A formula for the second-order expansion of the input-output
mutual information of multidimensional channels as the
signal-to-noise ratio goes to zero is obtained. While the
additive noise is assumed to be Gaussian, we deal with very
general classes of input and channel distributions. As special
cases, these channel models include fading channels, channels
with random parameters and channels with almost Gaussian noise.
When the channel is unknown at the receiver, the second term
in the asymptotic expansion depends not only on the
covariance matrix of the input signal but also on the fourth
mixed moments of its components. The second-order asymptotics of
mutual information finds application in the analysis of the
bandwidth-power tradeoff achieved by specific (not necessarily
optimum) input signaling in the wideband regime.
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