FPGA Implementation Of Eigenvalue Decomposition And Source Number Estimation In MUSIC Algorithm

DOA estimation,as an important research area of array direction finding technology,not only has a wide range of applications in military radar and sonar signals,but also has outstanding contributions in civil fields such as seismic exploration.The Multiple Signal Classification(MUSIC)algorithm proposed by R.O.Schmidt in 1979 is the cornerstone of feature decomposition algorithms,which has high precision and high resolution performance.However,this algorithm has a large amount of calculations and involves complex algorithms such as eigenvalue decomposition,which is difficult to implement in real time.In this context,this subject has studied the realization of an 8-element uniform circular array direction finding system based on FPGA.The work is as follows:1.Aiming at the problem of large amount of complex matrix operation in the MUSIC algorithm,the algorithm operation is transferred from the complex number domain to the real number domain by preprocessing.The preprocessing method is combined with the covariance matrix calculation to complete the behavior level description and comprehensive simulation of the covariance matrix calculation.2.The research on FPGA-based eigenvalue decomposition algorithm is carried out,and the round-robin sequence exchange method is improved,and the iteration efficiency of parallel Jacobi algorithm is improved.Based on this,On this basis,the systolic array structure is introduced,which can reduce the number of data access memory and improve the data throughput.For the non-linear operation in Jacobi algorithm,the CORDIC algorithm in vector mode is used to implement it.In addition,the rotation operation of the matrix is accomplished by using the lookup table method and the multiplier,which reduces the time of Jacobi algorithm.Based on the Jacobi algorithm,the module partition scheme of 8-order real symmetric matrix eigenvalue decomposition is proposed.Verilog language is used to describe the algorithm's behavior level,and the function and timing simulation of the algorithm are completed.3.After the eigenvalue decomposition,the number of sources is estimated by Akaike Information Criteria based on diagonal loading according to the distribution characteristics of eigenvalues.At the same time,to ensure the accuracy and speed of the algorithm in fixed-point quantization,the input eigenvalues are constrained by the preprocessing method of magnification or minification.This method can accelerate the convergence of Taylor series and prevent the overflow of fixed-point data.Moreover,the three-stage pipeline structure is used to expand the loop in the algorithm to accelerate the realization of the algorithm.4.The three modules of covariance matrix calculation,eigenvalue decomposition and source number estimation were used to complete interconnection debugging,and the static timing analysis of the whole algorithm at 100 MHz was completed.The whole system is designed based on the virtex-7 series Xc7v690 t chip and the Vivado2016.4 development environment.The eigenvalue decomposition module of the 8-order real symmetric matrix has a running time of 8.87 us under 100 MHz clock.Under the condition of parallelism degree 2,the running time of the source number estimation module is 3.13 us.