Hopefully your N effects number is not too big! This seems ripe for using mediation analyses and visualizing in within structural equation modeling.

You can construct a path analysis that shows the effect each has on the signal loss and also incorporation of the correlation. This visualization will help you write out the process in mathematic terms, where you may state the total effects, natural direct effects, and natural indirect effects. Unsure how the covariances may get incorporated (not experience with that), but that can be seen if you draw out the illustration.