On MMSE Estimation: A Linear Model Under Gaussian Mixture Statistics
John T. Flåm, Saikat Chatterjee, Kimmo Kansanen, Torbjörn Ekman · IEEE Transactions on Signal Processing · 2012
In a Bayesian linear model, suppose observation y = Hx + n stems from independent inputs x and n which are Gaussian mixture (GM) distributed. With known matrix H, the minimum mean square error (MMSE) estimator for x , has analytical form. However, its performance measure, the MMSE itself, has no such closed form. Because existing Bayesian MMSE bounds prove to have limited practical value under these settings, we instead seek analytical bounds for the MMSE, both upper and lower. This paper provides such bounds, and relates them to the signal-to-noise-ratio (SNR).