For DAB integration into the BMW system you have a number of options
BMW solutions....
1) Replacement headunit with built-in DAB + associated antennas = Quite expensive.
2) OEM add-on DAB module + associated antennas = Cheaper but needs specialist coding, plus quite a bit of fitting as it's located in the boot.
Non-BMW solutions.... (and in no particular order)
3) FM transmitter box with separate control... https://www.ebay.co.uk/itm/264990080187?hash=item3db2a3bcbb:g:34EAAOSwyTJf5x5O
4) Dension Gateway bluetooth with add-on DAB = expensive and giving you extras you already have, found a used one here... https://www.ebay.co.uk/itm/165170384464?hash=item2674ec0e50:g:wyAAAOSwo8Rhhqd4
5) Mr12volt add-on box that plugs into the MOST fibre optic line, you must have CD Changer added to the VO list for this to work... https://www.ebay.co.uk/itm/124978208317?_trkparms=ispr%3D1&hash=item1d19481e3d:g:CAwAAOSwJrVhe8qJ&amdata=enc%3AAQAGAAACkPYe5NmHp%252B2JMhMi7yxGiTJkPrKr5t53CooMSQt2orsSxXDXcCydCuSj2Tq2S%252F3GnpON8gDf0jtVVdaE4%252Faz6JLhCT2v133loA73F8EMytMxKr2gzxB0BCUHuZn%252FfzlXYUJ8LMkFiIIKG3OXJ1Bh8X583IIs0Sgimb9NAnXORNvCohOD01QLU8Gs07oD1LI8%252BW5pWY5uugA2ptFTmn%252FYBLFsjYGpLPieOlI%252BclF0W4n03rLnCb6dxnFzVee35bMCDjxmXMD7D26MMMFbQn6JI3i2zMu6rJeRAszxcZI0daA90Nnq8OShE0SDKLxY%252BUontjlfMV4iDvCpDhhTKK6w6b0Cv25rreJ8EhygbVR9oJoTECPpQHkjBlC3aa7Oyhk2%252FGjA3okhbzGMFxG87pPxs%252BxgU7vRZRM5%252FzEJIhh6A0e6W5sOQANKU%252FzeCcK0ThgK%252BuoYG0MiByA%252B0tzWXuYgOwmZh%252FW9duwpz4ji20csz8Uyuy5mUciO0NoiIlNPFQG%252BPk11rqabEphkM0%252BTDjEVB1lzPSkRVsuyQM%252Bn1F2p9rvSTUZTDu6ef4uauJH0ResXCq9cYrsZ2OLRThuReCww58hwQYIDwUEOZLI2YABUcFzV2%252BTKyr6I20pEDoIqQBMabvh5OXsYrv%252BFBWN%252FA4JFAhAkKKmXx2h2IdjlBuq6c1TzUHDNW7KsnzZgmszxOKyI%252FodY8COSoUgGiH%252BP7IhdpZejMKasWAqj1FwQlrmRQCzSglJwQ5KOj98EcEcGnzf9QwNlvPpX4vPO4aZMglv3oC3H8x7wGfwvtxjMMADk8z%252BkCDKKgtm1yz2cU0oGBgBMPHY0JJYLeQJjqY0z%252FVyJRW1RMeJ0%252FBsH6yGej3qHLKLh%7Cclp%3A2334524%7Ctkp%3ABFBMyrKtuKBf
6) Fistune add-on box, again into the MOST line so same as above... https://www.ebay.co.uk/itm/263957440375?hash=item3d7516e777:g:WkAAAOSw1Ndbqkuz
7) Autodab box, now this is exactly the same as what BMW offered as a dealer fit option. They do come up from time to time used... https://www.ebay.co.uk/itm/360557371399?hash=item53f2e4e007:g:k6YAAOSwnVZasW0X
8) Another Autodab product, this time it uses an app on your phone for control but not data usage... https://www.ebay.co.uk/itm/381494395017?hash=item58d2d68089:g:O9AAAOSwSdZWcr22
9) Another Autodab item, this time with a control and display screen... https://www.ebay.co.uk/itm/381987979302?hash=item58f0420026:g:wVoAAOSw4A5YuCQK
10) The final option is installing an MMI box into your iDrive system. This then connect with your phone to give you Apple CarPlay (for iPhones) or Android Auto (for Android phones). You then simply use one of the available radio apps for clear digital radio, this is dependent on phone signal, but then DAB is dependent on a digital radio signal. Obviously you get all of the benefits of the phone integration with this option for navigation and music as well.
Hope that helps
