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Acoustic environment has low signal-to-noise ratio(SNR); hence, array signal processing is always used for reducing noise and enhancing signal. Because the delay-and-sum beam forming method is robust, so it is almost widely used, but the array gain is limited by the array aperture. The actual underwater ambient noise is complex, which includes uncorrelated noise and correlated noise. The noise powers of array elements are unequal to each other. The noise covariance matrix is not a scaled identity matrix. Consequently, the performance of array signal processing method decreases obviously. Aiming at these two problems, a diagonal reducing method of the covariance matrix in the complex noise field is proposed. Firstly, a reducing matrix, which is defined as a diagonal matrix with unequal diagonal elements, is subtracted from the covariance matrix so as to reduce the noise, and a new matrix is obtained. Secondly, the delay-and-sum beamforming is done by using the new matrix to obtain the beaming output. The analytic solution and approximate solution of reducing matrix are obtained under the constraint condition that the output SNR attains its maximum. Thirdly, the estimation of the reducing matrix is determined by minimizing the function that is defined as the error between the covariance matrix and the estimated covariance matrix. This minimization problem is accomplished in an iterative method. Fourthly, if the noise is uniform white noise or the nonuniform white noise, this proposed method performs well. While, under the complex noise field the performance of the proposed method may be deteriorated. So the effects of the correlation of the noise field and the input SNR on the estimated error are analyzed. In fact, the weaker the correlation is, or the larger the input SNR is, the smaller the estimated error is. Lastly, the simulation experiment and the lake trial are implemented. The simulation results show that the diagonal reducing method of the covariance matrix reduces some ambient noises, the noise output power decreases, the output SNR increases, and the proposed method improves the performance of array signal processing. The experimental results show that the output SNR of the target by using the proposed method is increased by about 14 dB. The diagonal reducing method of covariance matrix has definite value for engineering application, and is computationally attractive.
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Keywords:
- underwater noise filed /
- diagonal reducing /
- beamforming /
- least square method
[1] Fishler E, Poor H V 2005 IEEE Trans. Signal Process. 53 3543
[2] Wu Y, Hou C, Liao G, Guo Q 2006 IEEE J. Ocean. Eng. 31 504
[3] Madurasinghe D 2005 IEEE Signal Process. Lett. 12 337
[4] Li M H, Lu Y L 2008 IEEE Trans. Aerosp. Electron. Syst. 44 1079
[5] Prasad S, Williams R T, Mahalanabis A K, Sibul L H 1988 IEEE Trans. on ASSP 36 631
[6] Moghaddamjoo A 1991 IEEE Trans. Signal Process. 39 219
[7] Liao B, Chan S C, Huang L, Guo C T 2005 IEEE Trans. Signal Process. 53 34
[8] Chen C E, Lorenzelli F, Hudson R E, Yao K 2008 IEEE Trans. Signal Process. 56 3038
[9] Van T H L 2002 Optimum Array Processing:Part IV of Detection, Estimation, and Modulation Theory（New York:Wiley) pp428-429
[10] Reddy V V, Boon P N, Khong A W H 2013 IEEE Trans. Signal Process. 61 2551
[11] Roy R, Kailath T 2016 Acta Phys. Sin. 65 144302 （in Chinese)[夏麾军, 马远良, 刘亚雄2016物理学报65 144302]
[12] Emanuël A P H, Sharon G 2007 J. Acoust. Soc. Am. 122 3464
[13] Robert P D 2004 Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference Manchester, England, May 10-12, 2004 p1
[14] Zhao A B, Zhou B, Song X J, Bi X J 2014 J. Harbin. Eng. Univ. 35 1327 （in Chinese)[赵安邦, 周彬, 宋雪晶, 毕雪洁2014哈尔滨工程大学学报35 1327]
[15] Petersen K B, Pederse M S 2012 The Matrix Cookbook（Denmark Tech. Univ. of Denmark) pp8-14
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[1] Fishler E, Poor H V 2005 IEEE Trans. Signal Process. 53 3543
[2] Wu Y, Hou C, Liao G, Guo Q 2006 IEEE J. Ocean. Eng. 31 504
[3] Madurasinghe D 2005 IEEE Signal Process. Lett. 12 337
[4] Li M H, Lu Y L 2008 IEEE Trans. Aerosp. Electron. Syst. 44 1079
[5] Prasad S, Williams R T, Mahalanabis A K, Sibul L H 1988 IEEE Trans. on ASSP 36 631
[6] Moghaddamjoo A 1991 IEEE Trans. Signal Process. 39 219
[7] Liao B, Chan S C, Huang L, Guo C T 2005 IEEE Trans. Signal Process. 53 34
[8] Chen C E, Lorenzelli F, Hudson R E, Yao K 2008 IEEE Trans. Signal Process. 56 3038
[9] Van T H L 2002 Optimum Array Processing:Part IV of Detection, Estimation, and Modulation Theory（New York:Wiley) pp428-429
[10] Reddy V V, Boon P N, Khong A W H 2013 IEEE Trans. Signal Process. 61 2551
[11] Roy R, Kailath T 2016 Acta Phys. Sin. 65 144302 （in Chinese)[夏麾军, 马远良, 刘亚雄2016物理学报65 144302]
[12] Emanuël A P H, Sharon G 2007 J. Acoust. Soc. Am. 122 3464
[13] Robert P D 2004 Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference Manchester, England, May 10-12, 2004 p1
[14] Zhao A B, Zhou B, Song X J, Bi X J 2014 J. Harbin. Eng. Univ. 35 1327 （in Chinese)[赵安邦, 周彬, 宋雪晶, 毕雪洁2014哈尔滨工程大学学报35 1327]
[15] Petersen K B, Pederse M S 2012 The Matrix Cookbook（Denmark Tech. Univ. of Denmark) pp8-14
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