Optimal Number of Relay Nodes in Wireless Ad Hoc Networks with Non–Cooperative Accessing Schemes

We determine the optimal number of relay nodes to be used between a given source–destination pair in a wireless ad hoc network. The optimal number of relay nodes is given by the route that requires the least sum transmit power with a guaranteed pre–assigned quality of service. We propose different non–cooperative accessing schemes and compare their performance for multihop transmission in ad hoc networks. Results show that remarkable gains can be achieved by multihop transmission compared to single hop transmission with a proper choice of the accessing scheme and the relay nodes to be used. Moreover, there exists an optimal number of relay nodes that is a direct function of the adopted accessing scheme, the system parameters and the network geometry. This optimal number decreases as the required transmission rate increases which remarkably shows that multihop transmission might not be suitable for very high data rate applications.