  This paper proposes a new sparse array source enumeration algorithm for
underdetermined scenarios with more sources than sensors. The proposed
algorithm decomposes the wideband signals into multiple uncorrelated frequency
bands, computes the narrowband spatial periodograms and then averages
periodograms to reinforce the sources' spectral information. The inverse
spatial Fourier transform of the wideband periodogram estimates the spatial
correlation function, which then populates the diagonals of a Hermitian
Toeplitz augmented covariance matrix (ACM) after lag redundancy averaging. A
modified minimum description length (MDL) criteria, termed MDLgap, is proposed
for source enumeration using the eigenvalues of the constructed ACM. MDLgap
provably never overestimates the number of sources present, and is
asymptotically consistent when the signals present span a limited dynamic
range. Numerical simulations show that the proposed MDLgap algorithm achieves
improved performance over existing approaches for underdetermined source
enumeration, especially in low snapshot scenarios.
