Impedance matching for analog audio from aircraft (high impedance) to USB audio IC
I designed a full duplex headset for 4 users using throat-microphone with squelch, AGC and headset for wind-positive pressurized air suits in the 70's for low level nuclear service in maintenance of 2ndary heat exchangers.  These were all conducted on a shared single wire pair without echoes for excess sidetone.

I  have left out a few details on sidetone cancellation, but characterizing the coughs , pops and noise from the audio, is a matter of spectrum analysis to detect the best SNR trigger that begins with true speech. A cough is noise and a throat mic has very insensitive to medium and high frequency  yet very sensitive to low frequency such as a cough.  So detecting bass impulse noise like a pop or cough is good for detection, but then use a mid-range bandpass filter to attenuate that noise.  This will improve the poor quality of throat microphones immensely.

So a precise answer without precise headset specs is impossible. 

If you get stuck "a little cough" is a good way to trigger the mic ON in exceptionally noisy environments.

Forget about impedance matching for audio electrical impedance.


** Pay attention to matching frequency spectrum for band pass, band stop and trigger matching..**


You only need to consider mic gain, speaker  damping factor and amplifying to match the signal/noise ratio spectrum.  ie match receiver theory

Forgive me on details, I designed it 45 yrs ago.