Optimal equalization cost functions and maximum a posteriori estimation

A new maximum a posteriori (MAP) formulation is shown to be a straightforward and intuitive way to derive optimal blind equalization cost functions. This MAP method provides a general, systematic way to derive blind adaptation methods using the given pdf of the input and a convolutional noise model. A general blind equalization/deconvolution cost function known as Gray's Variable Norm, is shown to be derivable using the MAP formulation presented here. Gray's Variable Norm (1979) is a superset of existing blind equalization cost functions, including the Godard and Sato algorithms as special cases. The MAP method is capable of deriving cost functions needed for a wide variety of problems, including those with infinite variance pdfs and even multichannel problems.<>