An Accurate Wideband Beampattern Synthesis Method Based on the Space-frequency Structure and the Space-time Structure Conversion
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摘要:
该文提出一种空时结构下的精确宽带波束赋形算法。在空频结构下，对各子带权值进行波束赋形优化。根据权值在满足共轭对称条件下，阵列幅度响应可以转换为线性函数这一原理，将波束赋形转换为凸优化问题。利用内点法得到最优权值后，通过空频结构与空时结构之间的权值转换关系，得到空时结构下的波束权值。该算法能够对宽带波束图进行精确地赋形，同时保证在期望方向上阵列响应具有线性相位特性。仿真结果验证了算法的有效性。
Abstract:An accurate wideband beampattern synthesis method based on the space-time structure is proposed. Making use of the property that the magnitude response can be translated into linear function under the condition of conjugate symmetric weights, the beampattern synthesis problem is transformed into the convex optimization problem. The weights of space-time structure can be obtained by utilizing the principle of relationship between the two structures, after the weights of space-frequency structure is calculated by the interior point method. The proposed method can realize the wideband beampattern synthesis accurately, meanwhile ensuring the linear phase characteristic of the array response. Simulation results demonstrate the effectiveness of the proposed method.
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表 1 3种方法的计算量比较
方法 迭代次数 每次迭代的运算量 式(13) $O\left(\sqrt {{K_4}(2{K_1} + {K_2} + {K_3}) + 2} \right)$ $O\left\{ (MN)^2[{K_4}(6{K_1} + 3{K_2}{+ 3}{K_3}) + 2{K_4} + 1]\right\} $ 式(14) $O\left(\sqrt {2{K_1} + {K_4}({K_2} + {K_3}) + 2} \right)$ $O\left\{ {(MN)^2}[6{K_1} + 3{K_4}({K_2} + {K_3}) + MN{\rm{ + }}3]\right\} $ 式(21) $O\left(\sqrt {2N} \right)$ $O\left\{ {(M/2)^2}[N(4{K_1} + 2{K_2} + 2{K_3}) + MN + 3N]\right\} $ 
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