A Spectrally Efficient Transmission Scheme for Half-Duplex Decode-and-Forward Relaying

We propose a spectrally efficient transmission scheme for the half-duplex relay channel. In the proposed scheme, the relay combines N detected r-dimensional symbols and generates M new r-dimensional symbols, where M < N, using a linear transformation. The proposed linear transformation preserves the signal energy, and it facilitates decoupled symbol detection at the receiver. We also present an optimized design for the case of complex scalar modulation (r = 2) with N = 2 and M = 1. This design increases the spectral efficiency by 33 % compared to conventional decode- or amplify-and-forward relaying.