The problem of communication among nodes in an is considered, where radio power decay and interference are limiting factors. It has been shown previously that, with simple multi-hopping, the achievable total communication rate in such a network is at most @math . In this work, we study the benefit of node cooperation in conjunction with multi-hopping on the network capacity. We propose a multi-phase communication scheme, combining distributed MIMO transmission with multi-hop forwarding among clusters of nodes. We derive the network throughput of this communication scheme and determine the optimal cluster size. This provides a constructive lower bound on the network capacity. We first show that in a rate of @math can be achieved with transmission power scaling of @math , where @math is the signal path-loss exponent. We further extend this result to , where we show a rate of @math can be achieved with transmission power scaling of @math in a random network with unit node density. In particular, as @math approaches 2, only constant transmission power is required. Finally, we study a random network with density @math and show that a rate of @math is achieved and the required power scales as @math .
@cite_7: We derive upper bounds on the transport capacity of wireless networks. The bounds obtained are solely dependent on the geographic locations and power constraints of the nodes. As a result of this derivation, we are able to conclude the optimality, in the sense of scaling of transport capacity with the number of nodes, of a multihop communication strategy for a class of network topologies.
@cite_11: Wireless networks with a minimum inter-node separation distance are studied where the signal attenuation grows in magnitude as 1 ρδ with distance ρ. Two performance measures of wireless networks are analyzed. The transport capacity is the supremum of the total distance-rate products that can be supported by the network. The energy cost of information transport is the infimum of the ratio of the transmission energies used by all the nodes to the number of bit-meters of information thereby transported.If the phases of the attenuations between node pairs are uniformly and independently distributed, it is shown that the expected transport capacity is upper-bounded by a multiple of the total of the transmission powers of all the nodes, whenever δ > 2 for two-dimensional networks or δ > 5 4 for one-dimensional networks, even if all the nodes have full knowledge of all the phases, i.e., full channel state information. If all nodes have an individual power constraint, the expected transport capacity grows at most linearly in the number of nodes due to the linear growth of the total power. This establishes the best case order of expected transport capacity for these ranges of path-loss exponents since linear scaling is also feasible.If the phases of the attenuations are arbitrary, it is shown that the transport capacity is upper-bounded by a multiple of the total transmission power whenever δ > 5 2 for two-dimensional networks or δ > 3 2 for one-dimensional networks, even if all the nodes have full channel state information. This shows that there is indeed a positive energy cost which is no less than the reciprocal of the above multiplicative constant. It narrows the transition regime where the behavior is still open, since it is known that when δ < 3 2 for two-dimensional networks, or δ < 1 for one-dimensional networks, the transport capacity cannot generally be bounded by any multiple of the total transmit power.
While in simple multi-hopping, increasing the transmission power does not improve the capacity scaling, Jovicic in @cite_7 show that the upper-bound on the network transport capacity scales linearly with node power. Similar results are shown in @cite_11 . Their results motivates using the extra degree of freedom provided by the choice of transmission power. We exploit this in the proposed collaborative scheme to increase the network capacity.