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The radiation characteristics of the omnidirectional periodic circular dielectric rod leaky-wave antenna with arbitrary grating profile are investigated by the network method combining with staircase approximation. In the analysis, the arbitrary grating profiles are transformed to a multilayer rectangular periodic structure, which is represented by a radial transmission line with a series current source. As a result, the calculations are greatly simplified and the effects of the grating profile on the performance of the grating antenna are systematically studied in a very efficient way. Some useful guidelines for the design and fabrication of the omnidirectional dielectric grating antenna are thereby suggested.