Beam Tracking for Interference Alignment in Time-Varying MIMO Interference Channels: A Conjugate-Gradient-Based Approach

In this paper, an adaptive beam tracking algorithm for interference alignment (IA) in time-varying multiple-input-multiple-output (MIMO) interference channels is presented. It is shown that obtaining a set of interference-aligning transmit beamforming matrices is equivalent to minimizing a certain Rayleigh quotient, and an approach based on the conjugate gradient (CG) method combined with metric projection is applied to this minimization problem to construct an adaptive algorithm for interference-aligning beam design. The convergence of the proposed algorithm in static channels is established, and the steady-state behavior of the proposed algorithm in time-varying channels is investigated by numerical simulations. The performance of the proposed algorithm is evaluated numerically, and numerical results show that the proposed algorithm performs well with low computational complexity.