Ergodic Capacity of OFDM AF Fixed Gain Relay System with Subcarrier Mapping Enis Kocan, Milica Pejanovic-Djurisic, Zoran Veljovic Faculty of Electrical Engineering University of Montenegro Podgorica, Montenegro enisk@ac.me , milica@ac.me , veljovic@ac.me Abstract—In this paper ergodic capacity of dual-hop OFDM amplify-and-forward (AF) fixed gain (FG) relay system, implementing capacity maximizing best-to-best subcarrier mapping (BTB SCM) scheme at the relay (R) station, is examined. Scenario without direct communication between the source of information (S) and destination terminal (D) is considered, with Rayleigh fading statistics on both hops. A closed form relation for the tight lower bound of the system ergodic capacity is derived. Comparisons of the obtained ergodic capacity results with the simulation results have confirmed the accuracy of the undertaken analytical approach. Thus, the derived analytical expression presents very useful and most accurate available tool for the performance assessment of the OFDM AF FG relay system with BTB SCM, considered to be interesting solution for the next generation of mobile cellular systems. Keywords-OFDM relay system; fixed gain; subcarrier mapping; capacity I. INTRODUCTION The ever increasing demands for capacity enhancement represent the reason of constant efforts in the direction of mobile cellular communication systems performance improvement. Therefore, a number of new technical solutions have been appeared, and among them is implementation of transmission concepts based on relay stations (R), [1]. Besides capacity improvements, incorporation of relay stations provides coverage extension of mobile cellular networks. Both accepted solutions for IMT-Advanced systems, LTE-Advanced and WirelessMAN-Advanced, will apply relay stations based on orthogonal frequency division multiplexing (OFDM), as OFDM is proven to be very successful modulation and transmission technique that can provide high data rates even in frequency selective fading channels. For the moment, a dual- hop relaying scenario, including one R station and no direct communication between the source of information (S) and destination terminal (D) is foreseen in the first phase of implementation. The current IMT-Advanced standards assume decode-and-forward (DF) based signal processing at R stations. R stations with amplify-and-forward (AF) signal processing, which also were, and still are, the subject of intensive research activities, are expected to become a part of some further IMT- Advanced system specifications, [2]. In that context, relay stations implementing AF signal processing can be considered as a very promising alternative since they are simpler for realization and introduce shorter latency than R stations with DF signal processing. At R stations with AF signal processing, fixed gain (FG) or variable gain (VG) may be introduced, depending on their ability to estimate the S-R channel. In OFDM based relay systems, AF VG relaying assumes continual estimation of all subcarrier channel transfer functions and implementation of a great number of amplification blocks. Actually, OFDM R station with AF VG relaying should have one amplification block for each subcarrier, what makes them to be not so cost-effective solution. On the other side, R station with AF FG relaying is easier for realization since it has just one amplification block, and the level of introduced gain is fixed. Therefore, we have chosen to analyze dual-hop OFDM AF FG relay system from the point of its impact on the capacity performance improvement of the next generation mobile cellular systems. When OFDM based relay systems are concerned, it is worth mentioning that the research interest does not abate, in spite of completed work on both accepted IMT-Advanced standards. The efforts of researchers are directed towards new solutions for performance improvement and/or optimization of the existing OFDM relay systems. When performance improvements are considered, one of the interesting solutions is subcarrier mapping (SCM) technique implemented at R station, which can enhance the capacity of OFDM based relay systems, [3]-[6], and/or improve bit error rate (BER) performances, [7]-[9]. In the case of OFDM dual-hop relay system with the three communication terminals, when the communication process between S and D is realized through R, SCM is performed in a way that the subcarriers from the first hop are mapped to the subcarriers on the second hop in accordance with their instantaneous signal-to-noise ratios (SNR), [3], [4]. For the capacity maximization, the subcarrier with the highest SNR from the first hop should be mapped to the subcarrier with the highest SNR on the second hop, then subcarrier with the second highest SNR from the first hop to the subcarrier with the second highest SNR on the second hop, etc. This kind of SCM scheme is denoted as best-to-best SCM (BTB SCM). The achievable capacity of dual-hop OFDM AF FG relay system with such SCM scheme has been examined through different approaches, [5], [6]. In [5] the authors have analyzed the achievable capacity of this system through numerical approach, while in [6] a closed-form solution for upper bound of the achievable ergodic capacity is obtained, all 978-1-4577-0580-9/12/$26.00 ©2012 IEEE