Performance Analysis of Dual-Hop OFDM Relay System with Subcarrier Mapping in Nakagami-m Fading

Subcarrier mapping (SCM) is considered to be crucial for capacity-maximization in orthogonal frequency division multiplexing (OFDM) relaying networks and has been investigated extensively. However, no study has examined its exact or approximate close-form analysis under Nakagami-m fading. This paper considers the ordered subcarrier pairing schemes, i.e., worst-to-best (WTB) SCM and best-to-best (BTB) SCM, for the analysis of bit error rate (BER) and capacity of a dual-hop OFDM amplify-and-forward (AF) relay system. The system-analysis is presented for Nakagami-m fading with emphasis on two special cases: one-sided Gaussian fading (m = 12) and Rayleigh fading (m = 1). Close-form expressions for the probability density function (PDF) and moment generating function (MGF) of end-to-end SNR are derived while considering fixed gain AF relays. The classical MGF and PDF based approaches are used to compare the BER performance of the system with WTB SCM and BTB SCM schemes. Close-form expressions for the upper bound on ergodic capacity are derived by analyzing Jensen's inequality. Accurate analysis is presented for integer m while the non-integer m values allow the derivations of approximate expressions. The accuracy of the suggested approximation is verified analytically as well as numerically. The simulation results validate the analysis in Nakagami-m fading channel.