Low Complexity Multi-target Localization Algorithm Based On Coprime Array

In recent years,with the rapid development of 5G communication technology and Internet of things(Io T)technology,positioning technology has increasingly become a research hotspot in mobile communication and Io T service industry.The positioning technology has been widely used in smart city,industrial logistics,smart home,retail management and other fields.In the positioning of 5G base station or other Io T equipment,the signal receiver generally adopts the sensor array arranged according to certain rules in the space to receive the target signal.Then a signal processing algorithm is utilized to extract the target parameter information contained in the signal to achieve the target localization.Compared with the uniform linear array(ULA)typically used in the base station side or other the Io T receiving devices,the coprime array can effectively improve the array aperture with the same number of physical array elements,so as to increase the target degree of freedom and parameter estimation accuracy.At the same time,it also has the advantage of reducing the hardware scale and cost.It has become a research hotspot in the field of array signal processing in recent years.At present,the actual deployment of positioning devices based on communication system will be limited by the deployment cost and space.One dimensional linear array with few array elements and short baseline is widely used by these devices.The following three technical challenges should be addressed if such a small-scale array is actually deployed.First,the demand for real-time Io T positioning becomes higher,but the timeliness is unsatisfying if the positioning algorithm takes too much time.Second,in Io T,the base station often needs to locate multiple targets at the same time,and the degree of freedom of the positioning algorithm is difficult to deal with such a large number.Third,in practical engineering,the array used by the base station is bound to have inherent errors caused by imperfect hardware,such as inter array coupling and position offset,which will affect the accuracy of target parameter estimation.In order to solve the above three problems,this paper considers seeking a breakthrough from the perspectives of accuracy,degree of freedom and real-time(or efficiency).This paper takes the coprime array model and its signal processing algorithm as the main research content,hoping to provide some references and new ideas for the scheme design of communication positioning system in the future.Therefore,the following research is carried out in this paper:Firstly,this paper studies the fast estimation algorithm of one-dimensional sparse spatial spectrum of coprime array,which improves the computational efficiency.When the element numbers in the virtual domain of coprime array is too large,the classical multiple signal classification(MUSIC)algorithm involves large matrix eigenvalue decomposition and dense spectral peak search,resulting in high computational complexity.This paper uses the method based on spatial response signal analysis to estimate the direction of arrival(DOA).Further,in order to reduce the calculation workload in the inverse discrete Fourier transform process,referring to the multi-scale transform method,this paper designs a DOA estimation algorithm based on inverse sparse Fourier transform(ISFT)for coprime array.By applying the proposed ISFT algorithm to the equivalent receive signal of virtual domain ULA,the corresponding spatial response signal is obtained.Then,the relationship between the spatial spectrum peaks and the source DOAs can be established by approximately analyzing the Fourier transform process.The peaks of spatial response signal are found out via a peak search process,and then Do A estimation is realized according to the corresponding relationship.The peak corresponding to each Do A is the estimated power.The proposed algorithm significantly improves the computational efficiency,which is expected to be used for the coprime array deployed to the base station in the future.Also,this method provides more possibilities for the real-time positioning.Secondly,this paper studies the two-dimensional positioning method based on coprime spacefrequency virtual array interpolation,which improves the degree of freedom.After the transmitter transmits the coprime frequency diversity signal,the problem that information loss is existed in the two-dimensional virtual domain of the receiver signal arises.A “hole” filling scheme of the twodimensional virtual array based on Decoupled atomic norm minimization(DANM)is proposed in this paper.First,the receive signal of a two-dimensional virtual frequency diversity array with “holes”is constructed by vectorizing the receive signal of the physical array.And a positive semidefinite programming problem is established based on DANM.Then,the positive semidefinite programming problem is solved to obtain the receive signal of the virtual frequency diversity array(FDA)after recovering the “hole”.Finally,according to the receive signal,a covariance matrix obeying the characteristics of doubly-Toeplitz structure is constructed.According to this matrix,the target positioning parameters are estimated by two-dimensional MUSIC algorithm.Since the missing information is supplemented after the ”hole” is restored,which is equivalent to supplementing the array elements of the virtual array,both the degree of freedom and parameter estimation accuracy are improved.The proposed scheme can be applied to the coprime FDA model deployed to the base station in the future to improve the degree of freedom and compensate the loss of accuracy.Finally,this paper studies the fast estimation method of two-dimensional spatial spectrum based on array manifold separation,which can reduce the inherent error of the array and improve the efficiency of the algorithm.On the one hand,coprime array can not avoid the influence of inherent errors such as coupling error and array element layout error in practical engineering application.On the other hand,the two-dimensional spatial spectrum estimation formed by the large bandwidth ranging based on 5G OFDM waveform and the DOA estimation,often involves intensive spectrum calculation and spectrum peak search.This results in high computational complexity.Aiming at the above two problems,this paper takes the advantage of manifold separation technology,whose offline stage calculates the sampling matrix,which contains the physical structure characteristics of the array,hence the inherent error of the array can be handled effectively.However,the key idea of array manifold separation is to transform the process of spectral peak calculation and search into the process of two-dimensional discrete Fourier transform of coefficient matrix,which consumes the main computational resources.Therefore,this paper further adopts the random slice-based sparse Fourier transform method to realize the fast two-dimensional spectrum estimation of target parameters.Of course,this scheme is not limited to coprime arrays,but can also be applied to other one-dimensional arrays deployed on 5G small base stations.