Integer Forcing-and-Forward Transceiver Design for MIMO Multipair Two-Way Relaying

In this paper, we propose a new transmission scheme, called integer forcing-and-forward ( IFF), for communications among multipair multiple-antenna users in which each pair exchanges their messages with the help of a single multiple-antenna relay in the multiple-access and broadcast phases. The proposed scheme utilizes integer forcing linear receiver ( IFLR) at the relay, which uses equations, i.e., linear integer combinations of messages, to harness intrapair interference. Accordingly, we propose the design of a mean square error ( MSE)-based transceiver, including precoder and projection matrices for the relay and users, assuming that perfect channel state information ( CSI) is available. In this regard, in the multiple-access phase, we introduce two new MSE criteria for the related precoding and filter designs, i.e., the sum of the equations MSE ( Sum-Equation MSE) and the maximum of the equations MSE ( Max-Equation MSE), to exploit the equations in the relay. In addition, the convergence of the proposed criteria is proven as well. Moreover, in the broadcast phase, we use the two traditional MSE criteria, i.e., the sum of the users' mean square errors ( Sum MSE) and the maximum of the users' mean square errors ( Max MSE), to design the related precoding and filters for recovering the relay's equations by the users. Then, we consider a more practical scenario with imperfect CSI. For this case, the IFLR receiver is modified, and another transceiver design is proposed, which takes into account the effect of channel estimation error. We evaluate the performance of our proposed strategy and compare the results with the conventional amplify-and-forward ( AF) and denoise-and-forward ( DF) strategies for the same scenario. The results indicate the substantial superiority of the proposed strategy in terms of outage probability and sum rate.