In multi-channel synthetic aperture radar (SAR), the azimuth non-uniform sampling tends to result in a large number of virtual point targets, which are not expected. Inverse filter algorithm provides a new idea for solving this problem. This way can be abstracted as a matrix inversion in essence, which becomes the key factor that affects the real-time and accuracy of multi-channel pre-processing. This study presents the implementation of matrix inversion method on field programmable gate array (FPGA), based on lower and upper triangular matrix (LU) decomposition algorithm. In this process, the efficient parallelism of FPGA and the rich floating-point intellectual property (IP) cores are fully utilised to speed up the process of inverting the matrix with a data type of 32-bit single-precision floating-point. In this design, the parallelism of the algorithm was fully considered and a hierarchical iterative processing strategy was adopted to realise the reconfigurable storage and computing unit both. At the same time, in order to achieve the balance of resources and efficiency, a reusable structure was proposed also, using the pipeline technology and appropriate data scheduling. Finally, Modelsim platform is used to observe the simulation results, and the performance can be detected combined with MATLAB platform. At last, the computational accuracy is up to $10 − 7$ , and the speedup ratio can reach about $1.461 × 10 3$ .

References

1. 1)
  - 5. Pei, L., Ding, Z.: ‘Data processing of multi-channel space-borne SAR’. IET Int. Radar Conf., Guilin, China, April 2009.
2. 2)
  - 2. Quegan, S.: ‘Spotlight synthetic aperture radar: signal processing algorithms’, J. Atmos. Sol.-Terr. Phys., 1995, 59, (5), pp. 597–598.
3. 3)
  - 6. Lin, Y., Zhang, J., Wu, Y., et al: ‘Matrix inversion algorithm for azimuth signal reconstruction in bistatic satellite HRWS-SAR system’, J. Radar, 2017, 6, (4), pp. 388–396.
4. 4)
  - 11. Lin, H.: ‘Implementation of matrix operation based on FPGA’. MS thesis, Nanjing University of Science and Technology, Nanjing, China, 2007.
5. 5)
  - 7. Brown, J.L.Jr.: ‘Multi-channel sampling of low-pass signals’, IEEE Trans. Circuits Syst., 1981, 28, (2), pp. 101–106.
6. 6)
  - 8. Cheng, P., Wan, J., Xin, Q., et al: ‘An improved azimuth reconstruction method for multichannel SAR using Vandermonde matrix’, IEEE Geosci. Remote Sens. Lett., 2017, 14, (1), pp. 67–71.
7. 7)
  - 3. Mittermayer, J., Lord, R., Borner, E.: ‘Sliding spotlight SAR processing for TerraSAR-X using a new formulation of the extended chirp scaling algorithm’. Proc. Int. Conf. Geoscience and Remote Sensing Symp., 2003 IGARSS, Toulouse, France, July 2003.
8. 8)
  - 10. Zhang, X.: ‘Matrix analysis and application’ (Tsinghua University Press, Beijing, China, 2013).
9. 9)
  - 4. Yin, W., Ding, Z., Lu, X., et al: ‘Beam scan mode analysis and design for geosynchronous SAR’, Sci. China, 2017, 60, (6), p. 060306.
10. 10)
  - 9. Xu, Z.: ‘Vandermonde matrix fast algorithm’ (Northwestern Polytechnical University Press, Xian, China, 1997).
11. 11)
  - 12. Matos, G.M.D., Neto, H.C.: ‘Memory optimized architecture for efficient Gauss-Jordan matrix inversion’. Proc. Int. Conf. Programmable Logic, Mar del Plata, Argentina, 2007.
12. 12)
  - 13. Wang, Y., Tao, H., Xiao, S., et al: ‘An implementation architecture design of LU decomposition in resource-limited system’. Proc. Int. Conf. IEEE Int. Symp. on Systems Engineering, Rome, Italy, 2015.
13. 13)
  - 1. Wu, C., Liu, K.Y., Jin, M.: ‘Modeling and a correlation algorithm for spaceborne SAR signals’, IEEE Trans. Aerosp. Electron. Syst., 1982, AES-18, (5), pp. 563–575.

FPGA-based reconfigurable matrix inversion implementation for inverse filtering of multi-channel SAR imaging

References

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