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On the simultaneous design of broadband beamformer filters and configuration

  • *Corresponding author: Ka-Fai Cedric Yiu

    *Corresponding author: Ka-Fai Cedric Yiu

This paper is supported by RGC Grant PolyU. 152200/14E and 152245/18E, and PolyU grant G-UAHF. The first author is also supported by National Natural Science Foundation of China 12171168, Natural Science Foundation of Guangdong Province 2021A1515010368 and 2020A1515010489, the Foundation of Department of Education of Guangdong Province 2020ZDZX3004

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  • For signal enhancement, beamforming remains to be an essential technique for many applications. In the design process, the microphone locations are prescribed and the signal from a target location is being enhanced. While the filter coefficients can be readily optimized, it is found that the signal enhancement capability depends significantly on the array configuration. Therefore, it is advantageous to consider both filters and microphone positions as design variables. In this paper, this problem is addressed. We formulate the beamformer design problem as a non-linear least square problem and propose Gauss-Newton algorithm to update both filters and configuration simultaneously during iterations. We illustrate by several designs to demonstrate the effectiveness of the proposed method.

    Mathematics Subject Classification: Primary: 90C30, 65K05; Secondary: 68U99.


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  • Figure 1.  The structure of a near-field beamformer

    Figure 2.   

    Figure 3.  Initial array configuration (Ex1)

    Figure 4.  Final array configuration (Ex1)

    Figure 5.  Convergence history of the algorithm

    Figure 6.  Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 7 $ (Ex1) with considering microphone positions

    Figure 7.  Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 7 $ (Ex1) without considering microphone positions

    Figure 8.  Initial array configuration (Ex2)

    Figure 9.  Final array configuration (Ex2)

    Figure 10.  Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 26 $ (Ex2) with considering microphone positions

    Figure 11.  Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 26 $ (Ex2) without considering microphone positions

    Table 1.  Comparison of the running times (Ex1)

    Gauss-Newton Matlab Nonlinear LS
    running time $ 8.7995 $(s) $ 1073.2 $(s)
     | Show Table
    DownLoad: CSV
  • [1] M. Brandstein and D. Ward, Microphone Arrays: Signal Processing Techniques and Applications, Springer Verlag, Berlin, 2001.
    [2] S. C. Chan and H. Chen, Uniform concentric circular arrays with frequency-invariant characteristics-theory, design, adaptive beamforming and DOA estimation, IEEE Trans. Signal Processing, 55 (2007), 165-177.  doi: 10.1109/TSP.2006.882109.
    [3] H. H. DamA. Cantoni and B. Li, A fast low complexity method for optimal zero-forcing beamformer MU-MIMO system, IEEE Signal Processing Letters, 22 (2015), 1443-1447. 
    [4] Z. G. FengK. F. C. Yiu and S. Nordholm, A two-stage method for the design of near-field broadband beamformer, IEEE Trans. on Signal Processing, 59 (2011), 3647-3656.  doi: 10.1109/TSP.2011.2133490.
    [5] Z. G. FengK. F. C. Yiu and S. Nordholm, Placement design of microphone arrays in near-field broadband beamformers, IEEE Trans. on Signal processing, 60 (2012), 1195-1204.  doi: 10.1109/TSP.2011.2178491.
    [6] S. GannotD. Burshtein and E. Weinstein, Signal enhancement using beamforming and nonstationarity with applications to speech, IIEEE Trans. Signal Processing, 49 (2001), 1614-1626. 
    [7] W. Kellermann, Beamforming for Speech and Audio Signals, in Handbook of Signal Processing in Acoustics (eds. D. Havelock, S. Kuwano, and M. Vorlander), Springer, New York, 2008.
    [8] R. KennedyD. Ward and T. Abhayapala, Nearfield beamforming using radial reciprocity, IEEE Trans. Signal Processing, 47 (1999), 33-40. 
    [9] H. Krim and M. Viberg, Two decades of array signal processing research: The parametric approach, IEEE Signal Processing Magazine, 13 (1996), 67-94. 
    [10] C. C. LaiS. Nordholm and Y. H. Leung, Design of steerable spherical broadband beamformers with flexible sensor configurations, IEEE Transactions on Audio, Speech and Language Processing, 21 (2013), 427-438. 
    [11] B. LauY. H. LeungK. L. Teo and V. Sreeram, Minimax filters for microphone arrays, IEEE Transactions on Circuits and Systems Ⅱ, 46 (1999), 1522-1525. 
    [12] B. LiC. WuH. H. DamA. Cantoni and K. L. Teo, A parallel low complexity zero-forcing beamformer design for multiuser MIMO systems via a regularized dual decomposition method, IEEE Transactions on Signal Processing, 63 (2015), 4179-4190.  doi: 10.1109/TSP.2015.2437846.
    [13] B. LiH. H. DamA. Cantoni and K. L. Teo, A first-order optimal zero-forcing beamformer design for multiuser MIMO systems via a regularized dual accelerated gradient method, IEEE Communications Letters, 19 (2015), 195-198.  doi: 10.1109/TSP.2015.2437846.
    [14] B. LiY. RongJ. Sun and K. L. Teo, A distributionally robust minimum variance beamformer design, IEEE Signal Processing Letters, 25 (2018), 105-109. 
    [15] B. LiY. RongJ. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, IEEE Transactions on Wireless Communications, 16 (2017), 464-474. 
    [16] J. Li and  P. StoicaRobust Adaptive Beamforming, John Wiley, Inc., Hoboken, New Jersey, 2006. 
    [17] Z. B. Li and K. F. C. Yiu, Beamformer configuration design in reverberant environments, Engineering Applications of Artificial Intelligence, 47 (2016), 81-87. 
    [18] Z. B. LiK. F. C. Yiu and Z. G. Feng, A hybrid descent method with genetic algorithm for microphone array placement design, Applied Soft Computing, 13 (2013), 1486-1490. 
    [19] Y. C. Lim and Y. Lian, The optimum design of one and two-dimensional FIR filters using the frequency response masking technique, IEEE Trans. Cir. and Sys. Ⅱ, 40 (1993), 88-95. 
    [20] S. Nordholm and Y. H. Leung, Performance limits of the broadband generalized sidelobe cancelling structure in an isotropic noise field, J. of the Acoustical Soc. of America, 107 (2000), 1057-1060. 
    [21] S. NordholmV. RehbockK. L. Teo and S. Nordebo, Chebyshev approximation for the design of broadband beamformers in the near field, IEEE Transactions on Circuits and Systems Ⅱ, 45 (1998), 141-143. 
    [22] J. Ryan and R. Goubran, Array optimization applied in the near field of a microphone array, IEEE Transactions on Speech Audio Processing, 8 (2000), 173-178. 
    [23] K. F. C. YiuX. Q. YangS. Nordholm and K. L. Teo, Near-field broadband beamformer design via multidimensional semi-infinite linear programming techniques, IEEE Transactions on Speech and Audio Processing, 11 (2003), 725-732. 
    [24] K. F. C. YiuM. J. Gao and Z. G. Feng, Design of near-field broadband beamformer using semi-definite programming, Int. J. Innov. Comput. Inform. Con., 8 (2012), 3755-3768. 
    [25] B. Van Veen and K. Buckley, Beamforming: a versatile approach to spatial filtering, IEEE ASSP Magazine, 5 (1988), 4-24. 
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