Target velocity estimation with FM and PW echo ranging Doppler systems I. Signal analysis

The theoretical foundation is presented for velocity estimation with a pulsed wave (PW) Doppler system transmitting linear FM signals. The Doppler system possesses echo ranging capabilities and is evaluated in the context of Doppler ultrasound for blood velocity measurement. The FM excitation signal is formulated and the received signal is derived for a single moving particle. This signal is similar to the transmitted signal, but with modified parameters due to Doppler effect and range. The demodulated received signal is subsequently derived and analyzed. It is shown that, due to the Doppler effect, this is a linear sweep signal as well. The velocity and range information obtainable from one and two consecutively received signals are described. The latter case establishes the basis for an FM Doppler system for blood velocity measurements.