Multipair Two-way Half-Duplex Relaying with Massive Arrays and Imperfect CSI

We consider a two-way half-duplex relaying system where multiple pairs of single antenna users exchange information assisted by a multi-antenna relay. Taking into account the practical constraint of imperfect channel estimation, we study the achievable sum spectral efficiency of the amplify-and-forward (AF) and decode-and-forward (DF) protocols, assuming that the relay employs simple maximum ratio processing. We derive an exact closed-form expression for the sum spectral efficiency of the AF protocol and a large-scale approximation for the sum spectral efficiency of the DF protocol when the number of relay antennas, M , becomes sufficiently large. In addition, we study how the transmit power scales with M to maintain a desired quality-of-service. In particular, our results show that by using a large number of relay antennas, the transmit powers of the user, relay, and pilot symbol can be scaled down proportionally to 1/M, 1/M , and 1/M for certain α, β, and γ, respectively. This elegant power scaling law reveals a fundamental tradeoff between the transmit powers of the user/relay and pilot symbol. Finally, capitalizing on the new expressions for the sum spectral efficiency, novel power allocation schemes are designed to further improve the sum spectral efficiency. Index Terms Amplify-and-forward, decode-and-forward, geometric programming, massive MIMO, power scaling law, two-way relaying. C. Kong, C. Zhong and Z. Zhang are with the Institute of Information and Communication Engineering, Zhejiang University, China. C. Zhong is also affiliated with the National Mobile Communications Research Laboratory, Southeast University, Nanjing, China (email: [email protected]). M. Matthaiou is with the School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, BT3 9DT, U.K. (email: [email protected]). E. Björnson is with the Department of Electrical Engineering (ISY), Linköping University, Linköping, SE-581 83, Sweden (email: [email protected]).