  We assume the direct sum <A> o <B> for the signal subspace. As a result of
post- measurement, a number of operational contexts presuppose the a priori
knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to
estimate the LA am- plitudes corresponding to subspace <A>. Taking into account
the knowledge of the orthogonal "interfering" subspace <B>\perp, the Bayesian
estimation lower bound is de-
rivedfortheLA-sparsevectorinthedoublyasymptoticscenario,i.e. N,LA,LB -> \infty
with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing
(CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for
the lower bound on the estimation of the non-zero entries of a sparse vector of
interest are derived and studied. The derived closed-form expressions enjoy
several interesting features: (i) a simple interpretable expression, (ii) a
very low computational cost especially in the doubly asymptotic scenario, (iii)
an accurate prediction of the mean-square-error (MSE) of popular sparse-based
estimators and (iv) the lower bound remains true for any amplitudes vector
priors. Finally, several idealized scenarios are compared to the derived bound
for a common output signal-to-noise-ratio (SNR) which shows the in- terest of
the joint estimation/rejection methodology derived herein.
