  We study the excess mean square error (EMSE) above the minimum mean square
error (MMSE) in large linear systems where the posterior mean estimator (PME)
is evaluated with a postulated prior that differs from the true prior of the
input signal. We focus on large linear systems where the measurements are
acquired via an independent and identically distributed random matrix, and are
corrupted by additive white Gaussian noise (AWGN). The relationship between the
EMSE in large linear systems and EMSE in scalar channels is derived, and closed
form approximations are provided. Our analysis is based on the decoupling
principle, which links scalar channels to large linear system analyses.
Numerical examples demonstrate that our closed form approximations are
accurate.
