Dual function radar and communication (DFRC) is a promising research direction within integrated sensing and communication (ISAC), improving hardware and spectrum efficiency by merging sensing and communication (S&C) functionalities into a shared platform. However, the DFRC receiver (DFRC-R) is tasked with both uplink communication signal detection and simultaneously target-related parameter estimation from the echoes, leading to issues with mutual interference. In this paper, a projection-based scheme is proposed to equivalently transform the joint signal detection and target estimation problem into a joint signal detection process across multiple snapshots. Compared with conventional successive interference cancellation (SIC) schemes, our proposed approach achieves a higher signal-to-noise ratio (SNR), and a higher ergodic rate when the radar signal is non-negligible. Nonetheless, it introduces an ill-conditioned signal detection problem, which is addressed using a non-linear detector. By jointly processing an increased number of snapshots, the proposed scheme can achieve high S&C performance simultaneously.