Motivated from results for the point-to-point block MIMO fading channels without channel knowledge, we propose an AF scheme for the non-coherent two-way relaying channel with the half-duplex constraint. The communication takes place in two phases, multicast and broadcast. In the multicast phase the terminals send the signals simultaneously. In the broadcast phase, the relays resend the signal received in the broadcast phase. The code construction is based on subspace packings in the Grassmann manifolds. We show, that although no channel knowledge is assumed at either the terminals or at the relays, the terminals are able to subtract the self-interference part of the received signal. The performance analysis shows that the noncoherent two-way relaying outperforms non-coherent one-way relaying and delivers the promise of increased spectral efficiency.
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