Correct-decision-feedback performance bounds for joint detection and estimation

A commonly used lower bound on the probability of error of joint detection/estimation algorithms is the correct-decision-feedback bound, which is derived under the assumption that estimation is performed using the transmitted sequence. Although it seems reasonable that this genie-aided receiver performs better than the original receiver, a formal proof of this fact is not available. In this work a proof is offered for the case when the joint detection/estimation algorithm is based on the generalized likelihood ratio test (GLRT), where the unknown parameter is modeled as a deterministic unknown constant. The results are then extended for a sub-optimal joint detection and estimation algorithm called the T-algorithm. Finally, by establishing an equivalence between the GLRT and the maximum likelihood sequence detection (MLSD) problem, the derived bound is found to be valid for a very important special case when MLSD is performed.