Lowcomplexity iterative detection in the presence of nuisance parameters

This work addresses the bit-wise optimal data detection problem when unknown nuisance parameters influence the observation at the receiver. For an arbitrary communications system, the optimal maximum a-posteriori detection problem is first defined as a marginalization of a joint distribution which statistically models the interaction of available sets of variables/parameters. Then, using a factor graph representation with an accompanying sum-product message passing algorithm, it is shown that the marginalization can be performed iteratively. To alleviate complexity due to the marginalization over continuous natured nuisance parameters, variational Bayesian approximation is introduced and it is shown that, if the nuisance parameters are constant for a period of time, the receiver has linear complexity.