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On the achievable rate of stationary Rayleigh flat-fading channels with Gaussian input distribution

For a Gaussian input distribution, we investigate the achievable rate of a stationary Rayleigh flat-fading channel under the assumption of unknown channel state information at transmitter and receiver side. The law of the channel is presumed to be known to the receiver. In addition, we assume the power spectral density of the fading process to be compactly supported. The contribution of the present paper is the derivation of an upper bound on the achievable rate for the special case of a rectangular power spectral density depending on the SNR and the spread of the power spectral density. For comparison, we also give a lower bound on the achievable rate which is already known from and holds for an arbitrary power spectral density.