Non-coherent communication in wireless point-to-point and relay channels: a geometric approach

Abstract

We address the problem of non-coherent transmission in block Rayleigh fading channels. We focus on the point-to-point MIMO channel and the wireless relay channel without direct link. The problem of non-coherent space-time coding can be given a geometric interpretation as a packing problem in the Grassmann manifold. We use the differentiable structure of the Grassmann manifold for code constructions for the non-coherent channel. We present several novel constructions which exploit the geometry of the Grassmann manifold. We propose code constructions from spherical codes and lattice packings and develop a method for recursive construction of high-dimensional codes. We also address the problem of non-coherent transmission in wireless relay networks. We focus on one-way and two-way relaying protocols with half-duplex constraints on the terminals. For the one-way relaying network we present novel distributed space-time codes based on Grassmann codes for the point-to-point MIMO channel. For the two-way relaying channel we first introduce the concept of non-coherent communication, showing that non-coherent communication is possible, although no channel knowledge is present at neither the terminals nor at the relays. Further, we present bounds on the achievable two-way rate in the non-coherent setup. We show that the upper and the lower bound meet in the high SNR regime and differ from the capacity within a constant. 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. Motivated from the results, we present two communication schemes. The first one is a differential scheme which extends over the known differential schemes for one-way relaying and adapts to the specifics of the two-way channel. The second scheme is a genuine non-coherent scheme, designed for the block channel model.