Tradeoffs between detection and estimation for multiple signals

A method for gauging the tradeoff between parameter estimation and order selection estimation performance for discrete parameters is developed. The method is based on evaluation of lower bounds on worst-case probability of estimation error and worst-case probability of order selection error subject to a constraint on maximum false alarm probability. Since each of the two bounds is derived by evaluating the performance of an optimal order estimator and an optimal parameter estimator, respectively, the bounds are achievable. It is shown that it is generally impossible to achieve simultaneously the order selection and parameter estimation lower bounds: there is a necessary compromise between estimation and order selection. The authors present numerical studies of these bounds for a common multiple signal model