Using time domain reflectometry, the complex dielectric spectra between 10 MHz to 20 GHz has been measured in the whole composition range at 10, 20, 30 and $40^{circ}C$ for the binary mixtures of ethylene glycol and dimethyl sulfoxide. For all the mixtures, only one dielectric loss peak was observed in this frequency range. The relaxation in these mixtures can be described by a single relaxation time using the Debye model. A systematic variation is observed in dielectric constant (${varepsilon}_0$) and relaxation time (${ au}$). The excess permittivity (${varepsilon}^E$), excess inverse relaxation time $(1/{ au})^E$, Kirkwood correlation factor (g) and thermodynamic parameters viz. enthalpy of activation (${Delta}H$) and Gibbs free energy of activation (${Delta}G$) have been determined, to confirm the formation of hydrogen bonded homogeneous and heterogeneous cooperative domains, the dynamics of solute - solute interaction and the hindrance to molecular rotation in the hydrogen bonded glass forming ethylene glycol - dimethyl sulphoxide system.