Different from current coherent-detection-based long-haul transmission systems, inter-and intradatacenter transmissions require a simpler transmitter and receiver. A promising way to significantly meet the demands of datacenter transmission is polarization division multiplexing intensity modulation with direct detection (PDM-IM-DD) using a Stokes vector receiver (SVR). However, for different SVR architectures, the corresponding demultiplexing matrix is required to recover the Stokes vectors from the detected signals, which are combined with an arbitrary state of polarization (SOP), will change the effect of noise dynamically and significantly influence the system performance. In this study, PDM-IM signals using four SVRs, i.e., a 90 • optical hybrid with 2 balanced photodetectors (BPDs) and 2 photodetectors (PDs), a 90 • optical hybrid with 4 PDs, a Stokes analyzer and a 3 × 3 coupler with 4 PDs, are studied theoretically and numerically. Theoretical system models using the four SVRs are developed, and the noise power variations are analyzed quantitatively based on these models. Moreover, the performance of the systems is also investigated for 224 Gbit/s polarization division multiplexing pulse amplitude modulation 4 level with direct detection (PDM-PAM4-DD) transmission in a simulation. The simulation results show that the bit error rate (BER) performance of the systems is consistent with the theoretical noise power variation curves. The theoretical analysis scheme is helpful for the practical design of SVR-based systems.