sensor while features that are common to multiple sensors are amortized. DCS led to a proliferation of research on the multi-measurement vector (MMV) problem [@chen2006trs; @cotter2005ssl; @Mishali08rembo; @Berg09jrmm; @LeeKimBreslerYe2011; @LeeBreslerJunge2012; @YeKimBresler2015]. The MMV problem considers the estimation of a set of sparse signal vectors that share common supports, and has applications such as radar array signal processing, acoustic sensing with multiple speakers, magnetic resonance imaging with multiple coils [@JuYeKi07; @JuSuNaKiYe09], and diffuse optical tomography using multiple illumination patterns. In MMV, thanks to the common support, the number of sparse coefficients that can be successfully estimated increases with the number of measurements. This property was evaluated rigorously for noiseless measurements using $l_0$ minimization [@DuarteWakinBaronSarvothamBaraniuk2013]. To address measurement noise, estimation approaches for MMV problems have included greedy algorithms such as SOMP [@tropp2006ass; @chen2006trs], $l_1$ convex relaxation [@malioutov2005ssr; @tropp2006ass2], and M-FOCUSS [@cotter2005ssl]. REduce MMV and BOost (ReMBo) has been shown to outperform conventional methods [@Mishali08rembo], and subspace methods have also been used to solve MMV problems [@LeeBreslerJunge2012; @YeKimBresler2015]. Statistical approaches [@ZinielSchniter2011] often achieve the oracle minimum mean squared error (MMSE). However, the performance limits of MMV signal estimation in the presence of measurement noise have not been studied.

Replica analysis is a statistical 