一種基于空頻結(jié)構(gòu)與空時(shí)結(jié)構(gòu)權(quán)值轉(zhuǎn)換的精確寬帶波束賦形算法
doi: 10.11999/JEIT180545 cstr: 32379.14.JEIT180545
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電子科技大學(xué)信息與通信工程學(xué)院 ??成都 ??611731
基金項(xiàng)目: 國家自然科學(xué)基金(61871085)，高?；究蒲袠I(yè)務(wù)費(fèi)(2672018ZYGX2018J010)
An Accurate Wideband Beampattern Synthesis Method Based on the Space-frequency Structure and the Space-time Structure Conversion
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School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Funds: The National Natural Science Foundation of China (61871085), The Fundamental Research Funds for the Central Universities (2672018ZYGX2018J010)
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摘要:
該文提出一種空時(shí)結(jié)構(gòu)下的精確寬帶波束賦形算法。在空頻結(jié)構(gòu)下，對各子帶權(quán)值進(jìn)行波束賦形優(yōu)化。根據(jù)權(quán)值在滿足共軛對稱條件下，陣列幅度響應(yīng)可以轉(zhuǎn)換為線性函數(shù)這一原理，將波束賦形轉(zhuǎn)換為凸優(yōu)化問題。利用內(nèi)點(diǎn)法得到最優(yōu)權(quán)值后，通過空頻結(jié)構(gòu)與空時(shí)結(jié)構(gòu)之間的權(quán)值轉(zhuǎn)換關(guān)系，得到空時(shí)結(jié)構(gòu)下的波束權(quán)值。該算法能夠?qū)拵Рㄊ鴪D進(jìn)行精確地賦形，同時(shí)保證在期望方向上陣列響應(yīng)具有線性相位特性。仿真結(jié)果驗(yàn)證了算法的有效性。
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關(guān)鍵詞:
- 寬帶波束賦形 /
- 空頻空時(shí)結(jié)構(gòu)轉(zhuǎn)換 /
- 線性相位 /
- 共軛對稱權(quán)值 /
- 2階錐規(guī)劃
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種方法的計(jì)算量比較
方法 迭代次數(shù) 每次迭代的運(yùn)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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