This paper delves into the collaborative design of receivers in integrated sensing and communication (ISAC) systems with imperfect communication channel state information (CSI). The ISAC systems involve the concurrent reception and processing of both communication and target echo signals, aiming for a harmonized performance in both functionalities. The imperfect communication CSI obtained at the BS is modeled as the sum of an accurately estimated part and a statistical error component with both channel mean and channel variance information. We introduce two distinct design strategies to address the joint sensing and communication challenge in signal processing at the receiver. The first strategy employs maximum likelihood (ML) detection, minimum mean squared error (MMSE) estimation, and interference cancellation (IC). The second strategy devises a custom MMSE estimator for target estimation, operating independently of the detector, forming a Non-IC design. Demonstrating that incorporating the structural information of the communication signal is crucial, our findings reveal that the Non-IC approach surpasses the IC method, achieving optimal performance. Numerical results are provided to validate the effectiveness of the proposed optimal designs.