That's a non-sequitur, I guess you mean if every sender sends one message per listener. I don't think it's a broad cast if it targets sole recipients per message.
Quite literally, I think, it could be modeled as a vector space in linear algebra. Each signal is in frequency space, which can be found from the fourier transform integrating the temporal space over different bandwidth channels per sender. You get N² only if the message size is proportional to N, if you will.
