Definately 2 channel adc usb soundcard

Tested and x2 channel

I have a 2 channel DelaySum beamformer here

It works but the FFT could likely do with porting to a Neon based FFT and approx cut load by x2
If have it set for x2 channels as the only reliable high quality card is the above with the 2 mic Pi hats being OK and can also be used.

Its the DOA GGC-PHAT that causes all the load and my target has been a Pi02W satelite which will run it happily the actual delay sum is no load in comparison as you just sum the samples by the delay calculated by the TDOA.
I do have a design for a 4 mic that only use 2x TDOA but because of the state of drivers and cards with no audio output also I have not bothered.

There is still the hugely important sync to KW so the beamformer locks on to a command sentence and been wondering dbus but think to much latency and likely file descriptor passing between unix processes through a Unix Socket is a much better idea to link the 2.

The beamformer is not a be all and end all but by beamforming to our ears the result is minimal but for recognition because of the deverb & de-echo effect it can greatly enhance recognition.