This paper investigates the impact of array switching patterns on the accuracy of parameter estimation of multipath components for a time division multiplexed (TDM) channel sounder. To measure fast time-varying channels, the conventional uniform array switching pattern poses a fundamental limit of the number of antennas that a TDM channel sounder can utilize. We propose a method, which is based on the simulated annealing algorithm, to find non-uniform array switching patterns for realistic antenna arrays, so that we can extend the Doppler estimation range of the channel sounder by suppressing the high sidelobes in the spatio-temporal ambiguity function. Monte Carlo simulations demonstrate that the optimal switching sequence leads to significantly smaller root mean square errors of both direction of departure and Doppler. Results can be applied in both vehicle-to-vehicle and mobile millimeter wave MIMO channel measurements.