On the pre-log of Gaussian fading relay channels

The capacity of additive white Gaussian noise relay channels under Gaussian fading is investigated. The transmitter, the relay, and the receiver are all considered to be ignorant of the fading realizations. Capacity upper and lower bounds are derived with focus on the capacity pre-log, i.e., the limiting ratio of the capacity to the logarithm of the signal-to-noise ratio. Conditions are presented under which the upper and lower bounds on the capacity pre-log coincide