Propagation of radio occultation signals through the tropical lower troposphere with severe refractivity gradients results in significant spreading of the signal spectrum. Under such conditions a signal acquisition technique which tracks large random troposphere-induced phase accelerations more reliably than a generic phase-locked loop has to be applied. This paper discusses the results of simulations of open loop tracking of radio occultation signals that were generated with data from high-resolution tropical radiosondes. The signal has to be down-converted in real time in the receiver on orbit to a low mean residual frequency by use of a phase (Doppler) model based on predicted orbits and refractivity climatology. The down-converted complex signal is then low-pass filtered and sampled. The phase in excess of the phase model must be reconstructed from the sampled and down-linked signal in postprocessing. This may require an additional down-conversion to eliminate (minimize) aliasing of harmonics in the spectrum. Then the accumulated phase can be reconstructed by resampling the signal at a higher rate to resolve the cycle ambiguities. A fast algorithm for prediction of the Doppler based on the refractivity climatology and an algorithm for the detection of Doppler mismodeling based on sliding window spectral analysis of the down-converted signal are developed and tested. The accuracy of the Doppler modeling, ±(15-20) Hz, the required filter bandwidth, 100 Hz, and the sampling rate, 50-100 Hz, are estimated.