Clutter suppression poses serious problems for airborne, bistatic radar systems. Suppression may be increased using space-time adaptive processing (STAP), but suppression of slow targets is poor and target detectability is compromised. Furthermore, sufficient independent and identically (IID) training samples cannot be obtained through the use of practical applications, and the STAP performance degrades significantly due to the inaccuracy of the estimated clutter-plus-noise covariance matrix, especially in nonstationary and heterogeneous environments. Here, we present a new airborne, bistatic radar system. We transform the array from a single polarized channel to two channels, each with two orthogonally polarized antennae, and combine polarization-dimensional information with that of the space-time domain; we term our algorithm “polarization-space-time adaptive processing”. This algorithm further suppresses clutter and enhances the detection of slow targets. Sparse recovery space-time adaptive processing (SR-STAP) can reduce the need for clutter samples and suppress clutter effectively using limited training samples for airborne radar. The algorithm first uses the clutter sparse recovery function of STAP to suppress clutter in the H and V channels. Then, polarization processing is employed to further restrict mainlobe clutter. We present numerical examples to demonstrate the effectiveness of the new technique.