Abstract: An algorithm based on compressive sensing is proposed for direction finding with correlative interferometry. It decomposes the measurement vector of a correlative interferometer into a noise-contaminated sparse representation with respect to the database, and performs reweighted l₁-norm optimization to approximate the optimal l₀-norm optimization, which updates the weights iteratively. Compared with the conventional method of correlation coefficient maximization, the proposed algorithm accounts for the spatial sparsity of the emitters, which leads to its capability of direction finding of multiple signals of the same frequency. Simulated results have demonstrated the performance of the proposed algorithm.