  Recent studies on MAC scheduling have shown that carrier sense multiple
access (CSMA) algo- rithms can be throughput optimal for arbitrary wireless
network topology. However, these results are highly sensitive to the underlying
assumption on 'static' or 'fixed' system conditions. For example, if channel
conditions are time-varying, it is unclear how each node can adjust its CSMA
parameters, so-called backoff and channel holding times, using its local
channel information for the desired high performance. In this paper, we study
'channel-aware' CSMA (A-CSMA) algorithms in time-varying channels, where they
adjust their parameters as some function of the current channel capacity.
First, we show that the achievable rate region of A-CSMA equals to the maximum
rate region if and only if the function is exponential. Furthermore, given an
exponential function in A-CSMA, we design updating rules for their parameters,
which achieve throughput optimality for an arbitrary wireless network topology.
They are the first CSMA algorithms in the literature which are proved to be
throughput optimal under time-varying channels. Moreover, we also consider the
case when back-off rates of A- CSMA are highly restricted compared to the speed
of channel variations, and characterize the throughput performance of A-CSMA in
terms of the underlying wireless network topology. Our results not only guide a
high-performance design on MAC scheduling under highly time-varying scenarios,
but also provide new insights on the performance of CSMA algorithms in relation
to their backoff rates and the network topology.
