Research on DOA Estimation of Multi-Component LFM Signals Based on the FRFT
- 1
- 2
- 3
- 4
Abstract
A novel algorithm for the direction of arrival (DOA) estimation based on the fractional Fourier transform (FRFT) is proposed. Firstly, using the properties of FRFT and mask processing, Multi-component LFM sig-nals are filtered and demodulated into a number of stationary single frequency signals. Then the one-dimensional (1-D) direction estimation of LFM signals can be achieved by combining with the tradi-tional spectrum search method in the fractional Fourier (FRF) domain. As for the multi-component LFM signals, there is no cross-term interference, the mean square error (MSE) and Cramer-Rao bound (CRB) are also analyzed which perfects the method theoretically, simulation results are provided to show the validity of our method. The proposed algorithm is also extended to the uniform circular array (UCA), which realizes the two-dimensional (2-D) estimation. Using the characteristics of time-frequency rotation and demodulation of FRFT, the observed LFM signals are demodulated into a series of single frequency ones; secondly, operate the beam-space mapping to the single frequency signals in FRF domain, which UCA in array space is changed into the virtual uniform circular array (ULA) in mode space; finally, the DOA estimation can be realized by the traditional spectral estimation method. Compared with other method, the complex time-frequency cluster and the parameter matching computation are avoided; meanwhile enhances the esti-mation precision by a certain extent. The proposed algorithm can also be used in the multi-path and Doppler frequency shift complex channel, which expands its application scope. In a word, a demodulated DOA esti-mation algorithm is proposed and is applied to 1-D and 2-D angle estimation by dint of ULA and UCA re-spectively. The detailed theoretical analysis and adequate simulations are given to support our proposed al-gorithm, which enriches the theory of the FRFT.
- G. Wang and X. G. Xia, “Iterative algorithm for direction of arrival estimation with wideband chirp signals,” IEE Proceed-ings of Radar, Sonar, Navig, Vol. 147, No. 5, pp. 233–238, 2000.
- A. Belouchirani and M. G. Amin, “Time-frequency MUSIC [J],” IEEE Signal Processing Letters, Vol. 6, No. 5, pp. 109–110, 1999.
- A. B. Gershman and M. G. Amin, “Wideband direction of mul-tiple chirp signals using spatial time-frequency distributions,” IEEE Signal Processing Letters, Vol. 7, pp. 152–155, June 2000.
- R. Tao and Y. S. Zhou, “A novel method for the DOA estima-tion of wideband LFM sources based on FRFT,” Transactions of Beijing Institute of Technology, Vol. 25, No. 10, pp. 895–899, 2005.
- P. Stoica and A. Nehorai, “Music, maximum likelihood, and cramer-rao bound,” IEEE Transactions on ASSP, Vol. 37, No. 5, May 1989.
- V. Namias, “The fractional Fourier transform and its applica-tion in quantum mechanics [J],” IMA Journal of Applied Mathematics, No. 25, pp. 241–265, 1980.
- L. B. Almeida, “Fractional Fourier transform and time-frequency representations [J],” IEEE Transactions on Signal Processing, Vol. 42, No. 11, pp. 3084–3091, 1994.
- Y. Q. Dong, R. Tao, S. Y. Zhou, et al., “SAR moving target detection and imaging based on fractional Fourier transform,” Acta Armamentarii (in Chinese), Vol. 20, No. 2, pp. 132–136, 1999.
- L. Qi, R. Tao, S. Y. Zhou, et al., “Adaptive time-varying filter for linear FM signal in fractional Fourier domain,” Proceedings of the 6th ICSP, Posts and Telecommunications Press, Beijing, pp. 1425–1428, 2002.
- R. Tao, L. Qi, and Y. Wang, “Principle and application of the fractional Fourier transform,” Tsinghua Publishing Company, Beijing, 2004.
- H. M. Ozaktas, O. Arikan, M. A. Kutay, et al., “Digital com-putation of the fractional Fourier transform,” IEEE Transac-tions on Signal Processing, Vol. 44, No. 9, pp. 2141–2150, 1996.
- L. Qi, R. Tao, S. Y. Zhou, et al., “Detection and parameter estimation of multicomponent LFM signal based on the frac-tion Fourier transform [J],” Science in China (Series E), Vol. 47, No. 2, pp. 184–198, 2004.
- X. D. Zhang, et al., Modern Signal Processing (Second editor), Tsinghua Publishing Company, Beijing, 2002.
- C. P. Mathews, “Eigenstructure techniques for 2-D angle esti-mation with uniform circular arrays,” IEEE Transactions on Signal Processing, Vol. 42, No. 9, pp. 2395– 2407, September 1994.