Design method of relative magnitude coefficients considering rotation of basis vectors in interference space on the K-user MIMO interference channel for downlink system

Recently, to improve the capacity of cell-edge user, interference alignment (IA) is an intense research interest. We focus on the IA extended to the multiple-input multiple-output (MIMO) interference network. In this method, each coordinated transmitter generates the beamforming vector to align interference from different transmitters into confined subspace at each receiver. Then, using singular value decomposition (SVD) with the relative magnitude coefficients, transmitters calculate the beamforming vectors and the received vectors. However, this method can not decide the value of the relative magnitude coefficients so that the system capacity is improved, because it is necessary to solve non-linear function of multivariable. In this paper, we propose the design method of the relative magnitude coefficient of interference channels to improve the system capacity using Brent's method. The proposed method can improve the system capacity, however, the system complexity increases because Brent's method needs multiple SVD calculation to calculate the null space. Therefore, in addition, we propose the complexity reduction method to calculate the null space of the matrix instead of SVD. Through simulation, we show that the proposed method achieves a higher system capacity than the conventional one. We also show that the proposed method that calculates the null space needs much lower complexity than SVD.