  This paper presents a performance analysis of the MUltiple SIgnal
Classification (MUSIC) algorithm applied on $D$ dimensional single-snapshot
spectral estimation while $s$ true frequencies are located on the continuum of
a bounded domain. Inspired by the matrix pencil form, we construct a D-fold
Hankel matrix from the measurements and exploit its Vandermonde decomposition
in the noiseless case. MUSIC amounts to identifying a noise subspace,
evaluating a noise-space correlation function, and localizing frequencies by
searching the $s$ smallest local minima of the noise-space correlation
function.
  In the noiseless case, $(2s)^D$ measurements guarantee an exact
reconstruction by MUSIC as the noise-space correlation function vanishes
exactly at true frequencies. When noise exists, we provide an explicit estimate
on the perturbation of the noise-space correlation function in terms of noise
level, dimension $D$, the minimum separation among frequencies, the maximum and
minimum amplitudes while frequencies are separated by two Rayleigh Length (RL)
at each direction. As a by-product the maximum and minimum non-zero singular
values of the multidimensional Vandermonde matrix whose nodes are on the unit
sphere are estimated under a gap condition of the nodes. Under the 2-RL
separation condition, if noise is i.i.d. gaussian, we show that perturbation of
the noise-space correlation function decays like
$\sqrt{\log(\#(\mathbf{N}))/\#(\mathbf{N})}$ as the sample size
$\#(\mathbf{N})$ increases.
  When the separation among frequencies drops below 2 RL, our numerical
experiments show that the noise tolerance of MUSIC obeys a power law with the
minimum separation of frequencies.
