Study On Phaseless Measurement Method In Millimeter-Wave/Terahertz Compact Antenna Test Range

With the commercial application of 5th Genaration(5G)wireless communication and the gradual deployment of 6th Genaration(6G)wireless communication,the Compact Antenna Test Range working in millimeter wave/terahertz(mmW/THz)band has received more attention in the last few years in academia and industries,because it can not only provide a highly reliable plane wave measurement environment for microwave devices to be measured,but also can work in a very wide spectrum bandwidth environment.In order to ensure the effective application of CATR in the mmW/THz band,the disturbance evaluation of the quiet zone in CATR is particularly important.In general,in order to ensure the high reliability of the CATR,the allowable range of maximum quiet zone amplitude/phase fluctuation error does not exceed±0.5dB/±5°.The direct acquisition of quiet zone phase becomes particularly difficult under the influence of unfavorable factors such as temperature variations,environmental noise,inaccurate positioning of the quiet zone scanning probe,and cable bending.In recent years,the phaseless measurement method,which only uses electromagnetic field amplitude information to indirectly achieve phase information reconstruction,has been applied into antenna measurement.The phaseless measurement method provides a new effective solution for quiet zone evaluation of CATRs.However,the phase reconstructions for CATRs have several technical challenges.Firstly,the half-wavelength sampling of the quiet zone for the large-aperture CATR operating at high frequency bands leads to too many unknown phase information to be recovered.However,too many unknowns can make it difficult for existing algorithms to achieve high precision phase retrieval.Secondly,the high correlation between the amplitudes in quiet zone of the CATR increases the difficulty of solving the nonlinear equations constructed during the phase recovery process.Thirdly,CATR is an ultra-wideband system,for which the proposed quiet zone phaseless measurement method should meet the requirements of high-precision phase rertieval in different operating bands,so the proposed methods should be reliable and universal in implementing quiet zone evaluation.Fourthly,the half-wavelength sampling interval is difficult to achieve in actual engineering,and the time cost due to the excessive total amount of sampling data is too high.Then,the quiet zone phaseless measurement with less sampled data is one of the technical difficulties to be solved.To address the above problems,this paper studies the key technologies and challenges related to the quiet zone phaseless measurement.The contents of this paper are as follows.1.The phase retrieval algorithms can easily get trapped into the local optima because of too many unknowns in the quiet zone phaseless measurement for large-aperture CATR operating in the mmW/THz band.This paper presents the modified alternating algorithm composed of Gerchberg-Saxton(GS)algorithm and Hybrid input-output(HIO)algorithm,i.e,the spatial phase perturbation(SPP)GS/HIO-HIO algorithm to address the problem.In order to complete the phase retrieval,the ideal two-dimensional Fast Fourier Transform(FFT)is used to realize the alternating iterative projection of spatial and spatial frequency domain(fourier domain)in quiet zone field.By introducing SPP,the proposed algorithm reduces the probability of falling into local convergence during the iterative process to a certain extent.Meanwhile,the problem that the algorithm falls into local convergence/saddle point during the iterative process is solved effectively by cascading GS/HIO and HIO.The simulation results show that the phase retrieval algorithm always converges to an optimal solution through a series of hierarchical optimization of the problem.The numerical phase retrieval of quiet zone at different operating frequencies are consistent with the ideal target phase when the ideal twodimensional FFT is used.Moreover,the maximum convergence error of simulation amplitude does not exceed 10×10-10 without considering the influence of environmental noise and probe sampling bias in quiet zone.When additive White Gaussian noise is introduced into the CATR,the normalized root mean square error(NRMSE)is less than3.6×10-3 with the signal to noise ratio(SNR)is not less than 45dB.2.This paper proposes a mmW metasurface lens aided phaseless characterization to further improve the effectiveness of quiet zone evaluation method for CATRs,because the two-dimensional FFT in the phase retrieval algorithm is too ideal.The lens composed of periodic modules of varying thickness is designed to change the phase of quiet zone.Meanwhile,two sets of amplitudes with little correlation can be obtained on the preset focal plane and the plane to be measured in quiet zone under the action of the lens.To further improve the accuracy of quiet zone phase retrieval,the random initial phase is preprocessed by spectral initialization,and then the phase retrieved by the SPP GS/HIO-HIO algorithm proposed in this paper.The simulation results show that the phase can be retrieved effectively without considering environmental noise and probe jitter,when the metamaterial lens operates in the designed reference frequency 220GHz.Additionly,the effective working bandwidth of metamaterial lens is analyzed and verified.When the CATR works in 198GHz-300GHz,the correlation between two sets of amplitudes is less than 0.5,and the determination coefficient of phase retrieval accuracy is not less than 0.8981.The simulation results show that the quiet zone phaseless measurement method of CATR based on the metamaterial lens and the SPP GS/HIO-HIO algorithm can effectively retrieve the phase in the 102GHz ultra-wideband.3.The quiet zone phaseless measurement method based on the millimeter-wave metamaterial lens and alternating iterative algorithm requires moving lens and cannot cover the whole band of the CATR.This paper presents a novel method based on the millimeter-wave metamaterial lens and defocusing planes amplitudes in terms of the problems encountered.Generally,a set of nonlinear equations are constructed based on the relationship between multiple defocusing planes field and the quiet zone field to be measured.Then the amplitude and phase of the quiet zone field to be measured can be reconstructed by solving the nonlinear equations with the Amplitude Flow(AF)algorithm under the random initial phase condition.In addition,several groups of amplitude with small correlation can be measured only by moving the scanning platform in actual engineering measurement.The simulation results show that the accuracy of the phase reconstruction of the quiet zone becomes higher as the number of measured defocusing planes increases.Moreover,the simulation results show that quiet zone field reconstruction of CATR can be achieved when the defocusing planes quantity is enough.4.Recent studies have shown that the phaseless measurement methods for quiet zone in the mmW large-aperture CATRs in practical engineering need a large number of amplitude measurements,thus led to great difficulty in related data processing.Meanwhile,the phaseless measurement method needs possess the stability,effectiveness,flexibility and applicability for ultra wideband CATRs.In this paper,a Zernike Fourier(ZF)function for random phase initialization preprocessing is proposed in this paper to solve the above problems.Furthermore,the function model between the measurements of the planes in quiet zone is established through the angular spectrum propogation.Then the phase can be retrieved from the model without any auxiliary equipment by using the serial alternating iteration and the Reweighted Wirtinger Flow(RWF)algorithm combined with ZF function preprocessing,respectively.Compared with the alternating iteration with the ZF function preprocessing,the RWF algorithm with the ZF function preprocessing performs better.The simulated results show that the lowest Mean Square Error(MSE)of phase retrieved by the RWF algorithm through two sets of multi wavelength sampled amplitude is 7.9×10-3.Additionly,the method has been experimentally verified in the Cassegrain-Gregory triple CATR.The experimental results show that the proposed method can retrieve the phase of quiet zone by only two groups of measured amplitudes when CATR working at 137GHz.Moreover,the recovery accuracy of horizontal axis and vertical axis are MSE=2.51×10-2 and MSE=7.12×10-2,respectively.