The proposed scheme offers a promising way to study the effect of modulated relativistic electron beam in a periodic plasma channel (wiggler). The fluid equations model is used to find out the numerical behaviour of the radiation wave. In this scheme, a modulated relativistic electron beam makes possible to generate and amplify the high power terahertz (THz) radiation pulses. Using this model, we have analyzed and calculated the nonlinear dispersion relation of the radiation wave. The radiation frequency of THz wave can be tuned by varying the wiggler wavelength and beam energy. The excitation of the radiation wave is being developed with the resonance between the modulated frequency of electron beam and radiation wave in the periodic plasma channel (wiggler field) via Cerenkov interaction along the axial direction of channel, which provides the maximum enhancement in the growth rate of the radiation wave. Additionally, the growth rate of the unstable mode of the radiation wave depends on beam energy and modulation index, and becomes larger as modulation index approaches unity.