ROOT-MUSIC Algorithm With Unitary Transformation And Searching By Step And Step And Its Complement With FPGA

The array antenna is not only an important part of the Third Generation mobile co- mmunication but also main content of the digital array radar system. DOA(Direction of Arrival)is the important content of digital array signal processing in the array antenna field, it plays an very important role in many field such as wireless communication, electronic countermeasure, parameter estimation, signal discrimination, wireless signal source location and so on. The signal subspace method is an important and very useful method in the array direction. After the several years of development, the subspace -based method has already produced a great deal of the high performance algorithms.for example, MUSIC(the Classification of the Multiple Signal) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). Among all the algorithms based on signal subspace method, MUSIC researched by R.O.Schmidt has the characteristic of high precision and high resolution. But it has heavy burden of computation; it has many difficulties in its application. Therefore, it is very meaningful to decrease its computation quantity and find out its high-speeded implementation methods.This paper firstly introduces the MUSIC algorithm and the related improved MUSIC algorithms. Then the paper studies the ROOT-MUSIC algorithm which we apply the unitary transformation and searching by step and step: it can be eigendecomposed in the real number domain by applying the unitary transformation, make the compu tation quantity of peak research much lower by adopting the polynomial of the ROOT-MUSIC algorithm to implement index of spectrum peak. Lastly, the dissertation studies how to implement the ROOT-MUSIC algorithm applying the unitary transformation and searching by step and step ,which contains forward spatial smoothing, The principle of FPGA in a eight-elements uniform linear array(ULA)system. Among them, the FPGA implementation is the main content, which has five parts:①Covariance matrix block: during the course of getting real symmetrical matrix though forward spatial smoothing, unitary transformation and complex matrix-multiply -ing, the dissertation works out the formula of the each data of the real symmetrical matrix in advance, then directly apply the formula to the circuit design and gets signal Covariance matrix with IIR filter to average datum. ②The eigenvalue decomposition block: the paper studies a algorithm of eigen -value decomposition which balance computation speed and resources to take up. it is suitable to FPGA implementation: The eigenvalue decomposition algorithm of Jacobi based CORDIC and series and parallel computation. It is based on two IP cores of the CORDIC algorithm;(the IP cores operate in the ROTATION mode and VECTOR mode) and it run serieal and parallel computation: Namely, during changing the off-diagonal elements of the matrix into zeros, the algorithm sweeps these elements one by one, but the computations of the related two rows and two columns of the matrix is parallel.③Inverse unitary transformation and the complex matrix multiplication: the complex matrix multiplication calculates column by column, but computation of each column is parallel.④Block of getting polynomial coefficient of the ROOT-MUSIC.⑤Peek research: Taking the method of look-up table instead of the computation of sine and cosine, applying polynomial of the ROOT-MUSIC algorithm to peek research, so computation quantity of peek research decrease.In the meantime, this dissertation shows the block diagram of hardware implementation and illustrates the flow diagram of the block.Each above-mentioned each block uses VHDL toto realize the described algorithms, and Each block is simulated and verified in the QUARTUSII of altera., and this paper shows the result of the simulation, the QUARTUSII simulation of the peek research shows: The whole algorithms realized with the VHDL can implements the function and can correctly estimate the DOA of signal.