  In this paper, we propose a new transmission scheme, named as Integer
Forcing-and-Forward (IFF), for communications among multi-pair multiple-antenna
users in which each pair exchanges their messages with the help of a single
multi antennas relay in the multiple-access and broadcast phases. The proposed
scheme utilizes Integer Forcing Linear Receiver (IFLR) at relay, which uses
equations, i.e., linear integer-combinations of messages, to harness the
intra-pair interference. Accordingly, we propose the design of mean squared
error (MSE) based transceiver, including precoder and projection matrices for
the relay and users, assuming that the perfect channel state information (CSI)
is available. In this regards, 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 squred errors (Sum MSE) and the maximum of the users' mean squared
errors (Max MSE), to design the related precoding and filters for recovering
relay's equations by the users. Then, we consider a more practical scenario
with imperfect CSI. For this case, IFLR receiver is modified, and another
transceiver design is proposed, which take into account the effect of channels
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 the outage
probability and the sum rate.
