Tight Bound for the Mean Node Degree in Ad Hoc Networks with pportunistic Communications

Many work has been devoted to evaluating the connectivity of ad hoc networks. In most of these works, radio links are assumed ideal, i.e. with no transmission errors. To fulfill this assumption, the reception threshold is assumed high enough so that considering valid only the radio links having a successful transmission probability above a target value. All unreliable links are thus dismissed making the work of routing protocols easier because the links are all stable. This approach proves to be suboptimal in terms of either capacity or energy reduction since long hops -albeit unreliable- may contribute significantly to the overall connectivity. An open issue is then to quantify how much the connectivity could be improved by taking unreliable links into account. This issue is addressed in this paper in the case of having block-fading channels. A tight bound is analytically derived for the mean node degree from a cross- layer point of view. Modulation, packet size, power detection level and link reliability are all considered in the proposed formulation.