Beyond the max range of an active sensor you will see nothing. It's just like dealing with radar in real life - if something is too far away, you won't get enough of a return from it for your sensor to pick up usefully. The only way to increase range is to use a larger emitter/receiver (higher HS) or use a wavelength that gets further while remaining usefully coherent (higher resolution), but that means you lose the ability to detect smaller things well.
You will want to have coverage of both kinds in your fleets - I usually mount a few large Deep Scan Arrays (5000+resolution, 2kt+) on larger ships alongside the standard AEMW units (100 resolution, 500t) that go on pretty much everything. Antimissile radars go onto dedicated PD ships. I do tend to build my ships big (100Kt+ for my line vessels), so YMMV on how big you make yours.
