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Fixed broadband beamformers for speech applications using small-sized microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. This paper describes two procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors. The first design procedure optimises the mean performance of the broadband beamformer and requires knowledge of the gain and phase probability density functions, whereas the second design procedure optimises the worst-case performance by using a minimax criterion. Simulations with a small-sized microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.