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Mathematical Problems in Engineering
Volume 2017, Article ID 5124059, 10 pages
Research Article

Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization

1School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
2Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing 210044, China

Correspondence should be addressed to Guo Ye-Cai; moc.361@iacey-oug

Received 10 April 2017; Accepted 5 July 2017; Published 30 August 2017

Academic Editor: Raffaele Solimene

Copyright © 2017 Guo Ye-Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program) problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.