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Direction of arrival using uniform circular array microphones

The use of uniform circular array UCA microphones for beamforming has recently been proposed as an alternate to cascaded quadrilateral topologies. As presented in numerous literature, the direction of arrival (DOA) of the acoustic signal of interest is most times critical in any beamforming algorithm that is being used. We resolve the DOA problem for a UCA.

Consider a far field source impinging N UCA microphones as shown in Figure 1:

N UCA microphones

Figure 1: N UCA microphones

Then it can be shown that the DOA estimate between any two pairs of microphones i,j will obey

\tau_{ij} = -2d \cos{\left(\frac{(j-i)\psi}{2}\right)} \cos{\left(\arcsin\left(\frac{\sin{\left((j-i)\psi\right)}}{2 \cos{\left((j-i) \frac{\psi}{2} \right)}} \right) +\theta\right)}, j > i , \{i,j\} \in [1 N]

Any of the well known approaches such as least squares or SRP-PHAT can be used to combine all estimates between paired microphones to estimate \theta.

VOCAL Technologies offers custom designed solutions for beamforming with a 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!

VOCAL Technologies, Ltd.
520 Lee Entrance, Suite 202
Amherst New York 14228
Phone: +1-716-688-4675
Fax: +1-716-639-0713
Email: sales@vocal.com