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By using surrounding periodic second-uniplanar compact electromagnetic bandgap (UC-EBG) ground plane, a microstrip patch antenna working at X-band with low radar cross-section (RCS) and high performance was designed. The main parameters such as return loss, impedance bandwidth, RCS, radiation patterns and gains are presented and discussed. Comparison of the patch antenna with the surrounding periodic second-UC-EBG ground suggests that the second-UC-EBG has much lower RCS than the standard patch antenna at a band range 2-18 GHz. In addition, gain, bandwidth and radiation patterns of the former are all improved when compared with those of the latter.