Signal and interference alignment via message passing for MIMO interference channels

A novel algorithm for the design of linear precoding and equalisation in multiple-input multiple-output interference channels is proposed that is based on the minimisation of the interference-plus-signal leakage. The interference-plus-leakage criterion, unlike the more conventional interference leakage metric for interference alignment, considers not only the power of the interference caused to unintended receivers but also the power of the useful signal that is 'spilled' outside the receiving subspace of the intended receiver. The proposed algorithm tackles the problem via the application of the min-sum message passing algorithm to a factor graph constructed on the interference graph of the network. The scheme can be seen as a generalisation of a number of previously proposed algorithms, including the alternating optimisation schemes for interference leakage minimisation and interference-plus-signal leakage minimisation. The approach inherits the advantages of these schemes of returning unitary precoding and equalisation matrices, hence simplifying the task of low-rate feedback to the transmitters and receivers, and of allowing a distributed implementation. Numerical results show that the scheme provides advantages in terms of achievable sum-rate and convergence with respect to the mentioned existing related strategies.