  We present a novel closed-form lower bound on the Gaussian-input mutual
information for noncoherent communication (i.e., in which neither transmitter
nor receiver are cognizant of the fading state) over a frequency-flat fading
channel with additive noise. Our bound yields positive (non-trivial) values
even in the most challenging case of zero-mean fast fading, a regime in which
the conventional approach of orthogonal time-multiplexed pilots is unavailing
and for which, to the best of the author's knowledge, no simple analytical
bound is known. Its derivation relies on endowing the transmit signal with a
non-zero mean, which can be interpreted as a pilot symbol that is additively
superimposed onto the information-bearing Gaussian signal. The optimal fraction
of transmit power that one should dedicate to this pilot is computed in closed
form and shown to tend to one half at low SNR and to a limit above $2-\sqrt{2}
\approx 0.586$ at high SNR. We further show how one can refine the bound for
the general case of non-zero mean fading. Finally, we state an extension of our
bound to the MIMO setting and apply it to compare superimposed vs. orthogonal
pilots on the SISO Rayleigh block fading channel.
