Limiting phase errors of passive wireless SAW sensing with differential measurement

This paper addresses a statistical analysis of the limiting estimate errors of the time delay (phase difference) between two reflectors of the passive wireless surface acoustic wave (SAW) sensor with single differential measurement. The estimation is provided in a sense of the maximum likelihood function at the ideal coherent receiver in the presence of Gaussian noise. Assuming the Gauss-shape interrogating radio frequency pulse, we prove that linear drifts in its amplitude and phase do not affect the distribution of the sensor phase (and phase difference) at the measurement point. Rigorous and approximate solutions for the mean and mean-square errors, along with the error probability for the estimate to exceed a threshold, are studied in detail. The plots are applied to evaluate the errors in a wide range of signal-to-noise ratios and thresholds. Practical recommendations for designers of the remote SAW sensor interrogating systems are also given.