Statistical estimates of phase errors of passive wireless saw sensors employing differential measurement

Summary form only given. Passive wireless surface acoustic wave (SAW) sensors are used to measure temperature, pressure and torque, identify the railway vehicle at high speed, etc. with a resolution of about 1%. Most frequently, the information bearer in such sensors is a time delay of the SAW estimated at the receiver. The basic principle utilized in such a technique combines advantages of the precise piezoelectric sensors, high SAW sensitivity to the environment, passive (without a power supplied) operation, and wireless communication between the sensor element and the interrogator. In this report, we address a statistical analysis of the estimate errors of the time delay (phase difference) between two reflectors of the passive wireless surface acoustic wave (SAW) sensor. The estimation is provided in a sense of the maximum likelihood function at coherent receiver in presence of Gaussian noise. Assuming the Gauss shape interrogating radio frequency (RF) pulse, we bring an important proof that the first time derivatives of its amplitude and phase do not affect the sensor phase (and phase difference) at the receiver. Rigorous and approximate relations for the mean error and mean square error (MSE) along with the probability for the estimate error to exceed a threshold are derived and studied in detail. The plots to evaluate the errors in a wide range of signal-to-noise ratios (SNRs) and thresholds are given. Practical findings for designers of the SAW sensor systems exploiting differential measurement are also pointed out.