In this paper, we study the two-way relay channel with energy harvesting nodes. In particular, we find transmission policies that maximize the sum-throughput for two-way relay channels when the relay does not employ a data buffer. The relay can perform decode-and-forward, compress-and-forward, compute-and-forward or amplify-and-forward relaying. Furthermore, we consider throughput improvement by dynamically choosing relaying strategies, resulting in hybrid relaying strategies. We show that an iterative generalized directional water-filling algorithm solves the offline throughput maximization problem, with the achievable sum-rate from an individual or hybrid relaying scheme. In addition to the optimum offline policy, we obtain the optimum online policy via dynamic programming. We provide numerical results for each relaying scheme to support the analytic findings, pointing out to the advantage of adapting the instantaneous relaying strategy to the available harvested energy.

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