  The simultaneous orthogonal matching pursuit (SOMP) is a popular, greedy
approach for common support recovery of a row-sparse matrix. However, compared
to the noiseless scenario, the performance analysis of noisy SOMP is still
nascent, especially in the scenario of unbounded noise. In this paper, we
present a new study based on the mutual incoherence property (MIP) for
performance analysis of noisy SOMP. Specifically, when noise is bounded, we
provide the condition on which the exact support recovery is guaranteed in
terms of the MIP. When noise is unbounded, we instead derive a bound on the
successful recovery probability (SRP) that depends on the specific distribution
of the $\ell_2$-norm of the noise matrix. Then we focus on the common case when
noise is random Gaussian and show that the lower bound of SRP follows
Tracy-Widom law distribution. The analysis reveals the number of measurements,
noise level, the number of sparse vectors, and the value of mutual coherence
that are required to guarantee a predefined recovery performance.
Theoretically, we show that the mutual coherence of the measurement matrix must
decrease proportionally to the noise standard deviation, and the number of
sparse vectors needs to grow proportionally to the noise variance. Finally, we
extensively validate the derived analysis through numerical simulations.
