  The use of multichannel data in line spectral estimation (or frequency
estimation) is common for improving the estimation accuracy in array
processing, structural health monitoring, wireless communications, and more.
Recently proposed atomic norm methods have attracted considerable attention due
to their provable superiority in accuracy, flexibility and robustness compared
with conventional approaches. In this paper, we analyze atomic norm
minimization for multichannel frequency estimation from noiseless compressive
data, showing that the sample size per channel that ensures exact estimation
decreases with the increase of the number of channels under mild conditions. In
particular, given $L$ channels, order $K\left(\log K\right)
\left(1+\frac{1}{L}\log N\right)$ samples per channel, selected randomly from
$N$ equispaced samples, suffice to ensure with high probability exact
estimation of $K$ frequencies that are normalized and mutually separated by at
least $\frac{4}{N}$. Numerical results are provided corroborating our analysis.
