Range ambiguities severely degrade the performance of the synthetic aperture radar (SAR) system. To make an improvement without increasing the system complexity, antenna pattern synthesis is a feasible method. To this end, a novel algorithm that can shape the mainlobe and suppress the range ambiguities simultaneously by relaxing the problem as a semidefinite relaxation (SDR) programming problem is proposed here for the first time. Compared to the algorithm with global optimization, the presented algorithm could find the desired pattern without the large occupation of computing resources and has great potential in raising the performance of SAR system. In addition, some simulations are carried out, and the results prove that the proposed algorithm has the superior ability to suppress the range ambiguities while controlling the beamwidth and dynamic range ratio (DRR).
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