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A coupled mode space approach within the nonequilibrium Green's function formalism is presented, which allows performing simulations of realistic carbon nanotube field-effect transistors (CNT-FETs) with no spatial symmetry. Computing time is significantly reduced with respect to the real space approach, since only few modes are needed in order to obtain accurate results. The advantage of the method increases with increasing nanotube diameter, and is a factor of 20 in computing time for a (25,0) nanotube. As a consequence, computationally demanding simulations like those required by a statistical investigation, or by a device performance study based on the exploration of the design space, become more affordable. As a further test of the method, we have applied the coupled mode space approach to double-gate CNT-FETs devices and devices with discrete distribution of doping atoms. In the latter case, nonballistic transport due to elastic scattering with ionized impurities in doped source and drain extensions occurs. We show that even in the case of very rough potential, the coupled mode space approach is accurate with very few modes, enabling atomistic simulations of statistical properties with reduced computational resources.