Abstract-We study the end-to-end resource allocation in an OFDM based multi-hop network consisting of a one-dimensional chain of nodes including a source, a destination, and multiple relays. The problem is to maximize the end-to-end average transmission rate under a long-term total power constraint by adapting the transmission power on each subcarrier over each hop and the transmission time used by each hop in every time frame. The solution to the problem is derived by decomposing it into two subproblems: short-term time and power allocation given an arbitrary total power constraint for each channel realization, and total power distribution over all channel realizations. We show that the optimal solution has the following features: the power allocation on subcarriers over each hop has the water-filling structure and a higher water level is given to the hop with relatively poor channel condition; meanwhile, the fraction of transmission time allocated to each hop is adjusted to keep the instantaneous rates over all hops equal. To tradeoff between performance, computational complexity and signalling overhead, three suboptimal resource allocation algorithms are also proposed. Numerical results are illustrated under different network settings and channel environments.

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