MSE is greater than the predicted MSE; this is due to randomness in our generated signals and channels. Note that we also compared the AMP simulation results to that of the M-SBL algorithm [@YeKimBresler2015], a widely used algorithm to solve the MMV problem. The M-SBL results were not as good. Indeed, because AMP is often an achievable to the MMSE, other algorithms are expected to provide greater MSE.

Conclusion {#sec:conclusion}
==========

We analyzed the minimum mean squared error (MMSE) for two settings of multi-measurement vector (MMV) problems, where the entries in the signal vectors are independent and identically distributed (i.i.d.), and share the same support. One MMV setting has i.i.d. Gaussian measurement matrices, while the other MMV setting has identical i.i.d. Gaussian measurement matrices. Replica analyses yield identical free energy expressions for these two settings in the large system limit when the signal length goes to infinity and the number of measurements scales with the signal length. Because of the identical free energy expressions, the MMSE’s for both MMV settings are identical. By numerically evaluating the free energy expression, we identified different performance regions for MMV where the MMSE as a function of the channel noise variance and the measurement 