On Optimal Transmission Range for Multihop Cellular Networks

In this paper analytical relationship between transmission range and the network connectivity is obtained as a function of number of nodes for CDMA based multihop cellular network (MCN). We show that for a network of n uniformly distributed nodes in a single cell of unit radius, the transmission range r should be sufficiently larger than radic(2 ln n/n-1) to achieve asymptotic full connectivity. The distribution of the nodes may not be uniform in case of mobility. In such case a mobility model dependent lower bound on transmission range is obtained. We show that for RWP model the lower bound for the nodes which lie completely inside the cell is same as the corresponding uniform node distribution case. However, for nodes on boundary the transmission range lower bound is ³radic(ln/n) which is larger than the corresponding uniform node distribution case. Our findings show that more transmission range is required at the boundary to establish better connectivity and hence a variable transmission range control mechanism is necessary. In addition to lower bound, we also propose a method to choose the optimal value of transmission range using a scheduling mechanism and ensure that the optimal value is always greater than the lower bound. Thus obtained transmission range could be used to select the transmission power of the nodes in a meaningful way and hence the nodes´ isolation could be avoided and the spectral efficiency can be increased. We demonstrate empirically, that the proposed transmission range control mechanism increases the network connectivity as well as spatial reuse of the resources.