Interferometric synthetic aperture radar (InSAR) is a method which may provide a means of estimating global topography with high spatial resolution and height accuracy. The paper presents a derivation of the signal statistics, an optimal estimator of the interferometric phase, and the expressions necessary to calculate the height-error budget. These expressions are used to derive methods of optimising the InSAR-system parameters, and are then used in a specific design example for a system to perform high-resolution global topographic mapping with a one-year mission lifetime, subject to current technological constraints. Finally, a Monte Carlo simulation of this InSAR system is performed to evaluate its performance for realistic topography. The results indicate that this system has the potential to satisfy the stringent accuracy and resolution requirements for geophysical use of global topographic data.