The DAB signal is highly compressed to enable more programmes to be broadcast in the same bandwidth. DAB radios have to uncompress the signal, which takes a lot of computing power and, hence, a lot of electrical power. For this reason DAB radios are heavy on batteries. I suggest you look for one with a mains adapter.
If you play an FM radio and a DAB radio together you will find there is a serious delay (several seconds) between the two broadcasts - this represents the computing power being used to uncompress the DAB signal.