Capacity of orthogonal relay channel and resource allocation

We consider an orthogonal relay channel, where the channel from the source to the relay and the channel from the source and the relay to the destination are orthogonal on time. Firstly, the upper bound and the lower bound of the capacity are proposed, and converge to the capacity, where the lower bound is based on partial decode-and-forward. Secondly, to maximize the capacity for Gaussian orthogonal relay channel, the resource allocation is studied. The simulations show that optimizing the time only brings very little loss about capacity compared to maximize all the possible parameters. The optimal time allocation is given analytically when optimizing the time only.