Design algorithm of relative magnitude coefficients using Brent's method on the K-User MIMO-IFC

Interference alignment (IA) is known as having a great effect on the capacity achieved at each receiver in interference channel, when used in conjunction with multiple-input multiple-output (MIMO) technology. Using coordinating base station(BS) transmission, the system generates the beamforming vector to align interference signals into confined subspace at each receiver, where the beamforming and subspace vectors are calculated using the relative magnitude coefficients. It is difficult to design these coefficients since it is needed to solve non-linear equations. In [12], we propose the design algorithm of the relative magnitude coefficients. Using Brent's method iteratively, our design algorithm improves system capacity largely. We assume the worst-case situation where all of 4 users receive the large interference signals from all of the 3 adjacent BSs, and the system model that a base stations has 5 transmit antennas and the other 3 BSs have 4 transmit antennas, where the sum of the number of the transmit antennas is 17. However, this required system is not general because one BS is assumed to have one more transmit antenna than the other BSs. In this paper, we extend the algorithm in [12] to be applicable for more general system where all the base stations have the same number of transmit antennas and the sum of the number of the transmit antennas is 16. As the extended algorithm, we propose how to select an un-eliminated interference signal and calculate the beamforming vectors and the interference signal spaces. In the extended algorithm, not all the interference signals are canceled; one interference signal with the smallest effect on the capacity is not canceled. That is because we can cancel 11 interference signals at maximum when there are 16 transmit antennas though there are 12 interference signals in our system model. We compare the capacities of the conventional algorithm and the extended one, and evaluate how much system capacity the proposed design algorithm can achieve in the situation where there is an un-eliminated interference signal. Through simulation, we show that the proposed design algorithm improves the degradation of the system capacity and achieve the fairness of capacities among users for the increase of the number of designed coefficients.