  A new, fair relay selection scheme is proposed for a dual-hop
decode-and-forward network with randomly-distributed relays. Most of the
reported works in the literature achieve fairness at the expense of degrading
the outage probability performance. In addition, they often assume that the
number and locations of the relays are known. In contrast, the proposed scheme
achieves fairness in a random field of relays without deteriorating the outage
probability performance. In this scheme, each relay maintains a countdown timer
whose initial value is a function of the relay location and a tunable parameter
which controls the level of fairness. The optimum value of this parameter is
evaluated in an offline manner so as to achieve fairness by making the average
powers consumed by the relays as close as possible. An exact analytical
expression is derived for the average power consumed by each relay. This
expression is then used to show the superiority of the proposed scheme over
opportunistic relaying and random relay selection schemes.
