## 4 Simulation Experiments
When CFAR detection was performed using data processed by standard LCMV with \(\mathbf{w}\), it was found that the number and location of targets could not be accurately obtained and the detection was ineffective (as shown in Figures 7b and 8b). In addition, the CFAR detection results of the data processed by the MIMO-based method are shown in Figures 7c and 8c. Although the corresponding detection results improved compared with the LCMV, the detection performance was still worse than the S-LCMV and it was difficult to accurately reflect the real situation of the casing changes. It should be noted that the detection results of CFAR based on S-LCMV were highly consistent with the actual pipeline damage locations, but there was still a certain degree of deviation from the actual because a known statistical distribution of noise is required to be assumed in typical radar systems, which may not be applicable to borehole casing. The above results validate that the CFAR is suitable for pipeline damage location detection, and the design of an improved CFAR detector to accurately detect both the number and location of targets in borehole application will be the focus of our future work. Figure 6: Weighted induced EMFs of an 8-receiver linear multicoil array at an early time. (**a**) S-LCMV; (**b**) LCMV; (**c**) MIMO; (**d**) DL. Figure 8: CFAR results of target detection at an early time. (**a**) S-LCMV; (**b**) LCMV; (**c**) MIMO. Figure 7: CFAR results of target detection at the late time. (**a**) S-LCMV; (**b**) LCMV; (**c**) MIMO. As a result of the above analyses, the S-LCMV algorithm is conducive to obtaining accurate detection results in practical applications, which can reduce the calculation cost in the signal processing process and effectively improve the inspection efficiency and accuracy. In practical applications, the proposed method may face some challenges due to the complexity and uncertainty of the downhole environment. On the one hand, when the downhole physical space is very limited and the number of array elements is required to be further reduced, the corresponding reduction in the value of \(K\) may make the model approximation error too large due to the small stage of the Legendre polynomials, resulting in unreliable detection results. In this case, further exploitation of the sparsity of PEC signals can be considered to introduce emerging signal processing techniques such as a compressive sensing method with dimensionality reduction properties to ensure detection performance, which will be thoroughly investigated as a new research direction in future work. On the other hand, the multi-layer cylindrical structure involves numerous structural and electromagnetic parameters, while the uncertainties in the downhole environment make it difficult to ensure the accuracy of these parameters, which in turn affects the effectiveness of the proposed method. To decrease the sensitivity of the proposed method to the errors of the background medium parameters, in future research, we will consider integrating some cumulant algorithms to achieve adaptive weighting, thus further improving the robustness of the method.