We consider a multi-carrier multi-user two-way relay network with multiple single antenna node pairs and a single nonregenerative relay with two antennas. In a conventional multi-user two-way relaying scheme where different node pairs transmit their data streams on different subcarriers, only one data stream per channel use can be achieved. Taking into account that the nodes can perform self interference cancellation, one antenna at the relay is sufficient to achieve one data stream per channel

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... use. Hence, the two antennas at the relay are not fully utilized. In this paper, using the interference alignment technique in spacefrequency dimensions, it is shown that when the number of users in the system is large, almost two data streams per channel use are achievable. The gain comes from the joint consideration of the spatial and frequency dimensions at the relay. A new projection based interference alignment algorithm is proposed. The ideas of signal alignment and channel alignment [1] are used to achieve the interference alignment solution. Furthermore, for the performance improvement of the proposed interference alignment scheme at moderate Signal to Noise Ratios (SNRs), a new gradient based method for optimization of the projection space at the relay is proposed.