  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.
