at Just_me
I also had the coughing engine syndrome where the rpm would dip by itself on idle and would shake the car like a cough.
But bmw fixed it by flashing the software that controls the rpm and works great now. when i had the problem i was getting extremely poor fuel economy as a result of the mixture of petrol and air was screwed up.
ol
They done software update three times. No luck.

looks good again and it didnt cost me much (2200 swedish kronor, less than half the price BMW wanted from me)