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The existing blind beamforming methods are effective only under the condition that the source signals have some special statistical or structural characteristics. Additionally, the structure of cascade model is complicated and the stability of parallel model is poor when dealing with multi-target signals. To address these problems, a novel blind beamforming algorithm for multi-target signals based on time-frequency (TF) analysis is proposed in this paper. The received array signals are first transformed into time-frequency domain by using quadratic time-frequency distributions (TFDs). Then, the single-source auto-term TF points which show energy concentration at a single signal are extracted through three operations:(i) removing noise points by setting a reasonable threshold, (ii) separating auto-term TF points from cross-term points, and (iii) selecting the single-source auto-term TF points from the auto-term ones. Moreover, these single-source auto-term TF points are classified by the principal eigenvector of their spatial time-frequency distribution matrixes. For each class of TF points, the uncertain set of signal steering vector is given, whose radius is defined as the ultimate range between the center and the elements in the class. Within the uncertain set, an optimization algorithm is provided to get the optimal estimation of the signal steering vector. Finally, the blind beamforming for multi-target signals is achieved based on the Capon method, which can enhance the desired signals and suppress the noise and interference signals. In addition, the influence of parameters selection, the clustering method of unknown source number, and the computational complexity of the proposed algorithm are analyzed. The proposed algorithm can achieve parallel output of multi-target signals under the condition that the array manifold and the direction of arrival (DOA) are unknown. Also, the complex iterative solving processing may be avoided and special limitations on signal characteristics are unnecessary. As a result, it has wide applicability and superior stability compared with the existing blind beamforming methods. Simulations illustrate that the proposed algorithm can well separate multi-target signals which are TF-nondisjoint to a certain extent. It can achieve a higher output signal to interference plus noise ratio (SINR) compared with the constant modulus algorithm (CMA), the independent component analysis (ICA) algorithm, and the joint approximate diagolization of eigenmald (JADE) algorithm. Furthermore, the output performance of the proposed algorithm is close to the optimal Capon beamformer.
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Keywords:
- time-frequency analysis /
- blind beamforming /
- optimal estimation of steering vector /
- Capon
[1] Xiao X, Xu L, Li Q W 2013 Chin. Phys. B 22 094101
[2] Wang Y, Fan W F, Fan Z, Liang G L 2014 Acta Phys. Sin. 63 154303 (in Chinese) [王燕, 吴文峰, 范展, 梁国龙 2014 63 154303]
[3] Xiao X, Song H, Wang L, Wang Z J, Lu H 2014 Acta Phys. Sin 63 194102 (in Chinese) [肖夏, 宋航, 王梁, 王宗杰, 路红 2014 63 194102]
[4] Treichler J R, Agee B G 1983 IEEE Trans. Acoust Speech. Sin 51 1702
[5] Agee B G 1986 Proc of ICASSP Tokyo, December, 1986 p1921
[6] Wong Q, Wong K M 1996 IEEE Trans. Sign. Process 44 2757
[7] Lee J H, Huang C C 2009 IEEE Antenn. Wirel. Pr 8 2009
[8] Ding Z, Nguyen T 2000 IEEE Trans. Sign. Process 48 1587
[9] You R Y, Chen Z 2005 Chin. Phys. 14 2176
[10] Lu S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[11] Tabbal A M, Merel P, Chaker M 1989 IEEE Millitary Commun. Cofn Boston, Oct, 1989 p0340
[12] Guo Y, Fang D W, Liang V H, Wang N Q 2002 Acta Elec. Sin. 30 831 (in Chinese) [郭艳, 方大纲, 梁昌洪, 汪宁清 2002 电子学报 30 831]
[13] Li H S, Zhao J W, Chen H W, Wang F, Guo Y C 2003 J. Electron. Information Technol. 25 1180 (in Chinese) [李洪升, 赵俊渭, 陈华伟, 王峰, 郭业才 2003 电子与信息学报 25 1180]
[14] Jafari M G, Wang W, Chambers J A, Hoya T, Cichocki A 2006 IEEE Trans. Sign. Process 54 1028
[15] Cardoso J F, Souloumiac A 1989 Proceedings of International Conference on Radar Signal Processing December, 1993 p362
[16] An Y, Du Z H, Xu K X 2013 Acta Phys. Sin 62 174208 (in Chinese) [安颖, 杜振辉, 徐可欣 2013 62 174208]
[17] Aissa-El-Bey A, Linh-Trung N, Abed-Meraim K, Belouchrani A, Grenier Y 2007 IEEE Trans. Sign. Process 55 897
[18] Xu G L, Wang X T, Xu X G 2010 Chin. Phys. B 19 014203
[19] Xie S L, Yang L, Yang J M, Zhou G X, Xi Y 2012 IEEE Trans. Neural Networks Lerning Syst 23 306
[20] Li J, Stoica P, Fan Z, Wang Z S 2003 IEEE Trans. Sign. Process 51 1702
[21] Luo Y H, Wang W W, Chambers J A, Lambotharan S, Proudler I 2006 IEEE Trans. Sign. Process 54 2198
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[1] Xiao X, Xu L, Li Q W 2013 Chin. Phys. B 22 094101
[2] Wang Y, Fan W F, Fan Z, Liang G L 2014 Acta Phys. Sin. 63 154303 (in Chinese) [王燕, 吴文峰, 范展, 梁国龙 2014 63 154303]
[3] Xiao X, Song H, Wang L, Wang Z J, Lu H 2014 Acta Phys. Sin 63 194102 (in Chinese) [肖夏, 宋航, 王梁, 王宗杰, 路红 2014 63 194102]
[4] Treichler J R, Agee B G 1983 IEEE Trans. Acoust Speech. Sin 51 1702
[5] Agee B G 1986 Proc of ICASSP Tokyo, December, 1986 p1921
[6] Wong Q, Wong K M 1996 IEEE Trans. Sign. Process 44 2757
[7] Lee J H, Huang C C 2009 IEEE Antenn. Wirel. Pr 8 2009
[8] Ding Z, Nguyen T 2000 IEEE Trans. Sign. Process 48 1587
[9] You R Y, Chen Z 2005 Chin. Phys. 14 2176
[10] Lu S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[11] Tabbal A M, Merel P, Chaker M 1989 IEEE Millitary Commun. Cofn Boston, Oct, 1989 p0340
[12] Guo Y, Fang D W, Liang V H, Wang N Q 2002 Acta Elec. Sin. 30 831 (in Chinese) [郭艳, 方大纲, 梁昌洪, 汪宁清 2002 电子学报 30 831]
[13] Li H S, Zhao J W, Chen H W, Wang F, Guo Y C 2003 J. Electron. Information Technol. 25 1180 (in Chinese) [李洪升, 赵俊渭, 陈华伟, 王峰, 郭业才 2003 电子与信息学报 25 1180]
[14] Jafari M G, Wang W, Chambers J A, Hoya T, Cichocki A 2006 IEEE Trans. Sign. Process 54 1028
[15] Cardoso J F, Souloumiac A 1989 Proceedings of International Conference on Radar Signal Processing December, 1993 p362
[16] An Y, Du Z H, Xu K X 2013 Acta Phys. Sin 62 174208 (in Chinese) [安颖, 杜振辉, 徐可欣 2013 62 174208]
[17] Aissa-El-Bey A, Linh-Trung N, Abed-Meraim K, Belouchrani A, Grenier Y 2007 IEEE Trans. Sign. Process 55 897
[18] Xu G L, Wang X T, Xu X G 2010 Chin. Phys. B 19 014203
[19] Xie S L, Yang L, Yang J M, Zhou G X, Xi Y 2012 IEEE Trans. Neural Networks Lerning Syst 23 306
[20] Li J, Stoica P, Fan Z, Wang Z S 2003 IEEE Trans. Sign. Process 51 1702
[21] Luo Y H, Wang W W, Chambers J A, Lambotharan S, Proudler I 2006 IEEE Trans. Sign. Process 54 2198
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