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Below is a brief tutorial on how to remove the E91 Antenna Diversity module which corrodes through getting wet, causing radio reception and/or remote central locking problems.

1. Open the glass window and pop off the 5 plastic screw covers with a small flat screwdriver.
2. Where the 5 covers were are two T20 Torx screws, remove them.
Two grey/white clips, use thin pliers to pull the centre pins out and to remove the clips.
The centre hole just has a 10mm nut which can be removed with a 10mm socket on the end of a bar.
[pic 1]

3. Close the glass window as the spoiler will now be loose.
4. Pull the spoiler down and then lift it away from the window.
5. Only the brake light wire from the spoiler and the water pipe for the rear window washer jet will keep the spoiler attached.
6. Remove the T20 Torx screws from the cover where the wires go in to, this will reveal the Diversity module.
[pic 2]

7. Below is a picture of the Diversity module that controls the radio antenna.
It should have numbers such as 6520-6934846-06.
8. To remove it simply unplug all connectors and unscrew the two 8mm nuts.
[pic 3]

9. Dry the whole thing out, try to remove the corrosion (perhaps with a dry toothbrush) and hope it works. Failing that, a replacement will cost around £200 from a main dealer.

n.b. When refitting a new one, run a bead of silocone around the top cover to seal it from the rain next time as BMW didn't seem to have done a good job sealing the ones on the E91 & E61.