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Use of omni-directional microphones is commonly assumed in the differential beamforming with uniform circular arrays. The conventional differential beamforming with omni-directional elements tends to suffer in low white-noise-gain (WNG) at the low frequencies and decrease of directivity factor (DF) at high frequencies. WNG measures the robustness of beamformer and DF evaluates the array performance in the presence of reverberation. The major contributions of this paper are as follows: First, we extends the existing work by presenting a new approach with the use of the directional microphone elements, and show clearly the connection between the conventional beamforming and the proposed beamforming. Second, a comparative study is made to show that the proposed approach brings about the noticeable improvement in WNG at the low frequencies and some improvement in DF at the high frequencies by exploiting an additional degree of freedom in the differential beamforming design. In addition, the beampattern appears more frequency-invariant than that of the conventional method. Third, we study how the proposed beamformer performs as the number of microphone elements and the radius of the array vary.