In this paper, we propose a new transmission scheme, named as IntegerForcing-and-Forward (IFF), for communications among multi-pair multiple-antennausers in which each pair exchanges their messages with the help of a singlemulti antennas relay in the multiple-access and broadcast phases. The proposedscheme utilizes Integer Forcing Linear Receiver (IFLR) at relay, which usesequations, i.e., linear integer-combinations of messages, to harness theintra-pair interference. Accordingly, we propose the design of mean squarederror (MSE) based transceiver, including precoder and projection matrices forthe relay and users, assuming that the perfect channel state information (CSI)is available. In this regards, in the multiple-access phase, we introduce twonew MSE criteria for the related precoding and filter designs, i.e., the sum ofthe equations MSE (Sum-Equation MSE) and the maximum of the equations MSE(Max-Equation MSE), to exploit the equations in the relay. In addition, theconvergence of the proposed criteria is proven as well. Moreover, in thebroadcast phase, we use the two traditional MSE criteria, i.e. the sum of theusers' mean squred errors (Sum MSE) and the maximum of the users' mean squarederrors (Max MSE), to design the related precoding and filters for recoveringrelay's equations by the users. Then, we consider a more practical scenariowith imperfect CSI. For this case, IFLR receiver is modified, and anothertransceiver design is proposed, which take into account the effect of channelsestimation error. We evaluate the performance of our proposed strategy andcompare the results with the conventional amplify-and-forward (AF) anddenoise-and-forward (DF) strategies for the same scenario. The results indicatethe substantial superiority of the proposed strategy in terms of the outageprobability and the sum rate.
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