Microphone Array Beamforming and Endfire Array (Part 3)

Note that the signal response at 90° is 6 dB lower than the signal response at 0°, and that its maximum output level is at zero frequency. An equalization filter is often applied to the output of the differential beamforming algorithm to flatten the frequency response.

The frequency of null values ​​should be screened in advance so that they do not interfere with the frequencies required for testing. However, the value should not be too high, otherwise the low frequencies will be excessively attenuated beyond the expected level.

In an end-fire differential array with a single sample delay (fS = 48khz) and 7mm mic spacing, the null frequency is approximately 24.5 kHz, and with a sample delay of 6 samples and a mic spacing of 84mm, the alias frequency is 4.2 kHz. Designs typically require the null frequency to be between these two samples, so that the null frequency is not so low as to interfere with the human voice bandwidth, or so high that the low frequency response is highly attenuated. With these requirements in mind, the distance between the two mics is typically chosen to match a delay between two and four samples. Again, this is all assuming fS = 48khz. All of these calculations scale linearly with the sample rate.

High-Order End-Fire Arrays

Higher order differential array beamformers can be created by adding additional microphones to the original two. This results in more rejection of sound from the rear and sides, but of course requires a longer physical distance for the beam to form. Figure 13 shows an example of such a second order (3 mic) endfire beamformer. A second order endfire beamformer can achieve 12 dB of side attenuation with the same null at the rear of the array as shown in Figure 14. Here, the blue line is the response of the first order (2 mic) beamformer and the red line is the response of the second order beamformer.

MEMS microphones are very thin devices, there are some non-zero heights to consider in array design. The acoustic center of the MEMS microphone diaphragm is at different distances above the glottis. This distance must be considered in addition to the thickness of the PCB to which the microphones are mounted when choosing the microphone spacing. If all microphones are mounted in the same manner (same PCB, same acoustic port length), then this is not an issue.

Advanced beamforming

This application note is intended to introduce the basics of microphone beamforming, but is by no means a comprehensive overview of this area of ​​processing. It is obviously possible to use arrays with different numbers of microphones and in different configurations, and the complexity of the signal processing algorithms can go far beyond the simple algorithms described in this application note. More advanced algorithms can be used for voice tracking and beam steering, even with only a small number of microphones. The arrays covered here are all linearly spaced, but more advanced higher-order beamformers can create arrays with different spacing between each pair of microphones. This configuration changes the null and aliasing frequencies and the signal-to-noise ratio between the different microphones, potentially producing an array with less noise and a wider usable frequency response.

Compare

Table 1 gives the advantages and disadvantages of broadside arrays and endfire arrays.