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.

Reciprocal acoustic transmission experiment at Mihara-Seto in the Seto Inland Sea, Japan

“…In many reciprocal transmission experiments, phase-modulated m-sequence signals have been used (transmitted) because of the high autocorrelation property of m-sequences, which is maximized when the m-sequences have periodicity (e.g., [7]). However, when one period of an m-sequence is transmitted, artifacts or truncation noise is generated at the beginning and ending of the correlated signal (e.g., [8]). Thus, in many studies, more than three periods of an m-sequence are transmitted, and the resulting correlation corresponding to the first and last periods of the m-sequence is discarded (e.g., [9]).…”

“…Indeed, truncation noises of one period of a higher-order m-sequence become smaller [8]. However, it is still good practice to use m-sequences as if the transmitted m-sequence signal has periodicity.…”

Ultrasonic position and velocity measurements for a moving object by the simultaneous transmission of preferred-pair M-sequences

“…In each cross-correlation function, there are three correlation peaks obtained by three-cycle transmission. To avoid the effect of truncation noise in M-sequence pulse compression, only echoes corresponding to the second M-sequence are considered [21]. Therefore, each cross-correlation function after 61.41 ms is used for subsequent processes.…”

Measurement of road surfaces by reflection characteristics of airborne ultrasound

“…To improve the signal-to-noise ratio (SNR) of the echo, pulse compression using a maximum-length sequence (Msequence) was employed [4,6,9,14,15]. An M-sequence is a pseudo-random binary code generated from a linear feedback shift register (LFSR).…”

“…There is truncation noise near the peaks caused by the 1st and 3rd cycles. Therefore, the peak caused by the 2nd cycle is used for measurement [15]. The wave around 20 ms is the echo that directly propagated from the loudspeaker.…”