In this paper, novel knowledge-aided space-time adaptive processing (KA-STAP) algorithms using sparse representation/recovery (SR) techniques by exploiting the spatio-temporal sparsity are proposed to suppress the clutter for airborne pulsed Doppler radar. The proposed algorithms are not simple combinations of KA and SR techniques. Unlike the existing sparsity-based STAP algorithms, they reduce the dimension of the sparse signal by using prior knowledge resulting in a lower computational complexity. Different from the KA parametric covariance estimation (KAPE) scheme, they estimate the covariance matrix using SR techniques that avoids complex selections of the Doppler shift and the covariance matrix taper. The details of the selection of potential clutter array manifold vectors according to prior knowledge are discussed and compared with the KAPE scheme. Moreover, the implementation issues and the computational complexity analysis for the proposed algorithms are also considered. Simulation results show that our proposed algorithms obtain a better performance and a lower complexity compared with the sparsity-based STAP algorithms and outperform the KAPE scheme in presence of errors in prior knowledge.