Non-Coherent Grassmann TCM Design for Physical-Layer Network Coding in Bidirectional MIMO Relaying Systems

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We investigate a bidirectional relaying system which uses physical-layer network coding and non-coherent multi-input multi-output (MIMO) signal processing. With non-coherent codes on Grassmannian manifold, a receiver employing generalized likelihood ratio test (GLRT) algorithm offers the maximum-likelihood performance even without any channel state information (CSI). We propose a new family of non-coherent Grassmann codes which enjoy a significant coding gain by introducing a trellis-coded modulation (TCM) through an affine-lattice convolution with exponential mapping. We develop a design method of individual TCM code-books for multiple users in non-coherent two-way relaying channels with network coding. Since the proposed scheme does not require CSIs, it effectively deals with time-varying fading channels.