Upper bounds on the sum capacity of the K-user Gaussian interference channel

The capacity region of the K-user Gaussian interference channel (GIC) is a long-standing open problem and even useful capacity outer bounds are little known in general. The significant progress on the degrees-of-freedom (DoF) capacity approximation for the K-user GIC has provided new insights into the problem of interest in the high signal-to-noise ratio (SNR) limit. However, such capacity approximation has been recently observed to reveal some limitations in predicting the capacity at realistic SNR. In this work, we derive new upper bounds on the capacity of the K-user GIC with complex channel gains to provide a more accurate and concrete perspective on capacity behaviors at finite SNR.