Channel identification with Doppler and time shifts using mixed training signals

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. These two parts may be separated in either the time or the frequency domain. We provide a necessary and sufficient condition on the channel identifiability 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. Some numerical examples are also presented