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Demodulate-and-forward (DmF) is an attractive approach when using cooperative diversity schemes in networks where only nodes with strict complexity constraints are allowed, such as sensor networks. In using DmF, the relay only demodulates, but does not decode, the received signal from the source node. Coding can be used at the relay to improve the performance over the relay-destination link. In unrelated work, relay selection has been shown to achieve full diversity order with low overhead by choosing the best relay node out of a pool of available relays to assist the source. A simple heuristic scheme for relay selection while using DmF is available, but this involves the exchange of channel parameters between the nodes, hence increasing the overhead. In this paper, we propose the use of the Bhattacharyya parameter (BP) to facilitate relay selection. The use of BP has the distinct advantage of incorporating the specific coding scheme used while retaining low computation load. As illustrated in our simulation results, the use of BP provides frame error rates quite similar to that obtained from exhaustive search. We should note that this BP-based relay selection scheme can also be applied to cooperation schemes where decoding is performed at the relay.