This letter studies a minimum mean square error (MMSE) relay strategy for multiuser amplify-and-forward relaying system consisting of M source-destination pairs between N relays with only a single antenna per node. We design jointly and explicitly optimal diagonal relay amplifying and destination decoder matrices under relay transmit power constraints. By adopting the derived optimal relay amplifying matrix, the MMSE cost function (CF) behavior is analytically and numerically investigated. In addition, it is analytically and numerically shown that the MMSE CF values are always less than M, regardless of N if M ≥ N. And an efficient iterative algorithm with a small number of iterations is proposed to solve the jointly desired optimization problem. Finally, simulation results show that the proposed scheme outperforms the existing ones.
Manuscript received October 8, 2015; revised March 9, 2016; accepted May 3, 2016. Date of publication June 7, 2016; date of current version March 23, 2018. This work was supported by the National Research Foundation of Korea under Grant 2013R1A2A1A0 1016423 funded by the Korea government (Ministry of Science, ICT and Future Planning). K. Chang is with the Department of Network Centric Warfare, Ajou University, Suwon 443-749, Korea (e-mail: j3trio@naver.com). J. Lim is with the Department of Computer Engineering, Ajou University, Suwon 443-749, Korea (e-mail: jaslim@ajou.ac.kr). K. Lee is with the Information and Communications Office, Air Force Headquarters, Gyeryong 321-929, South Korea (e-mail: kxlee1@wichita.edu). Digital Object Identifier 10.1109/JSYST.2016.2565513
