Effect of sample window length on the correlation between RF signal and pulsed Doppler signal intensity

Ultrasound pulsed Doppler systems, as used in medical applications, are based on the detection of the phase difference between a reference signal and the received radio frequency (RF) signal averaged over the sample window. Thereby, it is implicitly assumed that the phase of the received signal will increase linearly with depth. However, the ultrasound signal originates from particles with a random spatial distribution. Therefore, it may be anticipated that the accuracy of the estimate for the phase difference will not improve by elongating the sample window. To test this hypothesis, simulated random phase RF signals with various bandwidths were subjected to demodulation using a rectangular observation window of different lengths. It is concluded that the correlation coefficient between RF intensity and Doppler intensity goes down for long sample windows. Moreover, the coefficient of variation of the estimate for the intensity of the received signal decreases for an increasing length of the observation window. The variation coefficient of the Doppler amplitude remains very close to one for all signal and processing conditions. These observations demonstrate that for Doppler signal amplitude assessment, the effect of the length of the observation window should be taken into account.