We show an approach to beamforming an acoustic source using a diamond microphone topology. Consider the diamond array illustrated in Figure 1 below and suppose an efficient beamforming solution is desired.

Figure 1: Diamond microphone array topology for 16 microphones.

Define the angle of arrival to be the impinging angle at microphone $m_{0,1}$ as $\theta$. Suppose all received signals are summed up, such that

$X(w) = \frac{1}{16} \sum\limits_{n,r} S_{n,r} (w) = X_0 (w) H(w) + \frac{1}{16} \sum_{n,r} N_{n,r} (w)$
where $S_{n,r} (w) = X_0 e^{-jw\tau_{m_{0,1},m_{n,r}}} + N_{n,r} (w)$.

It can be easily shown that the effective filter, with respect to the pivot direction of arrival on microphone $m_{0,1}$, at the center of the top linear array, obeys

$H(w) = \frac{1}{16} + \frac{1}{16} e^{-jw \frac{2d}{c}\cos{\theta}} + \frac{2}{16} \sum\limits_{n=1}^{2} \cos{\left(wn\frac{d}{c} \sin{\theta}\right)} +\frac{2}{16} e^{-jw \frac{d}{c} \cos{\theta}}\sum\limits_{n=1}^{3} \cos{\left( w \left(n-0.5 \right)\frac{d}{c} \sin{\theta} \right)}+\frac{2}{16} e^{-jw \frac{2d}{c} \cos{\theta}} \sum\limits_{n=1}^{2} \cos{\left(wn\frac{d}{c}\sin{\theta}\right)}$

Now, suppose we have the angle of arrival already estimated, any beamforming algorithm together with filter $H(w)$ can be deployed to reduce the noise considerably.

VOCAL Technologies offers custom designed solutions for beamforming with a direction of arrival estimation, robust voice activity detector, acoustic echo cancellation and noise suppression. Our custom implementations of such systems are meant to deliver optimum performance for your specific beamforming task. Contact us today to discuss your solution!