  This paper proposes two coherent broadband focusing algorithms for spatial
correlation estimation using sparse linear arrays. Both algorithms decompose
the time-domain array data into disjoint frequency bands through discrete
Fourier transform or filter banks to obtain broadband frequency-domain
snapshots. The periodogram averaging (AP) algorithm starts in the frequency
domain by estimating the broadband spatial periodograms for all bands and then
averaging them to reinforce the sources' spatial spectral information. Taking
inverse spatial Fourier transform of the combined spatial periodogram estimates
the focused spatial correlations. Alternatively, the spatial correlation
resampling (SCR) algorithm directly computes the spatial correlations for each
band and then rescales the spatial sampling rate to align at a focused
frequency. The resampled spatial correlations from all frequency bands are then
averaged to estimate the focused spatial correlations. The spatial correlations
estimated from the AP or SCR algorithms populate the diagonals of a Hermitian
Toeplitz augmented covariance matrix (ACM). The focused ACM is the input of a
new minimum description length (MDL) based criteria, termed MDL-gap, for source
enumeration and the standard narrowband MUSIC algorithm for DOA estimation.
Numerical simulations show that both the AP and SCR algorithms improve source
enumeration and DOA estimation performances over the incoherent subspace
focusing algorithm in snapshot limited scenarios.
