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We propose and experimentally demonstrate a novel method to enhance the performance of the Brillouin optical correlation domain analysis (BOCDA) by analyzing the shape characteristic of the measured Brillouin gain spectrum. We theoretically analyze and simulate the operation of BOCDA, and it is found that the Brillouin signal peak generated at the correlation peak shows a sharp Lorentzian shape with a large value of convexity, while the background noise structure stacked from other positions shows a smooth trapezoidal shape with a small value of convexity. By extracting the convexity of measured BGS, the signal part can be enhanced while the noise part is suppressed drastically, which leads to an enlarged strain/temperature measurement range and a narrowed spatial resolution for BOCDA. This concept is verified by both numerical simulation and experiments. By using this method, a >16-mε/800-°C strain/temperature measurement range and a fivefold-improved spatial resolution are achieved experimentally without extra hardware complexity.