Single frequency spatial power combining using sparse array based on time reversal of electromagnetic wave

Abstract

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.