How Roomba Omnidirectional IR receiver work?

GoForSmoke:
Best way is probably with a ring of IR sensors.

And that is pretty much true.

I haven't looked at it (a Roomba), but a dome sensor usually uses a half-donut lens which has a smooth "dimple" or "crater" in the centre which uses total internal reflection to funnel light from any (more-or-less horizontal) direction down to the actual sensor.

But practically, just use four sensors pointing outwards to the compass points. Use diodes if necessary to "OR" the outputs.