Generalized Interference Alignment --- Part I: Theoretical Framework

TL;DR

This paper introduces a theoretical framework for generalized interference alignment (GIA), addressing fundamental issues like feasibility and transceiver design, to improve secrecy protection in wireless networks.

Contribution

It develops a comprehensive algebraic geometry-based framework for GIA, establishing feasibility conditions and algorithms, advancing the understanding of interference alignment for secrecy.

Findings

Determines necessary and sufficient feasibility conditions for GIA.

Provides algorithms for solving GIA problems.

Lays foundation for GIA implementation in secrecy applications.

Abstract

Interference alignment (IA) has attracted enormous research interest as it achieves optimal capacity scaling with respect to signal to noise ratio on interference networks. IA has also recently emerged as an effective tool in engineering interference for secrecy protection on wireless wiretap networks. However, despite the numerous works dedicated to IA, two of its fundamental issues, i.e., feasibility conditions and transceiver design, are not completely addressed in the literature. In this two part paper, a generalised interference alignment (GIA) technique is proposed to enhance the IA's capability in secrecy protection. A theoretical framework is established to analyze the two fundamental issues of GIA in Part I and then the performance of GIA in large-scale stochastic networks is characterized to illustrate how GIA benefits secrecy protection in Part II. The theoretical framework for GIA adopts methodologies from algebraic geometry, determines the necessary and sufficient feasibility conditions of GIA, and generates a set of algorithms that can solve the GIA problem. This framework sets up a foundation for the development and implementation of GIA.