In this study, we initiate an analysis of the clutter suppression mechanisms in Airborne Passive Radar Systems (APRS) using Space–Time Adaptive Processing (STAP). Additionally, based on the sparsity characteristics of airborne clutter and sparse filtering, we formulate a STAP model utilizing a sparse Generalized Sidelobe Canceller (GSC) filter structure. Subsequently, addressing limitations in conventional convex relaxation methods that directly substitute l₁ norm for l₀ norm, we introduce the pseudo-norm function g_r and apply it to the constructed STAP model in lieu of the l₀ norm. Furthermore, recognizing the prevalence of ’non-circular’ signals in the context of APRS scenarios, we employ the Wide linear Recursive Least Squares (WRLS) algorithm for solving (g_r-WRLS), demonstrating enhanced performance. Finally, the feasibility of the proposed approach is validated through simulated scenarios.