Time Reversal Study

Abstract

In this chapter we will examine ways to determine the input signal of a receiver from the receiver's output signal using a time reversal filter. The input signal is usually measured by a receiver, which will distort the input signal. Assuming that receiving system is a linear system, then its output information represents the input signal modified by the receiving system's impulse response. To compensate for the impact of the receiving system on the input signal, the impulse response of the receiving system is used to design a time reversal filter. The time reversal filter can compensate for signal distortion caused by the receiving system, thus restoring the input signal. In most applications the input information is of interest, and by knowing the impulse function of the receiving system, the input signal can be obtained. The time reversal filter was first proposed for acoustics [1, 2] and is widely used in communications [3-6]. In this chapter we will demonstrate how the time reversal filter can expedite the calibration of an angle of arrival (AOA) system in which the information of the input signal is used to find the angle information on the signal. Since an impulse function is difficult to generate in a laboratory environment, chirp signals can be used as an alternative to determine the impulse response. Based on the impulse response, a time reversal filter can then be determined and used to find the input signal. The impact of the chirp signal on the performance of the resulting time reversal filter is investigated in this chapter. The concept of fractional time delay, which delays the time less than the sampling period, is also discussed. This concept is important for calibrating an AOA measurement system.