What you need, SD, is an omnidirectional DAB antenna on the roof, and a masthead preamplifier.
Antenna
I had more trouble finding a suitable DAB masthead preamp, but there has to be one - doesn't there?
Of course, that will only work with a fixed tuner, not with a portable.
I had to put up an outdoor FM Yagi antenna last summer, because the FM broadcast signal at our house had deteriorated so much. It's fine again now, but I suppose the next requirement will be a masthead preamp for that