Sequence error probability lower bounds for joint detection and estimation

A commonly used lower bound on the probability of error of joint detection and estimation (JDE) algorithms is derived under the assumption that estimation is performed using the transmitted sequence, in a genie-aided fashion. Although it seems reasonable that this genie-aided receiver performs better than the original receiver, a proof of this fact is not available in the literature. In this letter, the validity of this bound is established for a general class of JDE algorithms, as well as for an important special case when the maximum-likelihood sequence detection criterion is used. The results are then extended to a well-known suboptimal JDE algorithm, namely, the Talgorithm. It is shown, however, that the technique used to prove this bound is not sufficient for establishing the validity of the bound for the M-algorithm and the per-survivor processing algorithm.