It's possible that they are using the orbital angular momentum of photons to communicate and we would not have discovered it, because we are not yet listening for it.

If every civilization that invents a radio gets past this phase we are now very fast (as we are soon going to do) advanced civilizations don't bother to encode their messages in a way that we listen now (we look mostly for phase and amplitude encoding)

Photons carry both Orbital Angular Momentum (OAM) and Spin Angular Momentum (SAM) OAM is relatively recent discovery (1990's). They exist just not in the light beams level but also at the single-photon level (very surprising).

Detecting photons with orbital angular momentum in extended astronomical objects: application to solar observations https://www.aanda.org/articles/aa/pdf/2011/02/aa14844-10.pdf

Optical orbital angular momentum (2017) http://rsta.royalsocietypublishing.org/content/375/2087/2015...

Entanglement of the orbital angular momentum states of photons https://www.nature.com/articles/35085529