Active control of noise propagating through apertures is commonly realized with closed-loop LMS algorithms. However, these algorithms require a large number of error microphones and provide only local attenuation. Slow convergence and high computational effort are additional disadvantages. We propose a wave-domain approach that converges instantaneously, operates with low computational effort and does not require error microphones. It inherently controls sound in all directions in the far-field. The soundfield from the aperture is matched in a least squares sense with the generated soundfield from the loudspeaker array using orthonormal basis functions. Compensation for algorithmic delay, induced by blockwise processing, can be based on microphone placement or signal prediction, at the cost of a loss in attenuation performance. Our simulation results indicate that wave-domain processing has the potential to outperform LMS-based methods in practical active noise control for apertures.