Clutter rejection is a key technique used by passive radars for target detection. Especially when using Single Frequency Network (SFN) configuration, the multipath clutter and ground clutter increase several times more than during a single illuminator situation, which means that the clutter extends in both the spatial and temporal dimensions. The high amount of clutter occupies numerous degrees of freedom when conventional spatial or temporal processing is used, leading to a large array requirement, a huge computational cost, or even a complete failure. This paper investigates a novel subcarrier-based processing technique that is tailored for Orthogonal Frequency Division Multiplex (OFDM) modulation with a Cyclic Prefix (CP-OFDM) to avoid the abovementioned predicament. The algorithm principle is initially illustrated and followed by a discussion about the unique characteristics of Subcarrier-based Spatial Adaptive Processing (SSAP), which include the Doppler response and its unusual main-lobe clutter case. Then, the robustness is researched by evaluating the performance under relaxed basic assumptions. The conclusions are demonstrated by conducting test using simulated and real data sets.