386 Y. YUNIDA, R. MUHARAR, Y. AWAY, ET AL., EFFICIENT RELAY SELECTION ALGORITHM FOR NAF COOPERATIVE … DOI: 10.13164/re.2020.0386 SIGNALS Efficient Relay Selection Algorithm for Non-Orthogonal Amplify-and-Forward Cooperative Systems over Block-Fading Channels Yunida YUNIDA, Rusdha MUHARAR, Yuwaldi AWAY, Nasaruddin NASARUDDIN Dept. of Electrical and Computer Engineering, Universitas Syiah Kuala, Banda Aceh, Indonesia nasaruddin@unsyiah.ac.id Submitted September 28, 2019 / Accepted March 3, 2020 Abstract. 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 devel- oped. The best relay is selected from a subset of available relay nodes based on the maximum criterion of their ca- pacity 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 consump- tion was also numerically evaluated to determine the opti- mized 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 quadra- ture amplitude modulation (QAM), the EE of the proposed RS scheme is 48.9% higher than that of binary phase-shift keying (BPSK) modulation. Keywords Block-fading, capacity bound, efficient relay selection, energy efficiency, non-orthogonal amplify- and-forward, power allocation 1. Introduction Cooperative networks in the wireless channel have been proven to increase the data rate and coverage area, and reduce the transmission power constraint in the com- munication process [1]. Generally, a better performance gain of cooperative systems can be obtained by relaying protocols such as decode-and-forward (DF) [2–4], and amplify-and-forward (AF) in [2, 5–7]. The DF protocol is more complicated than the AF protocol because the relay nodes must first decode the received signal from a source node and then forward the re-encoded signal to the desti- nation. In contrast, the AF protocol is more straightforward because the relay node only needs to amplify and re-trans- mit the amplified version of the information signal without other signal processing. The AF protocol, also called or- thogonal AF (OAF), was first introduced by Laneman et al. [2], in which time-division multiplexing (TDM) is used to split the transmission process into two phases. The first phase is called the broadcasting phase, where the source node transmits the information signal to the relay and the destination. The second phase is the cooperative phase, where the relay node re-transmits the amplified version of the information signal to the destination. However, this approach causes a loss of the data rate (bandwidth) as a result of an inactive source node in the second phase. To overcome this limitation, Nabar et al. [8] proposed a new AF protocol for half-duplex cooperative networks, called the non-orthogonal AF (NAF) protocol, where the source continuously transmits a new information signal during the second phase. By using the NAF protocol, the broadcast range and the received signal-to-noise ratio (SNR) can be maximized [9] and the relay nodes can transmit during both transmission phases simultaneously. For the block-fading channel scenario where the channel condition is changed during the second phase, Krikidis et al. [10] proposed another NAF-based protocol, called the block-fading NAF (BFNAF), which is compatible for low spectral efficiency. The BFNAF protocol has a similar transmission process to that of the classic NAF, except that the source re-transmits the same information signal during the second phase to increase the diversity gain. The improvement of the diversity gain in distributed networks such as cooperative and multiple-input multiple- output (MIMO) systems can be achieved by orthogonal transmission, pre-coding, maximum ratio combining (MRC), or distributed space-time coding (STC). The or- thogonal transmission has low spectral efficiency and suf- fers from a rate loss or bandwidth penalty [4]. In addition, with pre-coding design [11] and STC [12], the system needs exact channel state information (CSI) and precise symbol-level synchronization, which is hard to obtain.