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Acoustic environment has a low signal-to-noise ratio (SNR); hence, array signal processing is widely used for noise reduction and signal enhancement. The actual ambient noise includes uncorrelated noise and correlated noise. The received noises of the two arbitrary array elements are correlated. Consequently, the performance of array signal processing method decreases obviously. Aiming at this problem, the real-part elimination of covariance matrix method is proposed. Firstly, from a physical point of view, the noise signals can be generated by using a number of uncorrelated noise sources: the more the noise sources, the less the error between the noise from the model and the actual noise will be. Theoretically, the noise field is decomposed into the symmetrical noise field and the asymmetrical noise field. A number of noise sources generate the symmetrical noise fields; the directions of these noise sources are symmetric, and the powers of two arbitrary symmetric sources are the same. Secondly, the symmetry of the ambient noise is analyzed, as a result, the symmetrical noise can only affect the real part of the covariance matrix. Thirdly, the real part of covariance matrix is eliminated in order to reduce the noise, and then the delay-and-sum beamforming is achieved by using only the imaginary part. The advantages are that the output signal-to-noise ratio is increased and the noise output power is reduced obviously; the disadvantage is that it produces a false target. The azimuth of the actual target differs from that of the false target by 180, and the false target cannot be distinguished. Finally, to eliminate the false target, the real part of the signal covariance matrix is reconstructed by establishing a constrained optimization problem, which is solved by using the particle swarm algorithm. Then, the reconstructed covariance matrix composed of the imaginary part and the reconstruction of real part is applied to delay-and-sum beamforming, as a result, the false target is eliminated. The simulation results show that the real-part elimination of covariance matrix method reduces the symmetrical ambient noise, the noise output power is reduced, the output signal-to-noise ratio is increased, and this method improves the performance of array signal processing. The experimental results show that the output SNRs of two targets with using the imaginary part of covariance matrix are increased by 3.57 dB and 3.149 dB, respectively, and the output SNRs of two targets with using the reconstructed covariance matrix are increased by 7.027 dB and 6.985 dB, respectively. The real-part elimination of covariance matrix method is easy to implemente, and has a definite value for engineering application.
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Keywords:
- noise filed /
- noise reduction /
- real-part elimination /
- beamforming method
[1] Liang G L, Ma W, Fan Z, Wang Y L 2013 Acta Phys. Sin. 62 144302 (in Chinese) [梁国龙, 马巍, 范展, 王逸林 2013 62 144302]
[2] Yang Y X 2002 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [杨益新 2004 博士学位论文 (西安: 西北工业大学)]
[3] van Trees H L 2002 Optimum Array Processing: Part Iv of Detection, Estimation, and Modulation Theory (New York: Wiley) pp428-429
[4] Wang Y L, Chen H, Peng Y N, Wan Q 2004 Theory and Algorithms of the Spatial Spectrum Estimation (Beijing: Tsinghua University Press) pp2-6 (in Chinese) [王永良, 陈辉, 彭应宁, 万群 2004 空间谱估计理论与算法 (北京: 清华大学出版社) 第2-6页]
[5] Buckingham M J 2012 J. Acoust. Soc. Am. 131 2643
[6] Wenz G M 1972 J. Acoust. Soc. Am. 51 1010
[7] Yan S F, Ma Y L, Ni J P, Yang K D 2003 Tech. Acous. 22 30 (in Chinese) [鄢社锋, 马远良, 倪晋平, 杨坤德 2003 声学技术 22 30]
[8] Habets E A, Gannot S 2007 J. Acoust. Soc. Am. 122 3464
[9] Prasad S, Williams R T, Mahalanabis A K, Sibul, L H 1988 IEEE Trans. ASSP 36 631
[10] Moghaddamjoo A 1991 IEEE Trans. SP 39 219
[11] Li M H, Lu Y L 2008 IEEE Trans. AES 44 1079
[12] Farrier D R, Jeffries D J 1985 Proceedings of the ICASSP'85 Florida, March 26-29, 1985 p1788
[13] Goulding M M, Bird J S 1990 IEEE Trans. Veh. Technol. 39 316
[14] Shen W M, Ma Y L 1990 Proceedings of International Workshop on Marine Acoustics Beijing, March 26-30, 1990, p317
[15] Shen W M 1989 M. S. Thesis (Xi'an: Northwestern Polytechnical University) (in Chinese) [沈文苗 1989 硕士学位论文 (西安: 西北工业大学)]
[16] Zhang D H, Ma Y L, Yang K D, Pan Y 2008 Proceedings of CISP'08 Sanya China, May 27-30 2008 p552
[17] Wang L, Yang Y X, Wang Y 2012 Computer Simulation 29 192 (in Chinese) [王露, 杨益新, 汪勇 2012 计算机仿真 29 192]
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[1] Liang G L, Ma W, Fan Z, Wang Y L 2013 Acta Phys. Sin. 62 144302 (in Chinese) [梁国龙, 马巍, 范展, 王逸林 2013 62 144302]
[2] Yang Y X 2002 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [杨益新 2004 博士学位论文 (西安: 西北工业大学)]
[3] van Trees H L 2002 Optimum Array Processing: Part Iv of Detection, Estimation, and Modulation Theory (New York: Wiley) pp428-429
[4] Wang Y L, Chen H, Peng Y N, Wan Q 2004 Theory and Algorithms of the Spatial Spectrum Estimation (Beijing: Tsinghua University Press) pp2-6 (in Chinese) [王永良, 陈辉, 彭应宁, 万群 2004 空间谱估计理论与算法 (北京: 清华大学出版社) 第2-6页]
[5] Buckingham M J 2012 J. Acoust. Soc. Am. 131 2643
[6] Wenz G M 1972 J. Acoust. Soc. Am. 51 1010
[7] Yan S F, Ma Y L, Ni J P, Yang K D 2003 Tech. Acous. 22 30 (in Chinese) [鄢社锋, 马远良, 倪晋平, 杨坤德 2003 声学技术 22 30]
[8] Habets E A, Gannot S 2007 J. Acoust. Soc. Am. 122 3464
[9] Prasad S, Williams R T, Mahalanabis A K, Sibul, L H 1988 IEEE Trans. ASSP 36 631
[10] Moghaddamjoo A 1991 IEEE Trans. SP 39 219
[11] Li M H, Lu Y L 2008 IEEE Trans. AES 44 1079
[12] Farrier D R, Jeffries D J 1985 Proceedings of the ICASSP'85 Florida, March 26-29, 1985 p1788
[13] Goulding M M, Bird J S 1990 IEEE Trans. Veh. Technol. 39 316
[14] Shen W M, Ma Y L 1990 Proceedings of International Workshop on Marine Acoustics Beijing, March 26-30, 1990, p317
[15] Shen W M 1989 M. S. Thesis (Xi'an: Northwestern Polytechnical University) (in Chinese) [沈文苗 1989 硕士学位论文 (西安: 西北工业大学)]
[16] Zhang D H, Ma Y L, Yang K D, Pan Y 2008 Proceedings of CISP'08 Sanya China, May 27-30 2008 p552
[17] Wang L, Yang Y X, Wang Y 2012 Computer Simulation 29 192 (in Chinese) [王露, 杨益新, 汪勇 2012 计算机仿真 29 192]
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