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An improved genetic algorithm (GA) is proposed for beam forming of spaceborne Synthetic Aperture Radar (SAR), which is equipped with active phased array antenna (APAA). The basic idea of the approach is that the phase and amplitude distributions of the element excitations can be represented by a few basis functions, as any functions can be expressed by a set of the complete orthogonal basis functions. Furthermore, by optimizing the weights of basis functions, the beam shaping and sidelobe notch can be achieved. In this algorithm, Legendre Polynomials (LP's), sine and cosine are utilized to define phase and amplitude distribution, respectively. Considering the difference between the transmitting and the receiving channels of T/R module, phase-only synthesis with uniform amplitude and complex excitation control are applied in the transmitting mode and the receiving mode, respectively. Based on the proposed algorithm, we achieved great reduction in the number of variables, obtained smoother curves of the phase and amplitude distributions and accelerated the convergence process, in comparison with conventional GA. Finally, numerical simulation results are presented to verify the effectiveness of the algorithm.