Channel identification in the presence of doppler using mixed training signals

Channel identification in the presence of Doppler is not as well studied as channel identification that is free from Doppler due to the difficulty caused from the time-varying characteristics of the channel. In this paper, we present a method to identify channels with both Doppler and time shifts using mixed training signals. The training signals we use consist of two parts, where one part is a constant and the other part is a conventional training signal, such as a pseudo-random signal or a chirp signal. These two parts in a training signal may be separated either in the time domain or in the frequency domain. The constant signal part is used to identify the Doppler shifts, and the other part is used to identify the time shifts. The corresponding multipath amplitude coefficients and the synchronization between the Doppler shifts and time shifts are identified using both parts. We provide a necessary and sufficient condition on the channel identiflability in terms of the time and Doppler shifts when the mixed training signals are used. It can be shown that the condition holds almost surely in most cases of interest in practice. To prove the results, the concept of cycles for the Doppler and time shifts is introduced. Finally, some simple numerical examples are presented.