Research On Compressive Measurements Exploiting Coprime Frequencies For Direction Finding

The basic principle of array signal processing is to extract effective information of the signal through spatial characteristics,and the direction of arrival(DOA)estimation has become a key technology in its field with excellent estimation super-resolution capability in spatial-domain.To improve the accuracy and degree of freedom(DOF)of angle estimation,the expansion of the number of array elements and array aperture must be at the cost of system complexity,which is unrealistic in the practical application.To solve this problem,on the one hand,compressed sensing(CS)theory can be introduced into array design to reduce the complexity of digital baseband signal processing from RF front-end.On the other hand,sparse array can be utilized to reduce the number of antennas physically and guarantee the estimation performance.In addition,the multi-carrier frequency principle can be combined with the sparse uniform array structure to obtain the advantage in estimation performance.Therefore,this thesis aims at the implementation of DOA estimation with high accuracy and DOF by using array structure with limited antennas.The main content are summarized as follows:1)Data compression-based structure refers to the application of compressed sensing in system design.Without changing the hardware configuration of the array,the signal in the analog domain is linearly combined by using the combined network inserted in the antenna output,and the signal processing in the digital domain is carried out with lower complexity through fewer frontend circuits.The application of data compression-based structure in sparse array can obtain DOA estimation structure with high estimation performance and low system complexity.In this thesis,the compressed coprime array is taken as an example to model the received data and the general system of the compressed sparse array(CSA)structure.The system complexity is about M L of the original when the L-channel received signal is compressed to M-channel output.Then the DOA estimation method based on compressed sensing under this model is introduced,and the general expression of Cramér-Rao Bound(CRB)applicable to data-compression based structure is derived as the lower bound of estimation performance.Theoretical analysis and simulation results both prove that,compared with the sparse array of M-elements,the CSA structure of M-channel can obtain high estimation accuracy,as well as the DOF.2)Based on the principle of the multi-carrier frequency system and the coprime domain,the concept of the coprime array is extended in this thesis,and a coprime frequency-based uniform linear array(CF-ULA)structure is constructed.The inter-element spacing of the equivalent array is controlled by the coprime frequencies,and the high performance DOA estimation is realized at low hardware cost by using only the number of sensors and aperture of the actual ULA.Numerical analysis shows that to achieve the same estimation performance,the CF-ULA structure with transmission of Q carriers only needs about 1/Q elements of the traditional coprime array.This thesis constructs and explains the system model and principle of CF-ULA structure,and two improved DOA estimation methods are analyzed.Since the reflected signals with different carrier frequencies induce a group of additional phases at the receiver,under whose influence,the general formula of CRB is also derived.It is observed that CRB curves exhibit different asymptotic trends with the increase of signal-to-noise ratio(SNR)similar to that of sparse array,thus two CRB asymptotic expressions with the target number as the threshold are derived.Simulation results confirm that the estimation accuracy and number of DOFs are improved under the influence of additional phase.3)Integrating the characteristics of the compressive array and the CF-ULA structure,in order to reduce the hardware costs of the DOA estimation structure,and simultaneously,ensure the realization of high accuracy and DOF,a data compression-based CF-ULA structure and the corresponding DOA estimation method are proposed in this thesis.By reducing the number of sensors while compressing the data dimension,the equivalent virtual array ensures the estimation performance and reduces the cost of data processing in the digital domain at the same time.Considering that there is no applicable CRB for the performance analysis of the structure,the CRB general expression with the compression matrix and additional phase matrix coexistence is derived,whereas the conditions of CRB existence related to rank are also inferred.Through numerical simulation and comparison,compared with traditional CF-ULA structure with the same number of channels,the proposed structure has considerable advantages in the accuracy and number of DOFs of DOA estimation.