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This paper proposes two coherent broadband focusing algorithms for spatialcorrelation estimation using sparse linear arrays. Both algorithms decomposethe time-domain array data into disjoint frequency bands through discreteFourier transform or filter banks to obtain broadband frequency-domainsnapshots. The periodogram averaging (AP) algorithm starts in the frequencydomain by estimating the broadband spatial periodograms for all bands and thenaveraging them to reinforce the sources' spatial spectral information. Takinginverse spatial Fourier transform of the combined spatial periodogram estimatesthe focused spatial correlations. Alternatively, the spatial correlationresampling (SCR) algorithm directly computes the spatial correlations for eachband and then rescales the spatial sampling rate to align at a focusedfrequency. The resampled spatial correlations from all frequency bands are thenaveraged to estimate the focused spatial correlations. The spatial correlationsestimated from the AP or SCR algorithms populate the diagonals of a HermitianToeplitz augmented covariance matrix (ACM). The focused ACM is the input of anew minimum description length (MDL) based criteria, termed MDL-gap, for sourceenumeration and the standard narrowband MUSIC algorithm for DOA estimation.Numerical simulations show that both the AP and SCR algorithms improve sourceenumeration and DOA estimation performances over the incoherent subspacefocusing algorithm in snapshot limited scenarios.

Broadband Sparse Array Focusing Via Spatial Periodogram Averaging and Correlation Resampling