  Multiple measurement vector (MMV) problem addresses the identification of
unknown input vectors that share common sparse support. The MMV problems had
been traditionally addressed either by sensor array signal processing or
compressive sensing. However, recent breakthrough in this area such as
compressive MUSIC (CS-MUSIC) or subspace-augumented MUSIC (SA-MUSIC) optimally
combines the compressive sensing (CS) and array signal processing such that
$k-r$ supports are first found by CS and the remaining $r$ supports are
determined by generalized MUSIC criterion, where $k$ and $r$ denote the
sparsity and the independent snapshots, respectively. Even though such hybrid
approach significantly outperforms the conventional algorithms, its performance
heavily depends on the correct identification of $k-r$ partial support by
compressive sensing step, which often deteriorate the overall performance. The
main contribution of this paper is, therefore, to show that as long as $k-r+1$
correct supports are included in any $k$-sparse CS solution, the optimal $k-r$
partial support can be found using a subspace fitting criterion, significantly
improving the overall performance of CS-MUSIC. Furthermore, unlike the single
measurement CS counterpart that requires infinite SNR for a perfect support
recovery, we can derive an information theoretic sufficient condition for the
perfect recovery using CS-MUSIC under a {\em finite} SNR scenario.
