Orthogonal matching pursuit method based on FPGA

Abstract

The invention discloses an orthogonal matching pursuit method based on an FPGA. The orthogonal matching pursuit method based on the FPGA mainly solves the problems that an existing radar system is limited in complex algorithm processing capability and low in processing speed. The orthogonal matching pursuit method based on the FPGA comprises the following steps that according to radar echo data, an observation vector and a dictionary matrix are obtained; an error margin is initialized into the observation vector, zero padding is conducted on the error margin so that a difference value vector with the length being 2048 can be generated, and inverse Fourier transformation is conducted on the difference value vector by calling an FFT core; the modular square of data output by the FFT core is obtained, and the position of the maximum value is found out, namely a column position index with the maximum correlation of the error margin is found out; according to the found column position index, a column vector set is updated; Schmidt orthogonalization processing is conducted on the column vector set and the error margin is updated; the 2-norm of the error margin is obtained, whether the 2-norm is smaller than one or not is judged, and if the 2-norm is smaller than one, an original signal is recovered through a conjugate gradient algorithm. The orthogonal matching pursuit method based on the FPGA has the advantages of being higher in speed, occupying fewer resources, and being capable of being used for reconstructing Fourier-based large-scale dictionary matrices and Fourier-based high-sparsity signals.

Description

technical field [0001] The invention belongs to the technical field of digital signal processing, and in particular relates to an accelerated hardware implementation method for a complete signal reconstruction algorithm using observation signals, which can be used for synthetic aperture radar / inverse synthetic aperture radar and step frequency radar imaging. Background technique [0002] When the radar detects the target, due to the influence of the complex electromagnetic environment, the defects of the radar system itself, and the change of the target motion attitude, the echo data may be sparsely sampled. If the traditional Fourier analysis method is used, the target point will be defocused. and image blurring, so how to achieve sparse signal target detection and imaging is very important. In 2006, D.Donoho, E.Candes, T.Tao et al proposed a brand-new guidance theory for information acquisition, that is, compressed sensing CS. The data is sampled at a special standard sam...

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Problems solved by technology

[0004] 1) When implementing the OMP algorithm with FPGA, a large number of matrix-vector multiplication and vector-vector multiplication operations will be involved, and as the size of the dictionary matrix increases, the clock cycles and system resources occupied by matrix-vector multiplication will increase sharply. increase, which limits the improvement of solution speed and the optimization of hardware resources

[0005] 2) In the part of solving the least squares, the existing solution methods mostly use LU decomposition, QR decomposition, etc. to invert the matrix to solve the least squares problem. The disadvantage of this method is that when the size of the matrix increases, the calculation is complicated The degree will be greatly increased, and the corresponding calculation time will increase, thereby reducing the processing speed of the signal

[0006] 3) Most of the data types used in the prior art are fixed-point real numbers, while the data received by the radar are complex numbers containing phase information, and the practicability of the algorithm is not strong

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