Abstract: A message format and associated method for estimating the frequency and timing offset of a reference burst of a random access channel in a time-division multiple access communications system. A signal structure in which the continuous wave segment is split into two parts separated by some portion of the content of the random access channel burst is used to provide more precise frequency estimation. Iteration of separate frequency and timing estimation procedures is used to refine both estimates, as the individual estimation processes are more accurate when there is less error in the other parameter. Multiple hypothesis testing is used, in which more than one initial frequency estimate is carried through the iteration process, with thresholding to identify the best frequency offset. Reliable rejection of false ambiguities is achieved because the degradation in timing estimation, due to large frequency offsets, can be detected with thresholding.