Abstract: First-order steerable differential microphone arrays offer many advantages,such as small size,steerable mainlobe orientation,frequency-invariant array response,and have received much interest in the field of audio processing.However,differential microphone arrays are highly sensitive to microphone mismatches,which needs to be considered in practical design.As an important performance measure in array design,the front-to-back ratio directly characterizes the ability of a microphone array to suppress spatial noise and interference from the rear of microphone array.This paper studies the effects of microphone mismatches on the front-to-back ratio of the first-order steerable differential microphone array,and some properties are revealed.Based on the theoretical analysis,a worst-case optimization algorithm is proposed in the presence of random microphone mismatches.Simulations and real-world experiments are conducted to verify the correctness of the theoretical analysis and the effectiveness of the proposed optimization design method.