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Space-time adaptive processing (STAP) holds tremendous potential for the new generation airborne surveillance radar, in which the phased array antennas and pulse Doppler processing mode are adopted. A new STAP approach using the multiple-beam and multiple Doppler channels is presented here for airborne phased array radar. The approach with space-time multiple-beam (STMB) architecture is robust to array errors and has very low system degrees of freedom (DOFs). Hence, it has low sample support requirement and it is very suitable for the practical planar phased array radar under nonhomogeneous clutter environments. Meanwhile, a new nonhomogeneous detector (NHD) based on the correlation dimension (CD) is also proposed here, which is used as an effective method to screen tracing data prior to detection processing. It can further improve the performance of the STAP approach in the severely nonhomogeneous clutter environments. Therefore, a scheme that incorporates the correlation dimension nonhomogeneity detector (CD-NHD) with the STMB is recommended, which we term CD-NHD-STMB. The experimental simulation results indicate that: 1) the STMB processor is robust to array element error and has high performance under nonhomogeneous clutter environments; 2) the CD-NHD is also effective on the nonhomogeneous clutter. As a result, the CD-NHD-STMB scheme is robust to array element error and nonhomogeneous clutter, and therefore available for airborne phased array radar applications.