Differences in target radial velocities of different airborne radar are used for target detection in a multiple Airborne Early Warnings (AEWs) coordinated detection radar system; this subject is currently a popular research topic. In this paper, a collaborative detection radar system model comprised of multiple AEWs with different transmit waveforms is constructed. The Generalized Likelihood Ratio Test (GLRT) based adaptive detector is then proposed and the approximated statistical characters of the detector are analyzed. Finally, the moving target detection performances of three selected transmit waveforms are analyzed by computer simulation; results show that the detection performance of the collaborative detection radar system is influenced by the transmit waveform, and that the detection performances of different velocity targets are different with the same transmit waveform.