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In this paper, we propose novel l1-regularized space-time adaptive processing (STAP) algorithms with a generalized sidelobe canceler architecture for airborne radar applications. The proposed methods suppose that a number of samples at the output of the blocking process are not needed for sidelobe canceling, which leads to the sparsity of the STAP filter weight vector. The core idea is to impose a sparse regularization (l1-norm type) to the minimum variance criterion. By solving this optimization problem, an l1-regularized recursive least squares (l1-based RLS) adaptive algorithm is developed. We also discuss the SINR steady-state performance and the penalty parameter setting of the proposed algorithm. To adaptively set the penalty parameter, two switched schemes are proposed for l1-based RLS algorithms. The computational complexity analysis shows that the proposed algorithms have the same complexity level as the conventional RLS algorithm (O((NM)2)), where NM is the filter weight vector length), but a significantly lower complexity level than the loaded sample covariance matrix inversion algorithm (O((NM)3)) and the compressive sensing STAP algorithm (O((NsNd)3), where N8Nd >; NM is the angle-Doppler plane size). The simulation results show that the proposed STAP algorithms converge rapidly and provide a SINR improvement using a small number of snapshots.