In this paper a unified approach for power allocation (PA) problem inmulti-hop orthogonal frequency division multiplexing (OFDM) amplify-and-forward(AF) relaying systems has been developed. In the proposed approach, we considershort and long-term individual and total power constraints at the source andrelays, and devise decentralized low complexity PA algorithms when wirelesslinks are subject to channel path-loss and small-scale Rayleigh fading. Inparticular, aiming at improving the instantaneous rate of multi-hoptransmission systems with AF relaying, we develop (i) a near-optimal iterativePA algorithm based on the exact analysis of the received SNR at thedestination; (ii) a low complexity-suboptimal iterative PA algorithm based onan approximate expression at high-SNR regime; and (iii) a low complexity-noniterative PA scheme with limited performance loss. Since the PA problem inmulti-hop systems is too complex to solve with known optimization solvers, inthe proposed formulations, we adopted a two-stage approach, including a powerdistribution phase among distinct subcarriers, and a power allocation phaseamong different relays. The individual PA phases are then appropriately linkedthrough an iterative method which tries to compensate the performance losscaused by the distinct two-stage approach. Simulation results show the superiorperformance of the proposed power allocation algorithms.
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