The Optimal Packet Duration of ALOHA and CSMA in Ad Hoc Wireless Networks
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In this thesis the optimal transmission rate in ad hoc wireless networks is analyzed. The performance metric used in the analysis is probability of outage. In our system model, users/packets arrive randomly in space and time according to a Poisson point process, and are thereby transmitted to their intended destinations using either ALOHA or CSMA as the MAC protocol. Our model is based on an SINR requirement, i.e., the received SINR must be above some predetermined threshold value, for the whole duration of a packet, in order for the transmission to be considered successful. If this is not the case an outage has occurred. In order to analyze how the transmission rate affects the probability of outage, we assume packets of K bits, and let the packet duration, T, vary. The nodes in the network then transmit packets with a requested transmission rate of Rreq=K/T bits per second. We incorporate transmission rate into already existing lower bounds on the probability of outage of ALOHA and CSMA, and use these expressions to find the optimal packet duration that minimizes the probability of outage. For the ALOHA protocol, we derive an analytic expression for the optimal spectral efficiency of the network as a function of path loss, which is used to find the optimal packet duration Topt . For the CSMA protocol, the optimal packet duration is observed through simulations. We find that in order to minimize the probability of outage in our network, we should choose our system parameters such that our requested transmission rate divided by system bandwidth is equal to the optimal spectral efficiency of our network.