The fractional Fourier transform (FRFT) method has emerged in response to the demand for high-performance time-frequency\nprocessing technology. Next, the weighted fractional Fourier transform (WFRFT) method was developed, especially the\nsingle-parameter 4-weighted fractional Fourier transform (SP-4-WFRFT), which is most suitable for applications in digital\ncommunication systems. Therefore, in receiving systems, research on the scanningmethod of transformation order has also become\nthe focus of research under the condition of unknown transformation order. However, in the process of inverse transformation,\nthere are many problems, such as long scanning times and slow scanning speed. Thus, to improve the characteristics of a digital\ncommunication system based on SP-4-WFRFT, a cross-hierarchical scanning (CHS) method is established. A large number of test\nresults show that the CHS method can achieve fast recovery of data and estimation of transformation order.
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