  In this paper, we analyze the outage performance of different multicarrier
relay selection schemes for two-hop orthogonal frequency-division multiplexing
(OFDM) systems in a Poisson field of relays. In particular, special emphasis is
placed on decode-and-forward (DF) relay systems, equipped with bulk and
per-subcarrier selection schemes, respectively. The exact expressions for
outage probability are derived in integrals for general cases. In addition,
asymptotic expressions for outage probability in the high signal-to-noise ratio
(SNR) region in the finite circle relay distribution region are determined in
closed forms for both relay selection schemes. Also, the outage probabilities
for free space in the infinite relay distribution region are derived in closed
forms. Meanwhile, a series of important properties related to cooperative
systems in random networks are investigated, including diversity, outage
probability ratio of two selection schemes and optimization of the number of
subcarriers in terms of system throughput. All analysis is numerically verified
by simulations. Finally, a framework for analyzing the outage performance of
OFDM systems with spatially random relays is constructed, which can be easily
modified to analyze other similar cases with different forwarding protocols,
location distributions and/or channel conditions.
