Abstract
Fractional Fourier transform (FrFT) is a useful tool to detect linear frequency modulated (LFM) signal. However, the detection performance of the FrFT-based method will deteriorate drastically in underwater multi-path environment. This paper proposes a novel method based on time-reversal and fractional Fourier transform (TR-FrFT) to solve this problem. We make use of the focusing ability of time-reversal to mitigate the influence of multi-path, and then improve the detection performance of FrFT. Simulated results show that, compared to FrFT, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 8.75 dB. Lake experiments results indicate that, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 7.6 dB. The detection performance curves of FrFT and TR-FrFT detectors with simulated data and lake experiments data verify the effectiveness of proposed method.
Highlights
The linear frequency modulated (LFM) signal is a broadband signal and its bandwidth utilization is high
We propose a TR-Fractional Fourier transform (FrFT)-based method for LFM signal detection in the underwater multi-path environment
Considering time-reversal processing has the characteristics of energy focusing and compression, we propose a novel method based on time-reversal and fractional Fourier transform (TR-FrFT) to detect LFM signal in this complex environment
Summary
The linear frequency modulated (LFM) signal is a broadband signal and its bandwidth utilization is high. In the underwater acoustic channel [16], due to multiple reflections from boundaries or scatters, the received signal can be viewed as the superposition of a number of amplitude-weighted and delayed replicas of the original emitted signal In this scenario, the FrFT of LFM signal has multiple peaks [17] in the optimal order fractional Fourier domain. We propose a TR-FrFT-based method for LFM signal detection in the underwater multi-path environment. The result shows that the finite-length LFM signal in the FrFT domain follows the sinc function distribution under the condition that the rotation angle is αopt = arccot(−μ), which is called the optimal rotation angle This indicates that the LFM signal has its energy concentrated in the optimal order fractional Fourier domain, where the optimal order popt = 2αopt/π.
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