Abstract: The traditional post-Doppler adaptive processing approaches such as Factored Approach (FA) and Extended Factored Approach (EFA) can significantly reduce the computation-cost and training sample requirement in adaptive processing. However, their clutter suppression ability is considerably degraded with the increasing number of antenna elements. To solve this problem, a two-stage reduced-dimension adaptive processing method based on the decomposition of spatial data is proposed. This method decomposes the spatial data after Doppler filtering into a Kronecker product of two short vectors. Then a bi-quadratic cost function is obtained. The circular iteration is applied to solve the optimal weight. Experimental results show that the proposed method has the advantages of fast convergence and small training samples requirement. It has greater clutter suppression ability especially in small training samples support compared with FA and EFA.