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In this study, a novel fast wideband direction of arrival (DOA) estimation algorithm is proposed to reduce the computational complexity. First, a multiple measurement vector (MMV)-based compact structure for a wideband signal is established. Combined with the focus operation, the array manifolds of different frequency bins are transformed into the dictionary of the reference frequency. Then, two efficient novel methods named adaptive step-size-based null space tuning with hard thresholding and feedback (ASNHF) and MMV-ASNHF are proposed to process single measurement vector and MMV problem, respectively. Finally, wideband DOA estimation can be achieved by MMV-ASNHF algorithm. Compared with other algorithms, the proposed algorithm has higher accuracy at a low signal-to-noise ratio and lower computational complexity. Simulation results show that the proposed estimator is effective and feasible.