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
This paper proposes and analyzes a novel differential distributed beamforming strategy for decentralized two-way relay networks. In our strategy, the phases of the received signals at all relays are synchronized without requiring channel feedback or training symbols. Bit error rate (BER) expressions of the proposed strategy are provided for coherent and differential M-PSK modulation. Upper bounds, lower bounds, and simple approximations of the BER are also derived. Based on the theoretical and simulated BER performance, the proposed strategy offers a high system performance and low decoding complexity and delay without requiring channel state information at any transmitting or receiving antenna. Furthermore, the simple approximation of the BER upper bound shows that the proposed strategy enjoys the full diversity gain which is equal to the number of transmitting antennas.
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