  Distributed opportunistic scheduling is studied for wireless ad-hoc networks,
where many links contend for one channel using random access. In such networks,
distributed opportunistic scheduling (DOS) involves a process of joint channel
probing and distributed scheduling. It has been shown that under perfect
channel estimation, the optimal DOS for maximizing the network throughput is a
pure threshold policy. In this paper, this formalism is generalized to explore
DOS under noisy channel estimation, where the transmission rate needs to be
backed off from the estimated rate to reduce the outage. It is shown that the
optimal scheduling policy remains to be threshold-based, and that the rate
threshold turns out to be a function of the variance of the estimation error
and be a functional of the backoff rate function. Since the optimal backoff
rate is intractable, a suboptimal linear backoff scheme that backs off the
estimated signal-to-noise ratio (SNR) and hence the rate is proposed. The
corresponding optimal backoff ratio and rate threshold can be obtained via an
iterative algorithm. Finally, simulation results are provided to illustrate the
tradeoff caused by increasing training time to improve channel estimation at
the cost of probing efficiency.
