Joint optimal channel probing and transmission in collocated wireless networks

We consider a collocated wireless network where all links contend for a given channel and each link can hear others' transmissions. Due to channel fading, the link condition corresponding to a successful channel probing could be either good or bad. In the latter case, further channel probing may lead to better channel conditions, which in turn yields higher throughput. There is clearly a tradeoff between the throughput gain from better channel conditions and the cost for further channel probing. The desired tradeoff can be achieved by choosing the optimal stopping time for channel probing and the transmission rate, in the sense of maximizing the overall average throughput. Using optimal stopping theory, we show that the joint optimal channel probing and transmission (JOCPT) strategy is apure threshold policy, and interestingly, the threshold turns out to be the optimal average throughput, which is the solution to a fixed point equation. Since the optimal throughput usually cannot be obtained in closed form, we derive a lower bound and an upper bound on the optimal throughput, and devise an iterative algorithm to compute it. Finally, we use numerical examples to show that significant throughput gain can be achieved by the JOCPT strategy.