  The performance of a relay-based cellular network is greatly affected by the
relay location within a cell. Existing results for optimal relay placement do
not reflect how the radio propagation environment and choice of the coding
scheme can impact system performance. In this paper, we analyze the impact on
relaying performance of node distances, relay height and line-of-sight
conditions for both uplink and downlink transmissions, using several relay
coding schemes. Our first objective is to propose a geometrical model for
energy-efficient relay placement that requires only a small number of
characteristic distances. Our second objective is to estimate the maximum cell
coverage of a relay-aided cell given power constraints, and conversely, the
averaged energy consumption given a cell radius. We show that the practical
full decode-forward scheme performs close to the energy-optimized partial
decode-forward scheme when the relay is ideally located. However, away from
this optimum relay location, performance rapidly degrades and more advanced
coding scheme, such as partial decode-forward, is needed to maintain good
performance and allow more freedom in the relay placement. Finally, we define a
trade-off between cell coverage and energy efficiency, and show that there
exists a relay location for which increasing the cell coverage has a minimal
impact on the average energy consumed per unit area.
