  In this paper, we generalize the fundamental relation between the mutual
information and the minimum mean squared error (MMSE) by Guo, Shamai, and Verdu
[1] to K-User Gaussian channels. We prove that the derivative of the multiuser
mutual information with respect to the signal to noise ratio (SNR) is equal to
the total MMSE plus a covariance term with respect to the cross correlation of
the multiuser input estimates, the channels and the precoding matrices. We shed
light that such relation is a generalized I-MMSE with one step lookahead and
lookback, applied to the Successive Interference Cancellation (SIC) in the
decoding process.
