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We consider an amplify-and-forward (AF) cooperative diversity system where a source node communicates with a destination node directly and indirectly (through multiple relays). In regular multiple-relay cooperative diversity systems, all relay nodes relay the source signal using orthogonal channels (time slots, carriers, or codes) to avoid cochannel interference. Hence, for a regular cooperative diversity network with M relays, we need M+1 channels (one for the direct link and M for the M indirect links). This means that the number of required channels increases linearly with the number of relays. In this paper, we investigate the performance of the best-relay selection scheme where the "best" relay only participates in the relaying. Therefore, two channels only are needed in this case (one for the direct link and the other one for the best indirect link) regardless of the number of relays (M). The best relay is selected as the relay node that can achieve the highest signal-to-noise ratio (SNR) at the destination node. We show that the best-relay selection not only reduces the amount of required resources but also maintains a full diversity order (which is achievable by the regular multiple-relay cooperative diversity system but with much more amount of resources). We derive closed form expressions for tight lower bounds of the symbol error probability and outage probability. Since it is hard to find a closed-form expression for the probability density function (PDF) of SNR of the relayed signal at the destination node, we use an approximate value instead. Then, we find a closed-form expression for the moment generating function (MGF) of the total SNR at the destination. This MGF is used to derive the closed-form expressions of the performance metrics such as the average symbol error probability, the outage probability, the average SNR, the amount of fading, and the SNR moments. Furthermore, we derive the asymptotic behavior of the symbol error probability. From this asymptotic behavior, the diversity order and its dependence on the number of relays (M) can be explicitly determined. Simulation results are also given to verify the analytical results.

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