A new beam broadening synthesis technique for Synthetic Aperture Radar (SAR) antenna array, namely Projection Matrix Algorithm (PMA) is presented. The theory of PMA is introduced firstly, and then the iterative renewed manner is improved to resolve the unbalance problem under amplitude and phase control. In order to validate the algorithm correct and effective, an actual engineering application ... [Show full abstract] example is investigated. The beam synthesis results of 1.0∼4.5 times broadening under the phase only control and the amplitude and phase control using improved PMA are given. The results show that the beam directivity, the beam broadening, and the side-lobe level requirements were met. It is demonstrated that the improved PMA was effective and feasible for SAR application. © 2014, Science Press, Institute of Electronics, CAS and Springer-Verlag Berlin Heidelberg.