On the Generalized Degrees of Freedom of the K-user Symmetric MIMO Gaussian Interference Channel (1105.5306v4)

Abstract: The K-user symmetric multiple input multiple output (MIMO) Gaussian interference channel (IC) where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log (INR) / log (SNR) level. Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). Several interesting conclusions are drawn from the derived bounds. For example, when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is shown to be GDOF optimal. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance. It is also shown that many of the existing results on the GDOF of the Gaussian IC can be obtained as special cases of the bounds, e.g., by setting K=2 or the number of antennas at each user to 1.