Publication
We consider a cross-layer design of wireless ad-hoc networks. Traditional networking approaches optimize separately each of the three layers: physical layer, medium access and routing. This may lead to largely suboptimal network designs. In this work, we propose a jointly optimal design of the three layers, and we show a significant performance improvement over the conventional approach. In the first part of this thesis, our goal is to select appropriate performance metrics for the joint optimization problem. To that respect, we analyze several existing rate-maximization performance metrics for wireless ad-hoc networks: maximizing the sum of rates, max-min fairness and proportional fairness. We first show with several examples that it is not clear if and how max-min fairness can be defined on each one of the examples. We give a formal proof that the max-min fair rate allocation exists on a large class of sets of feasible rates, among which are the feasible-rate sets of all known ad-hoc networking examples. We also give a centralized algorithm to compute the max-min fair allocation whenever it exists. Next, we compare the three metrics for ad-hoc scenarios in terms of efficiency and fairness. We prove that, similar to wired networking,maximizing the sum of rates leads to gross unfairness and starvation of all but the flows with the best channel conditions. We also prove that, contrary to wired networking, max-min fairness yields all flows having the same rate, thus causing large inefficiencies. These findings offer theoretical explanations to the inefficiency and unfairness phenomena previously observed in the contexts of 802.11 and UWB networks. Finally, we show that proportional fairness achieves a good trade-off between efficiency and fairness and is a good candidate for a rate-based performance metric in wireless ad-hoc settings. Having shown that the proportional fairness is an appropriate optimization objective for our problem, in the second part of the thesis we consider a joint optimization of rates, transmission powers, medium access (scheduling) and routing, where the goal of the optimization is to achieve proportional fairness. We first analyze networks built on physical layers that have a rate which is a linear function of SNR at the receiver (such as UWB or low-gain CDMA systems). We find that the optimal solution is characterized by the following principles: (1)Whenever a node transmits, it has to transmit with the maximum power; otherwise it has to remain silent (0 - PMAX power control). (2) Whenever data is being sent over a link, it is optimal to have an exclusion region around the destination, in which all nodes remain silent during transmission, whereas nodes outside of this region can transmit in parallel, regardless of the interference they produce at the destination. (3) When a source transmits, it adapts its transmission rate according to the level of interference at the destination due to sources transmitting in parallel. (