We generalize the fundamental relation between the derivative of the mutual information and the MMSE to multiuser setups. We prove that the derivative of the mutual information with respect to the SNR is equal to the MMSE plus a covariance induced due to the interference, quantified by a term with respect to the cross correlation of the multiuser inputs’estimates, their channels, and their precoding matrices. We provide such relations for conditional and non-conditional components of the multiuser mutual information.
Mutual information and minimum mean-square error in multiuser Gaussian channels
IEEE MMTC E-Letters, Special issue on Latest advances on Wireless and Mobile Communications and Networking, 2015
Systèmes de Communication
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