The Channel Capacity Increases with Power

TL;DR

This paper proves that for memoryless vector channels, increasing average power does not decrease channel capacity, even with nonlinear distortions, by showing the equivalence of capacity maximization over different source distributions.

Contribution

It establishes that channel capacity remains non-decreasing with power increases for memoryless vector channels, regardless of nonlinear distortions, by demonstrating the equivalence of capacity maximization methods.

Findings

Channel capacity does not decrease with increased power.

Maximizing mutual information over different source distributions yields the same capacity.

Nonlinear distortions do not reduce the maximum achievable capacity.

Abstract

It is proved that for memoryless vector channels, maximizing the mutual information over all source distributions with a certain average power or over the larger set of source distributions with upperbounded average power yields the same channel capacity in both cases. Hence, the channel capacity cannot decrease with increasing average transmitted power, not even for channels with severe nonlinear distortion.