Resource Allocation for Asymmetric Multi-Way Relay Communication over Orthogonal Channels

We consider the wireless communication of common information between several terminals with the help of a relay as it is for example required for a video conference. The transmissions of the nodes are divided in time and there is no direct link between the terminals. The allocation of the transmission time and of the rates in all directions can be asymmetric. We derive a closed form expression of the optimal time allocation for a given ratio of the rates in all directions and for given signal-to-noise ratios of all channels. For specific channel conditions that guarantee that the network is not “too asymmetric” we further obtain a closed form expression of the optimal rate ratio such that the sum-rate is maximized under the assumption that the time allocation is optimally chosen. We also show that at least one of the terminals should not transmit own data to maximize the sum-rate, if the network is “too asymmetric”.