Should we add a floor rug or not?

I would love some advice from the Houzz community. I have brought home several rugs to try to define the lounge area, but not one has seemed right. I have tried ultra modern, contemporary and abstract. There have been pale coloured ones and others with bright patterns, but as we live a fair way from the shops, this is all getting very frustrating! I think the rug needs to be 3m x 2m. In this photo we have removed the glass coffee table to show the area more clearly. Can anyone suggest the right style to tie our open plan living space together? Any suggestions would be welcomed. As you can see, the ceiling is very high and the room gets a lot of light.