Spectral and Energy Efficiency in 3-Way Relay Channels with Circular   Message Exchanges
  Spectral and energy efficiency in 3-way relay channels are studied in this paper. First, achievable sum rate expressions for 3-way relay channels are derived for different relaying protocols. Moreover, an outer bound for the capacity of the 3-way relay channel is presented. Next, leveraging the derived achievable sum rate expressions, two algorithms for joint power allocation at the users and at the relay are designed so as to maximize the system energy efficiency. Numerical results are provided to corroborate and provide insight on the theoretical findings. 
Bho Matthiesen and Alessio Zappone and Eduard A. Jorswieck
cs.IT math.IT