Abstract: Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming. Firstly, a global optimization algorithm, which is based on phase compensation of the array manifolds, is used to construct the frequeney-invariant beampattern. Compared to some other methods presented recently, the proposed algorithm is not only available to get the global optimal solution, but also simple for physical realization. Meanwhile, a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix. The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon spectral estimator firstly, then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix, and finally calculate the adaptive beamformer weights with the reconstructed matrix. The design of beamformer is reformulated as a convex optimization problem. Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.