In this letter, we investigate the joint receiver design for integrated sensing and communication (ISAC) systems, where the communication signal and the target echo signal are simultaneously received and processed to achieve a balanced performance between both functionalities. In particular, we proposed two design schemes to solve the joint sensing and communication problem of receive signal processing. {\color{black} The first is based on maximum likelihood (ML) detection, minimum mean squared error (MMSE) estimation and interference cancellation (IC), and the other formulates a tailored MMSE estimator for target estimation that is independent to the detector, which form a Non-IC design. We show that with the structural information of the communication signal taken into account, the Non-IC approach outperforms the IC method and achieves optimal performance.} Numerical results are provided to validate the effectiveness of the proposed optimal designs.
