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In this paper, we investigate robust design methods for broadband beamformers in reverberant environments. In the design formulation room reverberation as well as robustness to amplitude and phase mismatches in the microphones have been included. Particularly, the direct path and the reflections are separated in the design such that there is a penalty on the reflective part. This approach is different from the commonly studied problem of dereverberation of a single point source as the investigated design is made over a region in space. A single point derverberation is not a very practical approach due to a high sensitivity to position changes. Thus in order to obtain more practical microphone array designs, we study methods that optimize performance over areas in space. The design problem has been formulated in four different ways; (i) using direct path only representing a traditional beamformer design method, (ii) using a robust design method which considers robustness against the microphone characteristics (gain and phase) by optimizing the mean performance, (iii) by including room impulse response in the design and finally, (iv) using both robustness and room impulse response in the design. Simulation results show that robust direct path based beamformer can achieve approximately the same performance as including room response in the design in many reverberation environments. The proposed method provides robustness over larger variations in the reverberation environment. This means that the robust direct path based method which is based on mean variations in gain and phase can be used in low- to medium ( $$T_{60}$$ T 60  = 100–300 ms) reverberant environments with good result.

Robust broadband beamformer design for noise reduction and dereverberation