On Capacity of Frequency Non-Selective Slowly Time-Varying Fatling Channel

We consider a frequency non-selective slowly time-varying Rayleigh fading code-division multiaccess (CDMA) additive white Gaussian noise (AWGN) channel. Assuming that the signature waveforms are time-limited to the symbol interval, we find the capacity region of the two-user symbol-synchronous channel. If the signature waveforms span several symbol intervals, we have to further assume that the fading process is constant over the duration of every codeword. In that case, we find the capacity and the optimal input power spectral density (PSD) in a parametric expression similar to that in the classical water-filling argument.