the block length and the ease of incorporating the a priori information of the input signals whenever possible. The proposed method can be used with any random process with a known autocorrelation function by use of an approximation to an autoregressive (AR) process. We show through extensive simulations that our method performs identical with the optimal block LMMSE filtering for Gaussian input signals.