Owing to the need of high-directivity radiation in fix-point communication, this thesis designs the metamaterial with 4-fold rotational symmetric unitcells. Using their nearing-zero refractive index along two polarizations, we can get gain-enhanced antenna radomes and place them above dual- and circular-polarized antenna to verify our idea. It is known that the group delay variation in a communication system causes the degradation of symbol error rate, and positive group delay (GD) causes delay in signal propagation. Therefore, this research studies the negative group delay (NGD) behavior of metamaterial. Through analyzing the GD of metamaterial equivalent circuit caused by poles and zeros, we design a novel NGD bandpass circuit. Furthermore, this thesis develops graphic method for group delay investigatiion and study the relationship between NGD, loss and gain in order to simplify the design of GD compensation circuit.