The research purpose and focus of this paper is to propose a new signal processing method that processes a photon echo heterodyne signal and can achieve a higher signal-to-noise ratio (SNR) intermediate frequency (IF) signal spectrum and signal time-frequency characteristics with an improved performance to improve the photon counting heterodyne radar speed measurement performance of variable-speed moving targets.

This study applies the adaptive sparse degree compression perception method to a variable-speed target heterodyne photon echo signal and solves the problem whereby the sparse degree of K can not be determined in advance. The reconstructed frequency spectrum has a relatively high SNR but error and some unfiltered noise are also found on the spectrum. Furthermore, according to the characteristics of concentrated and continuous Doppler spectrum components of the variable-speed target, density clustering is creatively applied to the denoising of the above-reconstructed spectrum, and the sparsity adaptive compression sensing and clustering algorithm are combined as a new heterodyne signal processing method of photon echoes. In this paper, the first part of the proposed signal processing method is to solve the frequency spectrum. This process is divided into four parts, namely compressed perception reconstruction of the IF spectrum, density clustering, denoising, and interpolation. First, the frequency spectrum is reconstructed by the sparsity adaptive matching pursuit (SAMP) algorithm according to the photon arrival time series, the IF signal spectrum is reconstructed, and compressed perception processing is performed. The lower amplitude of the spectrum component is assumed as noise, and only discrete signals whose amplitudes are significantly higher than noise are retained in the reconstructed IF spectrum. However, at this time, the reconstructed IF signal spectrum is not the final signal spectrum, and the noise signal with higher spectrum amplitude is still retained. Compared with the noise, the signal of the ideal spectrum of the variable-speed target must be continuously changing, so the reconstructed IF signal spectrum is processed by density clustering. The frequency component with the highest density can be obtained by classifying and sorting the spectrum of the reconstructed IF signal according to the density-based clustering, which can be determined as the frequency component of the IF signal. In addition, discrete points can also be obtained while clustering the reconstructed IF spectrum, which can be regarded as noise components and then denoised. However, because the compressed sensing algorithm has removed most of the noise components, and through signal processing such as clustering denoising, the obtained IF signal spectrum becomes a discrete spectrum, which is inconsistent with the continuous spectrum of the ideal variable-speed moving target. Therefore, the IF signal spectrum is interpolated and fitted to obtain the final IF signal spectrum. The second part of the proposed signal processing method is to obtain a time-frequency characteristic analysis method with improved performance. According to the principle of short-time Fourier transform to obtain the time-frequency characteristic of signals, we combine the sparsity adaptive compression sensing in this method with the time-frequency characteristic analysis method in this paper.

The simulation results show that the proposed method has excellent advantages. Compared with the traditional direct Fourier transform spectrum, the SNR is improved by up to 20 dB on average, and the average accuracy error is within 10% (Fig. 7). It is found that the smaller the signal Doppler broadening, the more obvious the advantage of this signal processing method. When the signal Doppler broadening is gradually increased or the spectrum is complex, the reconstruction effect and density denoising effect will be lower than expected value (Fig. 8). Meanwhile, the contrast of time-frequency maps obtained by the proposed signal processing method is much higher than that of the short-time Fourier transform, wavelet transform and Wigner-Ville distribution, which indicates that the readability of the time-frequency maps obtained using the proposed method is the best (Fig. 9). From the two evaluation indexes of contrast and information entropy, the performance of the proposed time-frequency characteristic analysis method is seen to be the best (Fig. 11). Finally, experiments are performed to verify that the confidence interval of the SNR improvement value of the signal processing method in this paper is [8.5 dB, 11.1 dB] with a confidence interval of 95%. Further, the confidence interval of the Doppler broadening accuracy error is [5.6%,7.4%] (Fig. 14), and the time-frequency analysis characteristics are consistent with the simulation results that were obtained (Fig. 15).

The results show that the proposed method is effective at improving the SNR and time-frequency distribution of signals to optimize the speed measurement performance of the photon counting heterodyne radar against variable-speed moving targets. This method proves the feasibility of extracting the motion information or fretting information of the next complex moving target. Therefore, further research is needed to understand the extraction method of motion information for complex moving targets.