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In this paper, an efficient relay selection (RS) algorithm for non-orthogonal amplify-and-forward (NAF) cooperative systems over block-fading channels, also known as block-fading NAF (BFNAF) protocol, is developed. The best relay is selected from a subset of available relay nodes based on the maximum criterion of their capacity bounds in half-duplex (HD) mode, together with the power allocation, to obtain the energy efficiency (EE) for the proposed RS scheme. We derived an exact closed-form expression of the outage probability and throughput for evaluating the system performance. The energy consumption was also numerically evaluated to determine the optimized EE of the proposed RS scheme for each transmission protocol with two modulation schemes. The numerical results indicated that the proposed RS scheme with the BFNAF protocol outperforms the previous RS scheme with orthogonal AF (OAF) protocol in terms of both the outage probability and the throughput as the number of relays is increased and the average transmit power is optimally allocated for each transmission phase. Moreover, in the case of the optimized EE, it is found that by using quadrature amplitude modulation (QAM), the EE of the proposed RS scheme is 48.9% higher than that of binary phase-shift keying (BPSK) modulation.

Efficient Relay Selection Algorithm for Non-Orthogonal Amplify-and-Forward Cooperative Systems over Block-Fading Channels