Non-Coherent Communication in Wireless Point-to-Point and Relay Channels: A Geometric Approach

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We address the problem of non-coherent transmission in point-to-point MIMO channels and wireless relay channels. We use the geometric approach where the problem of construction of space-time codes for non-coherent point-to-point channels has an interpretation as a packing problem in the Grassmann manifold. In this context, we propose code constructions which exploit the geometry of the Grassmann manifold. For networks with relays we present distributed space-time codes based on modified code constructions for the point-to-point channel. We address both the one-way relaying and the two-way relaying channel. For the two-way relaying channel we additionally present bounds on the achievable two-way rate in the non-coherent setup. As a byproduct we derive the degrees of freedom of the two-way network and show that amplify-and-forward is optimal strategy in the non-coherent setup.