On the DoF and secure DoF of K-user MIMO interference channel with instantaneous relays

摘要

Interference channel, in which multiple user pairs communicate over shared resources, is a building block of communications networks. Here, the K-user interference channel (IC) aided by J instantaneous relays (IRs), i.e. relays without delay, is considered. For KICJR networks, where K>2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$K>2$$end{document} and J>1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$J>1$$end{document}, the DoF performance and achievable schemes have not been investigated in literature. Here, we devise a novel achievable scheme, called restricted interference alignment (RIA), which restricts the received interference from each source at each destination in a limited sub-space, and then, aligns the restricted interferences. Furthermore, we develop an analytical tool for finding a tight upper bound on DoF of KICJR networks by analyzing the properness of the interference alignment equations. Moreover, we develop linear beamforming design for sources and relays based on the mean square error (MSE) minimization, as an achievable scheme. The performance evaluation results show that the achievable sum DoF by using the proposed RIA scheme and the MSE-based beamforming design match well with the derived upper bounds. Furthermore, the results confirm that the achieved sum DoF using the RIA scheme outperforms the existing achievable schemes. Motivated by these promising results, we further investigate impact of IRs in providing physical layer security, i.e. achieving secure DoF in interference networks. Specifically, we derive a lower bound on the achievable secure DoF by devising an achievable scheme, called transmission in the null space (TNS). This scheme makes the cross channels rank deficient and enables sources to select their transmit filters in the constructed null spaces. Performance evaluation shows that by leveraging IRs, the secure DoF performance of interference networks could be increased significantly. The proposed analytical framework in this work for rank deficiency-powered DoF analysis is expected to also attract attention from other research areas, e.g. beamforming design for millimeter wave communications.