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Spherical microphone arrays facilitate spatial analysis of sound fields. At the high frequencies the array performance is limited by spatial aliasing. In this paper we present a method to extend the bandwidth of the array through optimal aliasing cancellation. The advantage and novelty of the proposed method is that aliasing cancellation is achieved through signal processing without physically modifying configuration of the spherical microphone array. In this work we show that by taking into account the expected aliasing pattern with respect to the given array sampling scheme, a beamformer which suppresses the grating-lobes can be designed. This beamformer achieves a higher directivity-index at frequencies previously considered as out of the microphone array operating range, therefore increasing the overall frequency range of operation. A simulation example with a 32 elements spherical microphone array illustrate the proposed method.