  Recent work has shown that adaptive CSMA algorithms can achieve throughput
optimality. However, these adaptive CSMA algorithms assume a rather simplistic
model for the wireless medium. Specifically, the interference is typically
modelled by a conflict graph, and the channels are assumed to be static. In
this work, we propose a distributed and adaptive CSMA algorithm under a more
realistic signal-to-interference ratio (SIR) based interference model, with
time-varying channels. We prove that our algorithm is throughput optimal under
this generalized model. Further, we augment our proposed algorithm by using a
parallel update technique. Numerical results show that our algorithm
outperforms the conflict graph based algorithms, in terms of supportable
throughput and the rate of convergence to steady-state.
