Linear precoder designs for K-user interference channels

TLDR

The interference alignment algorithm achieves a theoretical bound on degrees of freedom for interference channel systems. The study proposes linear precoding and decoding schemes for K‑user interference channels, including a non‑iterative solution and an iterative algorithm that maximizes weighted sum rate. The non‑iterative design selects orthonormal precoding bases to maximize DOF and optimizes matrices per decoding scheme, while the iterative algorithm applies gradient descent on weighted sum rate to converge to a local optimum. Simulations demonstrate that the iterative algorithm outperforms existing methods in sum rate, and the non‑iterative method approaches a local optimum at high SNR while reducing complexity.

Abstract

This paper studies linear precoding and decoding schemes for K-user interference channel systems. It was shown by Cadambe and Jafar that the interference alignment (IA) algorithm achieves a theoretical bound on degrees of freedom (DOF) for interference channel systems. Based on this, we first introduce a non-iterative solution for the precoding and decoding scheme. To this end, we determine the orthonormal basis vectors of each user's precoding matrix to achieve the maximum DOF, then we optimize precoding matrices in the IA method according to two different decoding schemes with respect to individual rate. Second, an iterative processing algorithm is proposed which maximizes the weighted sum rate. Deriving the gradient of the weighted sum rate and applying the gradient descent method, the proposed scheme identifies a local-optimal solution iteratively. Simulation results show that the proposed iterative algorithm outperforms other existing methods in terms of sum rate. Also, we exhibit that the proposed non-iterative method approaches a local optimal solution at high signal-to-noise ratio with reduced complexity.