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The design of antenna pattern and transmitted signal for a coherent-side-looking (range-azimuth) synthetic antenna radar is studied. The general design criterion is to minimize all spurious responses in the ambiguity function under the restraints of finite antenna aperture and signal bandwidth. The problem is completely solved for any set of consistent constraints. The interplay between aperture size, range and azimuth resolution, and spurious response level for the optimum design is exhibited, and antenna aperture illuminations, signal amplitude and phase modulation, and pulse repetition frequency are specified.