Multiple relay selection enables a cooperative system to obtain better performance than single relay selection and yet avoid challenging problems such as synchronization that are associated with having all the relays transmit. While its benefits have been well characterized, the problem of developing distributed, scalable schemes that discover the best subset of relays remains to be fully investigated. The problem is challenging because the relays are spatially separated from each other and have only local channel knowledge. We investigate the popular, low feedback, and distributed timer scheme and derive a novel, optimal timer mapping that maximizes the probability of selecting the best two relays. This has applications in several cooperative schemes proposed in the literature. We derive several novel structural properties about the optimal mapping, which reduce the complexity of finding it from the large space of all functions to a one-dimensional search that can be solved using a computationally efficient, iterative algorithm. Our extensive benchmarking shows that the optimal mapping outperforms several relay discovery schemes proposed in the literature. The approach can be generalized to selecting the best l relays, as well.
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