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This paper focuses on direction-of-arrival (DOA) estimation of wideband signals, and a method named wideband covariance matrix sparse representation (W-CMSR) is proposed. In W-CMSR, the lower left triangular elements of the covariance matrix are aligned to form a new measurement vector, and DOA estimation is then realized by representing this vector on an over-complete dictionary under the constraint of sparsity. The a priori information of the incident signal number is not needed in W-CMSR, and no spectral decomposition or focusing is introduced. Simulation results demonstrate the satisfying performance of W-CMSR in wideband DOA estimation in various settings. Moreover, theoretical analysis and numerical examples show how many simultaneous signals can be separated by W-CMSR on typical array geometries, and that the half-wavelength spacing restriction in avoiding ambiguity can be relaxed from the highest to the lowest frequency of the incident wideband signals.