Research On DOA Estimation Based On Magnitude Measurements Under Array Amplitude And Phase Error

Direction-of-arrival(DOA)estimation can accurately estimate the direction of spatial signals,and is widely used in sonar,wireless communication and other fields.By expanding the antenna array dimension,the DOA estimation performance has been greatly improved.However,this will significantly increase the circuit power consumption and manufacturing cost.The low-power and low-cost magnitude antenna array composed of envelope detector can effectively alleviate the above problems.Unfortunately,the introduction of nonlinear devices leads to the loss of phase observation information and phase ambiguity,and the traditional DOA estimation algorithms are no longer applicable.Therefore,it is necessary to develop a DOA estimation algorithm that can deal with nonlinear distortion.Most of the existing DOA estimation algorithms assume that the array steering matrix is accurately known.In practice,interference such as array amplitude and phase error will disturb the array steering matrix and seriously affect the performance of the above algorithms.And the existing literature has less research on the error correction of magnitude antenna array.Therefore,this paper studies the magnitude antenna array from two aspects:DOA estimation and amplitude-phase error correction:1.The estimation performance of DOA is elegantly enhanced by expanding the dimension of traditional antenna array.Unfortunately,this will significantly increase the circuit power consumption and fabrication cost.To tackle this issue,a low-power-and-low-cost magnitude-aided antenna array(MA-AA)is proposed.Then,an efficient DOA estimation algorithm is developed in MA-AA.Firstly,initial DOAs are obtained by the classical multiple signal classification(MUSIC)algorithm based on several classical antennas.After griding the neighborhoods of these initial DOAs,the DOA estimation problem is converted into the recovery problem of sparse signals,which can be solved by generalized approximate message passing(GAMP).Due to the "space leakage" effect,non-zero clusters appear near the true DOA.Their positions(i.e.non-zero supports)provide DOA estimation.In addition,DOA and supports are almost unchanged in every snapshot,so common supports are shared among all snapshots.Therefore,the cluster relationships of supports are characterized by a one-order hidden Markov tree(HMT).Through the belief propagation(BP)on the HMT,binary probabilities of supports are updated.Moreover,the GAMP and BP alternatively exchange the statistical information about the gain and support variables.Among them,some unknown hyper-parameters are iteratively updated by expectation maximization(EM).Compared to current estimators,EM-BP-GAMP has lower orders of computational complexity,and shows state-of-the-art performance.It also enjoys higher DOA resolution,and can distinguish adjacent sources,which are failed to be found by MUSIC.With the EMBP-GAMP estimator,MA-AA can be more energy-efficient than the classical antenna array.The experimental results successfully verify these advantages.2.Aiming at the joint estimation of DOA and transmitter channel response under the magnitude measurements,according to the MA-AA system designed in research point 1,a joint DOA and channel response estimator is proposed under the framework of Bayesian inference.Due to the existence of nonlinear magnitude measurements and highdimensional integration,the joint posterior probability distribution functions(PDF)of DOA and channel response under hybrid MA-AA measurements has no closed solution,and their posterior mean has no closed solution.Therefore,the Metropolis-Hastings Markov chain Monte Carlo(MH-MCMC)sampling algorithm is modified to deal with nonlinear magnitude measurements.Then,the samples of DOA and channel response obeying their posterior PDF are generated,based on which,their posterior means are numerically calculated after the burn-in period.Compared with the existing estimation methods,the modified MH-MCMC has advantages in DOA estimation,channel response estimation and computational complexity.Based on MH-MCMC estimator,MA-AA is more energy-efficient than traditional antenna array.3.Aiming at the problem of DOA estimation with magnitude observations under array amplitude and phase error,a joint estimation algorithm of array amplitude and phase error and DOA is proposed.Firstly,initial DOA and initial amplitude-phase error of the traditional antenna are obtained through the classical MUSIC algorithm and least square(LS)algorithm,based on the traditional complex observations.Then,due to the existence of nonlinear magnitude measurements and high-dimensional integration,the joint posterior PDF of DOA and array amplitude and phase error under hybrid MA-AA measurements has no closed solution,and their posterior mean has no closed solution.Therefore,the Hamiltonian Monte Carlo(HMC)algorithm is modified to deal with nonlinear magnitude measurements.By means of the gradient information in the Hamiltonian dynamic equation,HMC suppresses effectively the random walk of the traditional MCMC method,and the Markov chain is converged quickly.Experimental results show that HMC can effectively deal with nonlinear observations,and jointly estimate DOA and array amplitude and phase errors.By using more snapshots and signal-to-noise-ratio(SNR),the estimation performance of DOA and the correction performance of amplitude and phase error are steadily improved.