Research On Frequency Acquisition Algorithm Of Laser Heterodyne Interference Signal For Space Gravitational Wave Detection

Gravitational wave detection in space is based on laser heterodyne interferometry.And the gravitational wave signal is retrieved by calculating the distance change between different satellite test masses through phase measurement.The phasemeter is the payload for high-accuracy phase measurement.The phase change of laser heterodyne interference signal is measured by using a digital phase-locked loop(DPLL).Due to the high precision,difficulty,and noise associated with the measurement task,the laser heterodyne interference signal is complex and primarily consists of the main carrier beat-note,two sideband beat-notes,ranging communication coding,and various noises.The phases of the three beat-notes contain various information such as the distance change between spacecraft,clock jitter and clock noise.During laser propagation from one spacecraft to another,a Doppler shift occurs due to their relative motion.This shift causes a frequency offset in the three beat-notes,but the exact offset is unknown as the relative motion is also unknown.This frequency offset can prolong the locking time of the DPLL,and in some cases,result in incorrect locking or even failure to lock.Consequently,phase measurement errors may occur,leading to serious consequences.As a result,it is crucial to determine the frequency of the three beat-notes before conducting the phase measurement.Currently,in the field of space gravitational wave detection,two frequency acquisition algorithms are used for the main carrier beat-note.The first algorithm is based on the theory of Discrete Fourier Transform(DFT),which converts the time-domain signal into a frequency-domain representation using the Fast Fourier Transform(FFT)calculation method.However,the frequency estimation error is relatively large due to the resolution of the discrete spectrum,which is limited by the number of sampling points.To calculate the frequency corresponding to the spectral peak,a simple peak-finding algorithm is used.The second method is based on the discrete wavelet packet transform,as proposed by Filippo Ales and others.However,residual noise in the bandwidth measurement and processing chain can cause a significant frequency uncertainty.It’s important to note that these methods only focue on the frequency acquisition of the main carrier beat-note,and the two sideband beat-notes are not discussed.In various fields such as digital signal processing,satellite communication,and electronic power systems,the discrete spectrum correction method is widely used to achieve highly accurate frequency estimation.This calibration technique is based on traditional spectrum analysis,and it corrects and compensates for the discrete spectrum by analyzing and processing the frequency domain of the signal.By using this method,signal spectrum calibration and reconstruction are achieved,which improves the frequency resolution and spectrum accuracy of the signal and enhances the accuracy of frequency estimation.There are several discrete spectrum correction methods,including the window function method,interpolation method,direct calculation method,phase correction method,and amplitude correction method.This article combines the Doppler frequency shift effect with the DPLL principle to analyze the laser heterodyne interference signal,providing insight into the frequency acquisition requirements for space gravitational wave detection.The article derives a general expression for the multi-frequency main lobe function of the windowed signal using a discrete spectral correction algorithm and the energy centroid principle.Additionally,a high-precision multi-frequency acquisition algorithm for laser heterodyne interference signals is designed.To overcome the reduced frequency acquisition accuracy due to signal phase modulation ranging and noise,the article proposes a method that applies error integration to reduce the impact of noise and improve the accuracy and noise resistance of the frequency acquisition results.The paper covers research on the basic principles of space gravitational wave detection,signal models of laser heterodyne interference,DPLL principles,and the derivation of the windowed signal spectrum main lobe function.The article also analyzes ranging communication codes and the hardware platform design of frequency acquisition algorithms.Technologies such as the FFT algorithm,energy centroid algorithm,error integration,and Coordinate Rotation Digital Computer(CORDIC)algorithm are applied.This paper outlines the overall process of the FPGA-based frequency acquisition algorithm,building upon a key analysis of critical technologies,and offers a detailed analysis of each module’s implementation process.The algorithm’s frequency acquisition accuracy is then evaluated,with results demonstrating that,when the input signal model is a laser heterodyne interference signal,the frequency range of the main carrier beat-note change is 2 MHz to 20 MHz and the communication codes rate is 2.5MHz with 1024 communication codes,the acquisition error of the main carrier beat-note is less than 1 Hz,and the acquisition error of the two sideband beat-notes is less than 10 Hz,with an acquisition time of 125 ms.These results meet the requirements of a real-time,high-precision frequency acquisition task.