Two-way decode-and-forward cooperative systems with signal space diversity

In this paper, a novel scheme is proposed to enhance the spectral efficiency of a two-way cooperative relaying system, where two source terminals exchange information directly and via K intermediate relays using the three-phase two-way decode-and-forward (DF) protocol. Signal space diversity (SSD) is incorporated into the two-way cooperative relaying system in the proposed scheme that exploits the inherent diversity in the modulation signal space by rotating and expanding the ordinary constellation. The proposed SSD-based three-phase two-way DF relaying scheme exchanges four symbols in three time slots and thus doubles the spectral efficiency as compared to the conventional three-phase two-way DF relaying system, where six time slots are required to exchange the same four symbols. This improvement in spectral efficiency is achieved without adding any extra complexity, bandwidth, or transmit power. A comprehensive analysis of the proposed scheme is carried out in this paper, and closed-form expressions for various performance metrics, including error probability, outage probability, and channel capacity, are derived. It is shown that the proposed scheme provides a diversity gain equal to one higher than the number of relays. The paper also studies different schemes for the optimization of relay position and power allocation. Finally, Monte Carlo simulations are performed which confirm the validity and accuracy of the analytical framework.