If it's a single channel white noise generator, then a coherent two-channel microphone setup (using hidden bugs or laser microphones) would already be sufficient to perform source-separation [1] between a single speaker and the white noise. I guess this is why you usually use multi-channel white noise generators, e.g. [2].

[1] https://en.wikipedia.org/wiki/Signal_separation

[2] https://www.spygadgets.com/white-noise-generator-with-6-tran...