The cyclic shift characteristic of the circular array co-variance matrix was used to study the super-directivity theory of the circular array based on the optimization of the aggregation coefficient.The maximum aggregation coefficient,the optimal beam pattern and the optimal weighted vector expressed by elementary function were obtained.The beam gain and the robustness parameters of the circular array varying with the radius ratio,and their influence on the array directivity were analyzed.An analytic and closed solution of the super-directivity of the circular array was given,and a method for decomposing and synthesizing characteristic beams was realized.Based on the characteristics of the noise signal of the airborne sound source,four criteria that should be followed when designing the super-directional circular array for the noise of the airborne sound source were given.Based on the measured radiation noise characteristics of a helicopter,a small-scale,super-directional receiver array was designed,and its performance was analyzed. The superiority of it was proved by comparison with the conventional circular and linear arrays.