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In order to solve the problem of the OFDM broadband signal processing, this paper introduced a algorithm for the direction of arrival (DOA) estimation of OFDM signal based on the wideband signal covariance matrix sparse representation. It averaged the triangle elements in the lower left corner of the main diagonal of the covariance matrix to form a new vector, and wrote the vector in the form of a redundant dictionary. The signal in a redundant dictionary the sparsity constraints formed a second-order cone constrained optimization problems, and then used toolbox SeDuMi to do DOA estimation. Theoretical analysis and simulation results show that the proposed method is an effective wideband signal DOA estimation algorithm and has high resolution in low signal-to-noise ratio and less number of snapshots, it is better than higher order cumulant algorithm and wideband focused matrix algorithm DOA estimation method. [ABSTRACT FROM AUTHOR]