A Fractional Fourier Transform Stepwise Simplification Algorithm for Wireless Signal Detection

Linear frequency modulation wireless signals can achieve good signal energy-focusing effect in specific time–frequency domains while shielding out interference signals mixed in the time domain. This characteristic can bring considerable improvements to wireless signal detection. Based on the mathematical theory of fractional Fourier transform, this paper proposes a pipelined stepwise simplification algorithm. The fractional Fourier transform is performed in three steps, such as a linear multiplication followed by a linear convolution and linear multiplication, and the committed step are analyzed. Compared to algorithms based on mathematical theory, the proposed algorithm is suitable for discrete signal sampling sequence operations and simplified for detection purposes. Its algorithm complexity is reduced to O (NlogN), solving the bottleneck problem of algorithm application. The effectiveness of the algorithm was verified through simulation, indicating that the research results are suitable for designing linear frequency modulation transmission and signal detection.