Wideband Source Enumeration Using Sparse Array Periodogram Averaging in Low Snapshot Scenarios

Abstract: 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.