This work provides analytical results on the canonical correlation analysis (CCA) of data sets from two spatially separated arrays of sensors. Our case studies cover both single source and multiple source signals in either white or colored noise fields for array signal processing. We derive analytical expressions of the canonical correlation for these examples and present a computer simulation analysis of empirical canonical correlations as a function of nominal correlation, signal-to-noise ratio (SNR), and sample support. Results obtained reveal an interesting fact that the canonical coefficients from CCA provide reliable information on the spatial correlation existing among data sets from two arrays only when the SNRs at both arrays are reasonably high. When sample correlation matrices (SCM) are used in the empirical CCA, reliable correlation can be estimated from CCA asymptotically (either at high SNRs from both arrays, or with a large number of snapshots in comparison with array dimensionality).