Truncation-noise characteristics of finite-length M-sequence

Abstract

The coding of a transmitted signal by a maximum-length sequence (M-sequence) is employed in the pulse-echo method with pulse compression for ultrasonic distance measurement. To estimate the distance, the time of flight (TOF) of an echo is determined from the cross-correlation function between the received signal and the reference signal that corresponds to the transmitted signal. When codes of the received signal and the reference signal match, a high correlation value is obtained in the cross-correlation function. On the other hand, when they do not match, a low correlation value is obtained. In the case of the finite-length M-sequence code, however, truncation noise is generated at the beginning and end of the cross-correlation function. In this study, truncation noise in autocorrelation functions of all patterns of M-sequence codes is quantitatively evaluated from the 4th order to the 15th order. The peak amplitude and intensity of truncation noise vary depending on the patterns of M-sequence codes. Therefore, they can be reduced by selecting suitable M-sequence codes.