Reduction of Doppler estimation error by multi-frequency transmission

In this paper, after introduction of symmetric multi- frequency signal, it will be presented how to estimate Doppler frequency from estimated frequency tones of returned echo. After that, three methods of Pisarenko, Prony and MUSIC for frequency estimation will be introduced, and then these methods are applied to estimate tone frequencies of a multi-carrier signal. It will be shown that estimation of Doppler frequency by multi-frequency signal transmission leads to less rms error than single-frequency signal, in the condition of equal SNR. Infact it will be suggested that distribution of the power of signal in spectrum instead of adding up all the power in one point, leads to less Doppler estimation error. By increasing in the number of frequencies, the rms error of estimation can come completely close to Cramer-Rao lower bound.