The invention relates to an improved process and system for the synthesis of dimethyl ether (DME) from a feedstock comprising H2 and COx, wherein x=1-2. The process according to the invention comprises (a) subjecting the gaseous mixture comprising synthesis gas originating from step (c) to DME synthesis by contacting it with a catalyst capable of converting synthesis gas to DME to obtain a gaseous mixture comprising DME; (b) subjecting a gaseous mixture comprising the gaseous mixture originating from step (a) to a separation-enhanced reverse water gas shift reaction; and (c) subjecting the gaseous mixture originating from step (b) to DME/synthesis gas separation to obtain DME and a gaseous mixture comprising synthesis gas, which is recycled to step (a). Herein, the feedstock is introduced in step (a) or step (b) and the molar ratio of H2 to COx in the gaseous mixture which is subjected to step (b) is at least (x+0.8). Also a system for performing the reaction according to the invention is disclosed.