Digital filter and forward full duplex (FF-FD) Relay: Exploiting the loop back signal

Shijian Gao, Xiang Cheng, Liuqing Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, we propose a novel digital filter-and-forward full-duplex (FF-FD) relaying system to exploit the loop-back signal (LBS). Unlike treating the LBS as a generic interference, we utilize the fact that the LBS actually conveys redundant information from the source to the destination in the relaying communication scenarios. Thus, the LBS could potentially be exploited instead of being cancelled. We prove that the FF-FD can achieve higher system achievable rate (SAR) than the amplify-and-forward full-duplex (AF-FD) system. To maintain the system linearity, a digital FF-FD relay is proposed without non-linear distortion induced in the digital domain. The relay can be modeled as a linear digital filter to exploit the LBS via linear filtering. The design challenge at the relay is accordingly shifted to optimizing its discrete frequency response (DFR) rather than the complicated interference cancellation design. Based on the metric of maximum SAR, the DFR is efficiently optimized with and without CSI at the source. A low-complexity yet near-optimal alternative is also provided to reduce the computation cost for large multi-carrier systems. Both theoretical analyses and simulations validate the considerable advantages of the proposed FF-FD over the conventional AF-FD, making FF-FD an appealing candidate for future relaying communications.

Original languageEnglish (US)
Article number8388741
Pages (from-to)5552-5563
Number of pages12
JournalIEEE Transactions on Wireless Communications
Issue number8
StatePublished - Aug 2018

Bibliographical note

Funding Information:
Manuscript received October 17, 2017; revised March 20, 2018; accepted May 28, 2018. Date of publication June 19, 2018; date of current version August 10, 2018. This work was supported in part by the National Natural Science Foundation of China under Grants 61622101 and 61571020, and in part by the Ministry National Key Research and Development Project under Grant 2016YFE0123100. The associate editor coordinating the review of this paper and approving it for publication was T. Lok. (Corresponding author: Xiang Cheng.) S. Gao is with the State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computing Sciences, Peking University, Beijing 100080, China, and also with the Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373 USA (e-mail:

Publisher Copyright:
© 2002-2012 IEEE.


  • Amplify-and-forward
  • DFR design
  • Digital filter-and-forward
  • Full-duplex relaying
  • SAR performance


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