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基于时间反演技术, 建立了稀疏阵列单频信号相干合成的数学模型, 定义了合成效率函数概念, 推导出合成信号幅度最大时刻目标点合成效率值的统计特征与相位误差及阵元数的关系表达式, 并通过理论分析与仿真计算研究了相位误差对时间反演单频信号合成效果的影响. 分析表明, 当其他参数确定时, 假设相位误差服从一定范围的均匀分布, 且相互独立, 则峰值功率时刻的合成效率均值与阵元数无关, 仅与误差分布范围有关; 峰值功率时刻的合成效率方差与两者均相关, 且误差分布范围确定时, 阵元数越大, 峰值功率时刻的合成效率方差越小. 仿真计算结果表明, 即使存在一定的相位误差, 利用时间反演技术, 仍可实现单频信号在目标点邻域的相干合成及能量聚焦; 对相位误差的控制精度应结合需求与实现条件折中考虑. 本文的方法与结论可为研究稀疏阵列功率合成在高功率微波武器等技术中的应用提供理论依据.Based on time-reversal (TR) technique, the model of single frequency spatial power combining using sparse array is established. The efficiency function of spatial power combining is defined. The expression for the relationship of the statistical characteristics of combining efficiency at the time of maximum amplitude with the phase error and the number of array elements is derived. The analysis shows that when other parameters are determined, if the phase errors of the array nodes are mutually independent, and obey the uniform distribution to a certain extent, the combing efficiency's mean would not be related to the number of array elements N, but related to the statistic parameter of phase error. The combing efficiency's variance is related to not only the statistic parameter of phase errors, but also N. Once the statistic parameter of phase error is fixed, the greater the value of N, the smaller the variance is. So, in the engineering application, a large number of small power nodes could be used to reduce the phase error's effect. In addition, the influence of phase error on the combining efficiency is investigated by both theoretical analysis and the numerical simulation. The results show that when the array elements work at the same frequency, polarization and antenna type, the parameter of phase error would affect the combing result. The smaller the parameter of phase error, the larger the power of the effective point is, and the more concentrative the effective points' distribution is; the greater the parameter of phase error, the smaller the power of the effective point is, and the more dispersed the effective points' distribution is. It is also seen that even though the phase error occurs, the spatial power combining can still be realized with the time reversal technique. The determination of the phase control precision is the compromise between the requirements and the possibility. The results presented in this paper are useful for developing the microwave weapons with high power and electronic warfare.
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Keywords:
- time reversal technique /
- single-frequency signal /
- sparse array /
- spatial power combining
[1] Fink M, Prada C, Wu F 1989 IEEE Ultrasonics Symposium 1 681
[2] Lerosey G, Rosny J D, Tourin A 2004 Phys. Rev. Lett. 92 186
[3] Carminati R, Pierrat R, Rosny J 2007 Opt. Lett. 32 3107
[4] Wang B Z, Zang R, Zhou H C 2013 J. Microwaves 29 25 (in Chinese) [王秉中, 臧锐, 周洪澄 2013 微波学报 29 25]
[5] Song Y, Guo N, Qiu R C 2011 IEEE Antenn. Wirel. Pr. Lett. 10 796
[6] Song Y, Guo N, Qiu R C 2012 IEEE Trans. Antennas Propag. 60 3933
[7] Naqvi H, Zein G E, Lerosey G 2010 IET Microwave Antennas Propag. 4 643
[8] Dubois T, Crussire M, Hlard M 2010 Proc. 4th Int. Conf. Signal Processing and Communication Systems 1 1
[9] Zhou H C, Wang B Z, Ding S, Ou H Y 2013 Acta Phys. Sin. 62 114101 (in Chinese) [周洪澄, 王秉中, 丁帅, 欧海燕 2013 物理学报 62 114101]
[10] Ding S, Wang B Z, Ge G D, Wang D, Zhao D S 2012 Acta Phys. Sin. 61 064101 (in Chinese) [丁帅, 王秉中, 葛广顶, 王多, 赵德双 2012 物理学报 61 064101]
[11] Wang B Z, Liang M S, Ji Q S, Gang B, Zhang Z M 2014 Chin. Phys. B 23 048403
[12] Chen Y M, Wang B Z 2012 Chin. Phys. B 21 026401
[13] Tu H L, Xiao S Q, Yang Z J, Wang B Z 2014 Acta Phys. Sin. 63 084102 (in Chinese) [屠惠琳, 肖绍球, 杨智杰, 王秉中 2014 物理学报 63 084102]
[14] Zhang J Y 2006 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [张嘉焱 2006 硕士学位论文(长沙:国防科学技术大学)]
[15] Lu T 2009 M. S. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [路通 2009 硕士学位论文 (成都:电子科技大学)]
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[1] Fink M, Prada C, Wu F 1989 IEEE Ultrasonics Symposium 1 681
[2] Lerosey G, Rosny J D, Tourin A 2004 Phys. Rev. Lett. 92 186
[3] Carminati R, Pierrat R, Rosny J 2007 Opt. Lett. 32 3107
[4] Wang B Z, Zang R, Zhou H C 2013 J. Microwaves 29 25 (in Chinese) [王秉中, 臧锐, 周洪澄 2013 微波学报 29 25]
[5] Song Y, Guo N, Qiu R C 2011 IEEE Antenn. Wirel. Pr. Lett. 10 796
[6] Song Y, Guo N, Qiu R C 2012 IEEE Trans. Antennas Propag. 60 3933
[7] Naqvi H, Zein G E, Lerosey G 2010 IET Microwave Antennas Propag. 4 643
[8] Dubois T, Crussire M, Hlard M 2010 Proc. 4th Int. Conf. Signal Processing and Communication Systems 1 1
[9] Zhou H C, Wang B Z, Ding S, Ou H Y 2013 Acta Phys. Sin. 62 114101 (in Chinese) [周洪澄, 王秉中, 丁帅, 欧海燕 2013 物理学报 62 114101]
[10] Ding S, Wang B Z, Ge G D, Wang D, Zhao D S 2012 Acta Phys. Sin. 61 064101 (in Chinese) [丁帅, 王秉中, 葛广顶, 王多, 赵德双 2012 物理学报 61 064101]
[11] Wang B Z, Liang M S, Ji Q S, Gang B, Zhang Z M 2014 Chin. Phys. B 23 048403
[12] Chen Y M, Wang B Z 2012 Chin. Phys. B 21 026401
[13] Tu H L, Xiao S Q, Yang Z J, Wang B Z 2014 Acta Phys. Sin. 63 084102 (in Chinese) [屠惠琳, 肖绍球, 杨智杰, 王秉中 2014 物理学报 63 084102]
[14] Zhang J Y 2006 M. S. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [张嘉焱 2006 硕士学位论文(长沙:国防科学技术大学)]
[15] Lu T 2009 M. S. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [路通 2009 硕士学位论文 (成都:电子科技大学)]
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