Article

On the geometry of wireless network multicast in 2-D

05/2011;
Source: arXiv

ABSTRACT We provide a geometric solution to the problem of optimal relay positioning
to maximize the multicast rate for low-SNR networks. The networks we consider,
consist of a single source, multiple receivers and the only intermediate and
locatable node as the relay. We construct network the hypergraph of the system
nodes from the underlying information theoretic model of low-SNR regime that
operates using superposition coding and FDMA in conjunction (which we call the
"achievable hypergraph model"). We make the following contributions. 1) We show
that the problem of optimal relay positioning maximizing the multicast rate can
be completely decoupled from the flow optimization by noticing and exploiting
geometric properties of multicast flow. 2) All the flow maximizing the
multicast rate is sent over at most two paths, in succession. The relay
position is dependent only on one path (out of the two), irrespective of the
number of receiver nodes in the system. Subsequently, we propose simple and
efficient geometric algorithms to compute the optimal relay position. 3)
Finally, we show that in our model at the optimal relay position, the
difference between the maximized multicast rate and the cut-set bound is
minimum. We solve the problem for all (Ps,Pr) pairs of source and relay
transmit powers and the path loss exponent \alpha greater than 2.

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Keywords

achievable hypergraph model"

efficient geometric algorithms

flow maximizing

flow optimization

following contributions

geometric solution

low-SNR networks

low-SNR regime

maximized multicast rate

multicast flow

multicast rate

optimal relay position

optimal relay positioning

optimal relay positioning maximizing

path loss exponent \alpha greater

single source

superposition coding

two paths

underlying information theoretic model