Abstract: In this paper, a novel algorithm for shaped-beam pattern synthesis is proposed based on quantization of element excitation amplitude. The algorithm is divided into three steps. First, traditional pattern synthesis, such as alternative projection, is performed to obtain the element excitation of the beam without amplitude constraints. Second, the probability density method is used to acquire the quantized amplitude of element excitations. Finally, the Semi-Definite Relaxation (SDR) method is employed to obtain the element excitation phase of each beam. In the above procedures, how to use the probability density method to obtain the quantized amplitude of the element excitation is the most important step. Each element excitation amplitude is replaced by the probability density variable. By setting the element excitation amplitude levels in advance and the probability of each element excitation amplitude when falling in the corresponding level, the probability density pattern is obtained. The difference between the probability density pattern and the ideal pattern is then minimized to acquire the quantized element excitation amplitude. The probability density method has the advantages in that the quantization levels can be acquired through footprints and arrays with arbitrary shapes, and hence can be applied in a wider background. Simulation verifies the superiority of the proposed algorithm.

Key words: embedded element pattern, probability density approximation, element excitation amplitude quantization, convex optimization, footprint pattern synthesis