How about as modulated neutrino or gravitational wave emissions. These would have the advantage of being essentially immune to interference by intervening matter, but are very difficult to generate or detect with current technology.
While that could be a possibility, the point was that they may use a physics which we know nothing about as the basis of their communications. It is also a possibility that our EM based communications are in a decided minority of possible choices.
Had Maxwell's other 196 quaternions been pursued, among the possibilities described are free energy, instant communications and physical travel between any two points anywhere at any distance... what the present day world would look like would be entirely different.
But since what they describe is impossible, they must be dismissed unfollowed...
We live in a world described by machines, but what if aliens live in worlds described by devices? You see the disparity here? We cannot comprehend what they are doing because we cannot ‘see’ their ‘technology’ -— and so cannot hear their communications.
We are looking in the wrong places, but are unable to cross the line to look in the right places, since we have defined those places as impossible.