Minimax Joint Detection and Estimation with the Bayesian Cost

Many practical problems involve joint detection and estimation, where performance of estimation and detection largely affects each other. This paper considers the hypothesis testing problem with unknown parameters in a jointly optimal way, whose goal is to choose the true hypothesis and to estimate the unknown parameters simultaneously. By minimizing the maximum Bayesian estimation cost function subject to the constraints on Bayesian or Non-Bayesian detection performance, we obtain the corresponding joint optimal detectors and estimators. Under the proposed framework, it yields a lower estimation cost compared with the method that deals with the detection and estimation problem separately, and also provides tradeoff between detection and estimation performance. Finally, numerical examples about spectrum sensing in cognitive radio systems show the flexibility and the superiority of the proposed approach compared with the classical Neyman-Pearson test and the generalized likelihood ratio test.