Some Analytical Results on Rate-Controlled Many-toOne Communication over Two Hops

We consider the problem of data-communication from the perimeter to the center of a circle. We present a class of transmission schedules that allow for greater energy-efficiency (as compared to direct communication) without degradation in throughput by exploiting the non-linear relationship between transmisson power and achievable rate. Some analytical results regarding the same are stated and proved. Besides, some observed trends for which we currently do not have a proof are also discussed. INTRODUCTION The many-to-one communication paradigm is extremely relevant in the emerging contexts of hybrid wireless networks as well as data gathering sensor networks. In this model of communication the point of data-convergence (base-station) becomes a bottleneck, thereby imposing a trivial upper bound of W on achievable aggregate capacity [1] where W is the maximum transmission rate possible. Some earlier work on many-to-one communication has considered hierarchical schemes wherein nodes are organized into clusters and intra-cluster communication occurs over a different channel than cluster-head to basestation (BS) communication [1], [2]. However we observe that even within the constraint of a single channel, it is possible to harness the potential for spatial re-use available in the network to obtain greater energy-efficiency while maintaining the same aggregate rate. We envisage a mechanism that exploits the non-linearity inherent in Shannon’s equation: W = B log(1+SINR), and improves on energy consumption by replacing a single high rate transmission with many spatially spread out low rate ones. We present a class of transmission schedules operating on a single channel that allow for more energy-efficient datacommunication from the perimeter to the center of a circle (as compared to direct communication) without degradation in throughput. Some analytical results regarding the same are stated and proved. We also discuss some observed numerical trends. RELATED WORK Upper bounds on the capacity of wireless networks have been proved first in [3] for ad-hoc networks, and thereafter in [4] and [5] for hybrid networks. In the context of networks where data converges at a single point, some analytical results based on the Protocol Model [3] have been reported in [1]. The trivial upper bound of W on aggregate capacity in a many-to-one network, where W is the maximum transmission rate possible, has been stated and proved. It has been shown that while W may be achievable in an arbitrary network with controlled node placement (when certain conditions on guard zone size are met), it is not achievable with high probability in a random network. However, Θ(W ) aggregate capacity is proved to be achievable with high probability in a random network. Work on energy-efficient communication, as in [6], has explored the energy gains obtainable by communicating via relays rather than directly. They develop a mathematical formulation for the relay region (if the receiver is located within this region relaying is certain to yield energy gains) while attempting to transmit information from one point to another. However, this work does not address the impact of relaying on capacity. It is a generally known fact that in the case of one-to-one communication between two points using a fixed rate, introduction of relays i.e. multiple hops reduces the attainable throughput for this single communication, as all links may not be simultaneously active. It is therefore relevant to consider capacity and energy in conjunction. This research is supported in part by Motorola, Inc.