In detailed balance model, the efficiency of single-junction solar cells can be potentially as high as 33.5% under AM 1.5G illumination. However the best state-of-the-art devices are still far lower than those figures, even the electronic quality is nearly perfect. Therefore the efficiency gap should stem from the light management inside solar cells. Recently, external radiation efficiency (ηext) derived from detailed balance model is emphasized to evaluate light management and photon recycling, which aggregates the loss of backward emission into substrate and non-radiative recombination. This factor can be highly relevant to the cell's performance, especially open-circuit voltage (Voc), and maximizing Voc is generally considered as the last mile to approach ultra-high efficiency limit. In this work, we try to quantify the Voc enhancement in GaAs solar cells by enhancing light extraction. The simulation tools are RCWA simulation and photon recycling model NREL developed recently. The top structures we simulate here are TiO2 cones arranged in three PC/QPC lattices. After our calculation, the QPC 12-folds symmetry can make the biggest Voc enhancement 11.21meV compared with bare one, and the structure also possess extraordinary omni-directional anti-reflection ability for maintaining high Jsc. Our results also show that using this way to enhance Voc is especially suitable for cells with ordinary material quality. Therefore, the requests of ideal top structures for solar cell's use are not only near-perfect anti-reflection, but the ability to maximize light extraction if no feature of angular filter exists.