Calculation of Bounds on the Ergodic Capacity for Fading Channels with Dependency Uncertainty

Modern applications of wireless communication systems often have strict performance requirements. Due to its random nature, channel fading is one of the most limiting factors to provide such guarantees. Even if knowledge about the statistics of the individual links to each antenna is available, there usually are additional uncertainties, e.g., imperfect channel-state information (CSI) or dependency uncertainty between multiple fading links. In this work, we consider the latter and show that a rearrangement algorithm can be applied to calculate the minimum and maximum ergodic capacity for fast fading channels when only the marginal fading distributions are known but the joint distribution is unknown. The algorithm can be used for any number of channels and supports arbitrary marginal distributions. The results are useful for communication system designers, e.g., using the worst-case ergodic capacity for robust system design.