A time-domain implementation of data-independent robust broadband beamformers with lowfilter order

Robust beamforming under uncertainties in the loudspeakers directivity pattern

“…Fig. 4 compares the WNG resulting from the filters computed with Tikhonov regularization with the WNG resulting from filters computed from (18). Notice that the proposed methodology is able to guarantee an improved robustness in the whole frequency band of interest.…”

“…In the following paragraph, we compare the array responsê f tik (k) produced by filters computed from (5) adopting Tikhonov regularization, as suggested in [16], with the array responsef rls (k) produced by filters computed from (18). The coefficient for the Tikhonov regularization has been set to −20 dB.…”

“…In [17] Mabande et al present a method which incorporates a constraint for the White Noise Gain (WNG) into a leastsquares beamformer design and still leads to a convex optimization problem that can be solved directly. An extension to time-domain design has been presented in [18]. In [19] Lai states, however, that it is difficult to select an appropriate level of WNG for any given set of errors in speaker positions and/ or directivity.…”

Design of minimax robust broadband beamformers with optimized microphone positions

“…Additionally, the stopband and transition-band constraints also become convex and can be replaced by the convex formulations in (23) and (29). Consequently, the simplified optimization problem becomes minimize ∥C k δ + d k ∥ ∞ + W δ rlx (59) subject to:…”

“…The second drawback is the assumption that the array can have any length; such an assumption may not be applicable in certain applications such as in hearing aids and in-car communication systems where there are physical constraints on the array aperture size. Furthermore, as evident from earlier designs for superdirective narrowband arrays [12]- [16], broadband beamformers designed for physically-compact applications can likewise become very sensitive to errors in array imperfections and therefore robustness constraints need to be incorporated in the design [3,17]- [23]. In [17]- [21], the statistics of microphone characteristics are taken into account to derive broadband beamformers that are robust to microphone mismatches, while in [3,22,23] the white noise gain (WNG) is incorporated in the design to ensure that the beamformer is robust to spatial white noise and array imperfections.…”