adpative filtering limitations

Hi all,
I'm simulating a transmission under simulink.
Here are the characterisics.

emitter
QPSK modulation
Factor 2 oversampling

channel
Fir filter [1 0.2 1 0.2 0.3 0.5] case 1
filter [1 0.2 0.1 0.2 0.3 0.5] case 2


receiver
adaptive filtering (LMS algorithm)

In the first case my filter does estimate properly the channel
wherease in the second case i recuperate a good constellation.

My question is , are traditional adaptive filtering technics still
working when the transmission channel superimpose several path with
the same power as the main path. (case 1)

Thanks for your help!
Fabien