[fsmv]

This idea was featured in The Three Body Problem trilogy.

The problem is modulating the signal. The only way is to move large masses quickly.

[alfiedotwtf]

I'm thinking you could also create gravity waves by annihilating matter and then creating matter over and over. If you could get a bit of that wave to reflect back to you and then sync your creation/annihilation, you could build a huge wave over time