Structurally Constrained Receivers for Signal Detection and Estimation

A general approach to the problem of designing structurally constrained receivers for signal detection and estimation is proposed. The approach is based on the constrained Bayesian methodology wherein risk-minimizing inference (or decision) rules are modified (constrained) by replacement of true posterior probabilities with estimated posterior probabilities. The estimators are structurally constrained minimum-mean-squared-error (MMSE) estimators for random posterior probabilities. This methodology is, in essence, an extension and generalization of the well-known linear MMSE estimation methodology. The approach is employed to design linearly constrained coherent receivers for signals in additive and multiplicative noise, and quadratically constrained noncoherent receivers for signals in additive noise. An analysis of these receivers shows that they are very similar to those that are optimum for additive Gaussian noise. The methodology provides a unified theory of receiver design based on the constrained MMSE criterion. This unification yields new insight into this old approach, clarifying both strengths and weaknesses of the approach.