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In this paper, a new non-orthogonal multiple-access scheme, trellis tone modulation multiple-access (TTMMA), is proposed for peer discovery of distributed device-to-device (D2D) communication. The range and capacity of discovery are important performance metrics in peer discovery. The proposed trellis tone modulation uses single-tone transmission and achieves a long discovery range due to its low Peak-to-Average Power Ratio (PAPR). The TTMMA also exploits non-orthogonal resource assignment to increase the discovery capacity. For the multi-user detection of superposed multiple-access signals, a message-passing algorithm with supplementary schemes are proposed. With TTMMA and its message-passing demodulation, approximately 1.5 times the number of devices are discovered compared to the conventional frequency division multiple-access (FDMA)-based discovery.

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