Approach Research On Localization Of Passive Intermodulation Sources Based On Time Reversal Electromagnetic Imaging

Passive intermodulation(PIM)interference in phased array and other base antennas has been a significant factor to affect the high-speed development of the modern wireless communication system towards the applications of fifth and even sixth generation communication.On account of the spatial radiation from the element of the phased array and other structures,the radiated passive intermodulation(R-PIM)sources are generated at the positions with the nonlinear effects,such as the mutations in the metal skin of phased array components and dust or oxidation,resulting in producing the R-PIM interferential signals.Eventually,the performance of the modern wireless communication system will be declined.Because of the complex electromagnetic environment of the phased array and its surroundings,the localization of R-PIM source is still faced with the great theoretical and technical challenges.Due to the mechanism of the adaptive “spatialtemporal focusing”,the imaging method based on the time reversal technique has been expected to become a new solution to locating the R-PIM source inside phased array.The accurate localization of R-PIM sources has a positive scientific research significance to enhance the performances of the modern wireless communication system.However,the traditional time reversal imaging methods still have shortcomings in terms of the highly precise imaging,low computational complexity and the suppression of the fake peak.Facing the above issues in existing imaging methods and technologies,this paper has carried out the localization of the R-PIM sources based on the time reversal electromagnetic imaging from the basic principle.The main work and contributions are summarized as follows.Firstly,the localization of R-PIM source based on the cascaded time reversal imaging has been proposed and studied.The weakly correlation filter(WCF)to obtain the optimized frequency points and the optimal noise vector are used to eliminate the redundant data in the frequency band.The imaging pseudo-spectrum distribution mapping at each optimized frequency point is analyzed.Moreover,the normalized image pseudo-spectrum images of several optimized frequency points are cascaded and multiplied.Consequently,the large pseudo-spectrum value of imaging at the location of R-PIM source target is maintained and the imaging pseudo-spectrum at the locations of the non-R-PIM source target are suppressed.This method eliminates the misjudgment of the estimated location of R-PIM source caused by fake peaks and “dirty” images,which can provide a “clean” image to locate the R-PIM source.Combined with the numerical simulation examples,the cascaded time reversal imaging method can distinguish effectively two R-PIM sources with a spacing of 0.45 ,which has verified the advantages of super-resolution and accurate imaging,compared with the traditional multifrequency time reversal imaging method.Secondly,the localizations of R-PIM sources based on subspace imaging decomposed and estimated from the truncated time reversal operator(TTRO)are proposed and studied.Although the redundant data in the frequency band can be eliminated in cascade time reversal imaging,but the computational complexity at single frequency still needs to be reduced.Therefore,the physical significance of TTRO is discussed,and the signal subspace and noise subspace generated by decomposing the TTRO directly are deduced theoretically.Meanwhile,the noised subspace estimated from the TTRO by constructing orthotropic equations is also proved in detail.This proposed method only needs the low dimensional decomposition or orthodontic estimation of TTRO without decomposing the full time reversal operator,which has the characteristics of “low-complexity” imaging.Combined with numerical simulation examples,the subspace imaging decomposed and estimated from the TTRO can save more than 95%runtime consumption at a large-scale array compared with the traditional singlefrequency time reversal imaging method,which has demonstrated the advantages of low computational complexity and fast imaging.Thirdly,the estimated subspace imaging based on the optimal truncated space frequency-operator(OTSF)is proposed and studied.On the basis of the estimated subspace of TTRO,the OTSF truncated matrix composed of row vectors of larger Euclidean norm in SF-MDM are obtained.According to the propagated linear operator,the OTSF constructing relevant orthogonality equations to estimate the noise subspace of SF-MDM is mainly deduced,which is extended to estimate the noise subspace from the data of SF-MDM.The numerical simulation results show that,the single static data imaging based on OTSF estimation subspace can distinguish multiple R-PIM sources.Compared with the time reversal imaging method based on SF-MDM,the proposed imaging method also performs the advantages of low computational complexity and fast imaging.Finally,the experimental system and platform of localization of the imitated R-PIM source based on the proposed time reversal imaging methods are constructed.Additionally,the experimental studies of localization of the imitated R-PIM source placed inside the semi-closed metal cavity haven been carried out.The experimental results show that,compared to the multiple dimensions data used in traditional imaging methods,the proposed novel time reversal imaging methods only requires one column vector to realize the less than 0.13 of the relative errors.Consequently,the feasibility and effectiveness of localization of the imitated R-PIM source based on the proposed time reversal imaging methods are investigated.