A Spectrally Efficient Signal Space Diversity-Based Two-Way Relaying System

This work proposes a new transmission scheme for multirelay two-way relaying systems, where two end-sources communicatewith each other via a set of relays. In the proposed scheme, we consider signal space diversity and time division broadcast protocol jointly to increase spectral efficiency without sacrificing the system reliability. The idea behind this consideration is that original data symbols are rotated before transmission, and then the inphase and quadrature components of these rotated symbols are transmitted through the cooperation of the end-sources and the relays. By doing so, the end-sources exchange four symbols over three time slots instead of two, i.e., doubling the number of transmitted symbols. In addition, relay selection is incorporated into this scheme to achieve a further increase in spectral efficiency. For relay selection, two different strategies are discussed: reactive and proactive relay selections. These strategies differ depending on whether relay selection is performed after or before the start of transmission. Specifically, for each relay-selection strategy, we first obtain a closed-form expression for the end-to-end (E2E) error probability with an arbitrary constellation, which accounts for all the resulting nonuniform constellation cases due to constellation rotation. Subsequently, with the derived expressions, we then formulate an optimization problem that considers the joint optimization of the rotation angle and the transmit powers at the end-sources and the relays. The objective of the optimization problem is to minimize the E2E error probability of one of the end-sources, while satisfying a set of total and individual transmit power constraints and a predefined threshold for the E2E error probability of the other end-source. Numerical results verify the theoretical analysis, and show that the scheme proposed herein provides not only higher spectral efficiency, but also more reliable transmission.