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In this paper, a hop-by-hop relay selection strategy for multi-hop underlay cognitive relay networks (CRNs) is proposed. In each stage, relays that successfully decode the message from previous hop form a decoding set. Taking both maximum transmit power and maximum interference constraints into consideration, the relay in the decoding set which has the largest number of channels with an acceptable signal-to-noise ratio (SNR) level to the relays in the next stage is selected for retransmission. Therefore, relay selection in each stage only relies on channel state information (CSI) of the channels in that stage and does not require the CSI of any other stage. We analyze the performance of the proposed strategy in terms of endto-end outage probability and throughput, and show that the results match those obtained from simulation closely. Moreover, we derive the asymptotic end-to-end outage probability of the proposed strategy when there is no upper bound on transmitters’ power. We compare this strategy to other hop-by-hop strategies that have appeared recently in the literature and show that this strategy has the best performance in terms of outage probability and throughput. Finally it is shown that the outage probability and throughput of the proposed strategy are very close to that of exhaustive strategy which provides a lower bound for outage probability and an upper bound for throughput of all path selection strategies.

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