Summary: The purpose of this monograph is to introduce both classic and recent capacity theorems for the two-user Gaussian interference channel including both the single-antenna case and the multiple-antenna case.
This monograph starts with the single antenna case and introduces the Han and Kobayashi achievable rate region and its various subregions [S. T. Han and K. Kobayashi, IEEE Trans. Inf. Theory 27, 49–60 (1981; Zbl 0452.94006)]. Several capacity outer bounds are then presented, which, together with the achievable rate region, yields several capacity results for the single-antenna Gaussian interference channel, including the capacity region for strong interference and the sum-rate capacity for Z interference, noisy interference, mixed interference and degraded interference.
For the more complex multiple-antenna case, the interference state is no longer determined solely by the interference strength as in the single-antenna case. Instead, the structure of the interference in different multi-dimensional subspaces plays an equally important role. As a result of this multiple-dimensional signaling, new interference states including generally strong, generally noisy and generally mixed interference are introduced to obtain capacity theorems that generalize those for the single-antenna case.