In this work, we propose a differential beamforming (DBF) scheme for bi-directional communication between two single-antenna terminals via a multi-antenna relay station (RS). The proposed scheme utilizes differential phase-shift keying modulation to enable beamforming at the RS without knowledge of the instantaneous channel state infor mation (CSI) at any entity in the network. In our differential scheme, receive and transmit beamforming at the RS is performed based on the implicit CSI contained in the received signals in the preceding time slots.Thus, the DBF scheme is applicable even if the communication channels are time-variant. For time-invariant channels, we show that our DBF scheme is associated with a performance penalty of 3 dB as compared to the ideal amplify-and-forward relaying scheme, which requires perfect CSI. Our simulation results confirm the analytical results for time invariant channels. For time-variant channels, the simulation demonstrate a high performance gain of the DBF scheme compared to schemes of the literature.Index Terms-Amplify-and-forward relaying, bi-directional relaying, differential phase-shift keying, differential beamforming, relay networks

A multi-pair two-way relaying scenario with multiantenna mobile stations is considered. The bidirectional communications between the mobile stations are supported by an intermediate non-regenerative multi-antenna relay station. It is assumed that the mobile stations can subtract the backpropagated self-interference. Different relay transceive filter design approaches which utilize the fact that the mobile stations can perform self-interference cancellation are introduced. First, a self-interference aware MMSE transceive filter is derived. Second, a multi-antenna MMSE extension of the zero-forcing block-diagonalization based approaches is proposed and an upper bound for these approaches is given. The proposed transceive filters require less antennas at the relay station and achieve higher sum rates compared to conventional relay transceive filter approaches which do not exploit the capability of the mobile stations to perform self-interference cancellation.

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Abstract-In this paper, we consider a non-regenerative multigroup multi-way relaying scenario in which each group consists of multiple half-duplex nodes. Each node wants to share its data with all other nodes within its group. The transmissions are performed via an intermediate non-regenerative half-duplex multi-antenna relay station, termed RS, which spatially separates the different groups. In our proposal, all nodes simultaneously transmit to RS during a common multiple access phase and RS retransmits linearly processed versions of the received signals back to the nodes during multiple broadcast (BC) phases. We propose a novel transmit strategy which exploits analog network coding (ANC) and efficiently combines spatial transceive processing at RS with joint receive processing at each node over multiple BC phases. A closed-form solution for an ANC aware relay transceive filter is introduced and closed-form solutions for the joint receive processing filters at the nodes are presented. Furthermore, self-interference cancellation and successive interference cancellation are exploited at the nodes to improve the joint receive processing. By numerical results, it is shown that the proposed transmit strategy significantly outperforms existing multi-way strategies.Index Terms-Multi-way relaying, non-regenerative relay, analog network coding (ANC), minimum mean-squared error (MMSE).