With the development of compressive sensing theory

the space-time adaptive processing (STAP) technology based on sparsity of space-time power spectrum (STPS) receives a growing interest.This paper firstly reviews the traditional STAP algorithms and shows analysis of sparsity of STPS from three different points of view and potential advantages of STAP technology based on sparsity of STPS.Then

the current developed STAP algorithms based on sparsity of STPS are categorized into three classes

such as STAP based on prior knowledge of array manifold

STAP based on sparse recovery of STPS and STAP based on both prior knowledge of array manifold and sparse recovery of STPS.It also performs an overview of those algorithms.Finally

based on the progress of the existing research

some key issues to enhance the performance of clutter suppression and moving target detection are introduced

which include intrinsic mechanism analysis of sparsity

space-time steering dictionary design

easy parameters setting

fast and low complexity algorithms design

robust algorithm design

STAP algorithms based on sparse recovery of STPS design by exploiting different types of prior knowledge

and constant false alarm rate detector design of STAP based on sparsity of STPS and validation using measurement data.