  Many communication applications incorporate event-triggered behavior, where
the conventional Shannon capacity may not effectively gauge performance.
Consequently, we advocate for the concept of identification capacity as a more
suitable metric for assessing these systems. We consider deterministic
identification codes for the Gaussian AWGN, the slow fading, and the fast
fading channels with power constraints. We prove lower bounds on capacities for
the slow and the fast fading channels with side information for a wide range of
fading distributions. Additionally, we present the code construction with
efficient encoding which achieves the lower bound on capacity both for the slow
and the fast fading channels. At last, we prove the same lower bound on the
capacity of the fast fading channel without side information, i.e. the same
lower bound holds even when the receiver doesn't know the fading coefficients.
As a result we show that compared with Shannon's message transmission paradigm
we achieved completely different capacity scaling for deterministic
identification codes for all relevant fading channels.
