Minimum Energy-per-Bit Wireless Multi-Hop Networks with Spatial Reuse

In this paper, a tradeoff between the total energy consumption-
per-bit and the end-to-end rate under spatial reuse in
wireless multi-hop network is developed and analyzed. The endto-
end rate of the network is the number of information bits transmitted
(end-to-end) per channel use by any node in the network
that is forwarding the data. In order to increase the bandwidth
efficiency, spatial reuse is considered whereby simultaneous relay
transmissions are allowed provided there is a minimum separation
between such transmitters. The total energy consumption-per-bit
includes the energy transmitted and the energy consumed by the
receiver to process (demodulate and decoder) the received signal.
The total energy consumption-per-bit is normalized by the distance
between a source-destination pair in order to be consistent
with a direct (single-hop) communication network. Lower bounds
on this energy-bandwidth tradeoff are analyzed using convex optimization
methods. For a given location of relays, it is shown that
the total energy consumption-per-bit is minimized by optimally
selecting the end-to-end rate. It is also demonstrated that spatial
reuse can improve the bandwidth efficiency for a given total energy
consumption-per-bit. However, at the rate that minimizes the total
energy consumption-per-bit, spatial reuse does not provide lower
energy consumption-per-bit compared to the case without spatial
reuse. This is because spatial reuse requires more receiver energy
consumption at a given end-to-end rate. Such degraded energy efficiency
can be compensated by varying the minimum separation of
hops between simultaneous transmitters. In the case of equi-spaced
relays, analytical results for the energy-bandwidth tradeoff are
provided and it is shown that the minimum energy consumptionper-
bit decreases linearly with the end-to-end distance.