## 1 Introduction  
Ultrasonic guided wave (UGW) testing is a promising nondestructive testing method that affords low attenuation, high propagation velocity and high accuracy, and it can be utilised for high-efficiency, non-contact, long-distance and large-scale detection of a pipeline [1, 2]. There are two inherent characteristics of dispersion and multi-mode in UGW, which are manifested in the fact that UGW velocity varies with the frequency and the geometry of the waveguide, and multiple modes of UGWs exist at a given frequency [3]. When a UGW propagates in a waveguide, it travels in various modes: longitudinal L(0,\(m\)), torsional T(0,\(m\)) and flexural F(\(n\),\(m\)), where \(n\) and \(m\) denote circumferential order and module [4]. The ideal axisymmetric modes L(0,2) and T(0,1) in their non-dispersive regions are preferred in UGW testing for reducing the interpretation complexity of the detection signal, where L(0,2) UGWs with high propagation velocity are more sensitive to circumferential defects compared with those of the T(0,1) UGW [5]. The pure UGW with desired mode is difficult to be excited singly, where UGWs with undesired modes can also be excited for the imperfect experimental conditions and multi-mode characteristics, and the mode conversion may be caused when the UGW with the desired mode encounters asymmetric defects, of which flexural UGWs may arise [6]. The wave packets of UGWs with desired, undesired and flexural modes may be overlapped for the difference in the propagation velocity, indicating that signal energy spreads out over time and space domain, and it is not conducive to UGW testing interpretation on account of the low signal resolution [7, 8]. [PERSON] et al. [7] refer to UGWs other than the desired mode as coherent noise. There are some studies using pulse compression (PuC), which increases the excitation energy while modulating the signal, to improve the signal resolution, and the received signal is extracted by cross-correlation with an excitation signal [9]. [PERSON] et al. [10] studied the modulation effects of Chiript, Barker and Golay codes with a small main lobe width and found that the SNRs (Signal to Noise Ratios) after modulation by the above three methods were significantly higher than those using a Hanning window sinusoidal signal. [PERSON] et al. [11] proposed a hybrid coding excitation method using the convolution of the Barker and Golay code, and the results showed a significant improvement in SNR and peak sidelobe levels to approximately 32 dB and approximately \(-\)24 dB, respectively. However, PuC requires the design of excitation waveform, the performance of optimal excitation sequence depends on the detection conditions and the elimination of coherent noise is limited [12]. Dispersion compensation (DC) is another signal processing method commonly applied in UGW testing, where the coherent noise can be eliminated by reversing the effect of dispersion and multi-mode on the desired mode UGW in the time/space domain [13]. [PERSON] et al. [14] obtained UGW signals through an original 64-element phased array, extracted wavenumber and spectrum analysis coherent noise, used [PERSON]'s electromechanical reciprocity relationship and variational method to extract mode contributions and finally used a dispersion compensation method to eliminate the coherent noise. On the basis of DC, [PERSON] et al. [15] proposed two wideband Lamb wave time-frequency dispersion analysis methods: time-frequency compensation transform and time-frequency de-dispersion transform, and the results show that both methods can obtain high-resolution Lamb wave signals. However, DC requires a priori knowledge of dispersion and propagation distance, which is often difficult to know in the UGW testing of long-distance pipelines and unknown pipeline structures [16].