  By relying on a wireless backhaul link, relay stations enhance the
performance of cellular networks at low infrastructure cost, but at the same
time, they can aggravate the interference issue. In this paper, we analyze for
several relay coding schemes the maximum energy gain provided by a relay,
taking into account the additional relay-generated interference to neighboring
cells. First, we define spatial areas for relaying efficiency in log-normal
shadowing environments and propose three easily-computable and tractable
models. These models allow the prediction of 1) the probability of
energy-efficient relaying, 2) the spatial distribution of energy consumption
within a cell and 3) the average interference generated by relays. Second, we
define a new performance metric that jointly captures both aspects of energy
and interference, and characterize the optimal number and location of relays.
These results are obtainable with significantly lower complexity and execution
time when applying the proposed models as compared to system simulations.We
highlight that energy-efficient relay deployment does not necessarily lead to
interference reduction and conversely, an interference-aware deployment is
suboptimal in the energy consumption. We then propose a map showing the optimal
utilization of relay coding schemes across a cell. This map combines two-hop
relaying and energy-optimized partial decode-forward as a function of their
respective circuitry consumption. Such a combination not only alleviates the
interference issue, but also leads to a reduction in the number of relays
required for the same performance.
