How Microphone Arrays Detect and Cancel Noise
Arrays filter by direction instead of frequency, using arrival time differences. Here is how beamforming works and why it made ANC calls usable.
A microphone array uses several microphones spaced a known distance apart to work out where a sound came from, then filters by direction rather than by frequency. Because a wave reaches each microphone at slightly different times, comparing those arrivals lets the system separate a voice in front from noise at the side. That spatial filtering is what makes hands free calling and modern noise cancellation work.
A single microphone can only tell you how loud something is and what frequencies it contains. Two or more give you direction, and direction turns out to be the most useful discriminator available, because the sound you want and the sound you do not usually arrive from different places.
How direction is extracted from timing
Sound travels at roughly 1,125 feet per second. Two microphones four inches apart will therefore see a wave arriving from one side about 300 microseconds apart, and from directly ahead at the same instant.
That difference is the time difference of arrival, and it maps directly onto an angle. With two microphones you get a cone of possible directions. With three or more in a plane you get a bearing. With a three dimensional arrangement you get a full direction in space.
The spacing sets the usable frequency range, and it is a genuine constraint. Microphones spaced further apart resolve low frequencies better but produce ambiguity above the frequency where the spacing exceeds half a wavelength. This is why smart speaker arrays use six or seven microphones in a small circle rather than two microphones far apart.
Beamforming
Once the geometry is known, the array can be steered.
The simplest method, delay and sum, applies a small delay to each microphone so that sound from the chosen direction lines up in phase across all of them and adds together. Sound from every other direction arrives misaligned and partially cancels. The result is a virtual microphone pointed where you want it, formed entirely in software.
More capable systems use adaptive beamforming, which continuously adjusts the weighting applied to each microphone to place nulls in the directions the noise is coming from. Minimum variance distortionless response is the common approach: keep the target direction at unity gain and minimize everything else.
The practical result in a smart speaker is that it can hear a wake word from across a room while music plays from its own driver a few inches away. In a conference phone it means the voice of whoever is speaking is picked up while the air conditioning and the corridor are attenuated.
Why arrays matter for noise cancellation
Active noise cancellation depends entirely on the quality of its reference signal. The system generates an inverted copy of the noise, so if the reference is contaminated with the sound it is meant to preserve, it will try to cancel that too.
An array solves this by separating the two before the cancellation stage. A beam pointed outward picks up the environment as the noise reference. A beam pointed at the wearer’s mouth picks up speech to transmit. The cancellation runs on the first without touching the second.
This is the difference between early noise cancelling headsets, where your own voice sounded strangled to the person on the other end, and current ones where it does not. The phase inversion itself has not changed much, and our explainer on phase shifting in noise cancellation covers why. What improved is the array feeding it.
Arrays also help with the transparency and ambient modes on modern earbuds, since selectively passing through sound from one direction while suppressing others requires knowing which direction each sound came from.
Finding noise sources with an array
The same maths runs in reverse for diagnosis. Point an array of dozens of microphones at a machine, a building facade or a car, compute the arrival times at every element, and you can map where the sound is radiating from.
Displayed as a color map over a camera image, this is an acoustic camera, and it is standard equipment in automotive and industrial noise engineering. It answers the question that used to take a day of moving a single microphone around: which part of this thing is actually making the noise.
Resolution follows the same rules as before. Locating a 200 Hz source precisely needs a physically large array, because the wavelength is nearly six feet. High frequency sources can be pinpointed with a compact one.
Where arrays fall down
Reverberation is the main enemy. In a hard, echoey room, sound arrives at the array from every direction after bouncing, so the timing information that direction finding depends on gets smeared. A beamformer that works well in a furnished living room can perform poorly in a tiled kitchen.
Diffuse noise is the second problem. Traffic rumble entering through a wall has no single direction, so there is nothing for the array to steer away from.
Two sources on the same bearing cannot be separated by direction alone, which is why a person speaking directly behind the person you want to hear remains a hard case.
And low frequencies stay difficult, because the wavelength is long compared with any array small enough to fit in a device. This is the same limitation that caps active cancellation, arriving from a different direction.
Frequently asked questions
What does a microphone array do?
It uses the tiny differences in arrival time between several spaced microphones to determine which direction a sound came from, then filters by direction rather than by frequency. That lets a device amplify sound from one bearing while suppressing everything else, which is how smart speakers hear a wake word across a room and how conference phones pick out a speaker from background noise.
How many microphones does an array need?
Two is enough to determine a cone of possible directions, three or more in a plane gives a bearing, and consumer smart speakers typically use six or seven arranged in a small circle. More elements improve directivity and noise rejection, but the spacing matters as much as the count, since the geometry sets which frequencies can be resolved without ambiguity.
Do microphone arrays improve noise cancellation?
Substantially, by improving the reference signal the cancellation runs on. An array can separate outward facing environmental noise from the wearer’s own voice before the inversion stage, so the system cancels the environment without also cancelling the speech it is meant to transmit. This is the main reason call quality on noise cancelling headsets improved so much.
What is beamforming?
Applying a calculated delay to each microphone in an array so that sound from a chosen direction arrives in phase across all elements and reinforces, while sound from other directions arrives misaligned and partially cancels. The effect is a highly directional virtual microphone created in software, which can be steered electronically without moving anything.