  This paper investigates the location-based relay selection problem, where the
source node chooses its relay from a set of spatially deployed
decode-and-forward relays. The advantages of location-based relay selection are
the elimination of excessive relay switching rate and the feedback reduction
avoiding the requirement of having full channel state information at the source
node. For a homogeneous Poisson point process of candidate relays, we first
derive the distribution for the distance of the relay (relative to the source
and destination nodes) selected by the optimum location-based relay selection
policy. This result is independent of the functional form of the path-loss
function as long as it is a non-increasing function of the transmitter-receiver
separation. By utilizing the derived optimum relay distance distribution, we
then obtain analytical expressions for the average rate and outage probability
by considering the power-law decaying path-loss function for the no-fading and
Rayleigh fading communication scenarios. It is observed that the optimum relay
selection policy outperforms the other common selection strategies notably,
including the ones choosing the relay closest to the source, the relay closest
to the destination and the relay closest to the mid-point between source and
destination.
