Least-squares approach to interference alignment in multiuser MIMO interference channels

Abstract

In this thesis, beam design for signal space interference alignment for K-user multi-input multi-output (MIMO) interference channels is investigated. For timeinvariant channels, the iterative least squares (ILS) algorithm based on a linear formulation exploiting conditions for interference alignment is proposed and its convergence is established. As an extension of this, recursive algorithms called least squares with iteration and recursion (LSINR) in slowing-fading channels are also developed using matrix perturbation theory. Based no the proposed linear formulation, the recursive beam design algorithm obtains the current beams by updating with the previous ones in slowly time-varying channels. The proposed least squares approaches to interference alignment enable to achieve the comparable sum throughput performance with faster convergence and lower complexity. In the first part, a problem of interference alignment for K-user constant MIMO interference channels is considered. Necessary and sufficient conditions for interference alignment are converted to a system of linear equations that have dummy variables. Based on this linear system equation, a new ILS algorithm for beam design for interference alignment is proposed by minimizing the overall interference misalignment. The proposed algorithm consists of solving a least squares problem iteratively to find the beam coefficients and dummy variables. Convergence of the proposed algorithm is proven, and its complexity is analyzed. Sum rate performance of the proposed algorithm is evaluated numerically. It is shown that the proposed algorithm has faster convergence and lower complexity than the previous method with a comparable performance in the most practical case of two receive antennas, i.e., all transmitters send single date stream. Even in the multi-steam cases, the the maximum degrees of freedom (DoF) are achieved with some loss of signal to noise ratio (SNR). Next, interference aligning beam design in slo...