parallel acoustic paths must be minimized
it just won't work well to try to solve it at the helmet speaker level, its not impossible
You seem to be ignoring frequency. I am sure we could get deep into the details and leave everyone else bored.
What I said is accurate. What you said in the quote above, is accurate at shorter wavelengths
; I agree with you at higher frequencies.
Perhaps my previous post was unclear. My apologies for boring everyone.
At 20 Hz for example, the distance between a helmet speaker + cancellation mic setup, and the ear drum, is not going to make much difference. Multiple paths are nearly irrelevant. Active noise cancellation at lower frequencies would not be difficult to do with helmet speakers. Active noise cancellation inside automobiles, buildings, etc work this way--there are no microphones near your ears, and the paths are nearly omnidirectional.
At shorter wavelengths, such as wavelengths shorter than the distance between the helmet speaker and the eardum, yes, it becomes much more difficult. Somewhere around 1 kHz or so, it is going to become increasingly challenging. With multiple paths, at higher frequencies . . . it is like trying to invert chaos.
It is MUCH easier to block higher frequencies by absorption means, like ear plugs, padding, panels, noise control, etc.
It is MUCH easier to mitigate lower frequencies with active cancellation.
You sound like you dabble in electrical engineering, so let me try this metaphor: at lower frequencies, active noise cancellation operates in a "far field" like model; there are no significant multiple paths.