Orthogonal Precoder for Integer-Forcing MIMO

This paper focuses on orthogonal precoding for integer-forcing linear receiver and shows it has two advantages over unitary precoding. Orthogonal precoding exhibits lower complexity than unitary precoding because the dimension of orthogonal matrices is half that of unitary matrices for a fixed number of antennas. Moreover, orthogonal precoding outperforms unitary precoding in terms of achievable rate and error-rate. Despite its promising advantages, it is not easy to find the optimal precoding matrices because it involves an orthogonality constraint and the shortest lattice vector problem. To solve this, we separate the optimization problem into two sub-problems and propose methods based on the steepest gradient with Lie groups and a random search algorithm. The proposed methods have low complexity and are applicable to any MIMO dimension. For high-order QAM, the proposed orthogonal precoder outperforms X-precoders which are designed specifically for QAM.