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.Comment: Minor Revision at IEEE Transactions on Signal Processin
