  This article proposes novel sparsity-aware space-time adaptive processing
(SA-STAP) algorithms with $l_1$-norm regularization for airborne phased-array
radar applications. The proposed SA-STAP algorithms suppose that a number of
samples of the full-rank STAP data cube are not meaningful for processing and
the optimal full-rank STAP filter weight vector is sparse, or nearly sparse.
The core idea of the proposed method is imposing a sparse regularization
($l_1$-norm type) to the minimum variance (MV) STAP cost function. Under some
reasonable assumptions, we firstly propose a $l_1$-based sample matrix
inversion (SMI) to compute the optimal filter weight vector. However, it is
impractical due to its matrix inversion, which requires a high computational
cost when in a large phased-array antenna. Then, we devise lower complexity
algorithms based on conjugate gradient (CG) techniques. A computational
complexity comparison with the existing algorithms and an analysis of the
proposed algorithms are conducted. Simulation results with both simulated and
the Mountain Top data demonstrate that fast
signal-to-interference-plus-noise-ratio (SINR) convergence and good performance
of the proposed algorithms are achieved.
