# Adaptive Linearization for the Sub-Nyquist Photonic Receiver Based on Deep Learning
## 3 Results and Discussion
Figure 3: **(a)** The performance of the deep Resnet under training; **(a)** The training loss curve, the validation loss curve, and the learning rate curve as the training epochs increased; **(b)** The distribution of the number of training samples with different training \(MAE\) losses; **(c)** The distribution of the number of test samples with different testing \(MAE\) losses on the testing set. Figure 5a,b show the intuitive effects of eliminating spurs of a single-tone sinusoidal signal in the perspectives of the time domain and frequency domain. The frequency of the input signal was 0.60 GHz and was folded to 430 MHz by the sub-Nyquist photonic link. Simultaneously, the down-converted second harmonic (170 MHz), third harmonic (260 MHz), and fourth harmonic (340 MHz) occurred due to the nonlinearity of the MZM and LNA. As shown in Figure 5a, the signal rectified by the Resnet model was more inclined to a standard sinusoidal signal, as a result of dispelling the intricate spurious distortions and noise floor of the raw signal data. As depicted in Equation (8), the spurious suppression ratio \((SSR)\) of the sampled analog photonic link can be equivalently defined as the ratio of the power of the signal to the power of the largest harmonic or distortion, which can be calculated from the spectra. The \(SNR\) could be calculated as the power of the signal to the power of the noise, as depicted in Equation (9). From the perspective of the frequency domain in Figure 5b, the \(SSR\) improved by about 42.15 dB, owing to the deep learning method. Specifically, the second harmonic was suppressed by about 64.26 dB, and the third harmonic was suppressed by about 41.98 dB. Simultaneously, the noise floor in the first NZ declined from about \(-80\) dBm to \(-95\) dBm on average. \[SSR(dB)=10 log\bigg{(}\frac{P_{signal}}{P_{\text{max},distortion}}\bigg{)} \tag{8}\]  
\[SNR(dB)=10 log\bigg{(}\frac{P_{signal}}{P_{NF}}\bigg{)} \tag{9}\]  
In addition, the intermodulation distortions in multi-carrier scenarios can be effectively suppressed by using the proposed deep learning method. In the proof-of-concept experiments, the input multi-carrier RF signals were emulated by dual-tone sinusoidal signals at frequencies of 200 MHz and 220 MHz, as shown in Figure 5c,d. The input powers of the dual-tone signals were 16 dBm. Correspondingly, the third-order intermodulation distortions (IMD3) were located at 180 MHz and 240 MHz, respectively. Figure 5c shows a comparison of the measured waveform of the raw dual-tone signals with sophisticated  
Figure 5: Examples of spurious elimination for a single-tone sinusoidal signal with the frequency of 0.60 GHz, which was down-converted to the frequency of 430 MHz. (**a**) Comparison of the time-domain waveform before and after rectification by Resnet model; (**b**) Elimination of spurious spectral components of the down-converted second harmonic (170 MHz), third harmonic (260 MHz), and fourth harmonic (340 MHz). Examples of spurious suppression testing by dual-tone signals with frequencies of 200 MHz and 220 MHz; (**c**) Comparison of the time-domain waveform before and after rectification by Resnet model; (**d**) Result-contrast effects of the suppression of the third intermodulation products (180 MHz and 240 MHz), the sum frequency (420 MHz), and other cross-modulation distortions in the frequency domain. spurs and the rectified waveform after the deep learning linearization. Figure 5d depicts the spurious suppression effects of the deep learning method in the frequency domain. The \(SSR\) of the first Nyquist zone was optimized from 16.93 dB to 40.98 dB, and increased by 24.05 dB. The IMD3 with a frequency of 180 MHz was suppressed from \(-\)35.06 dBm to \(-\)59.20 dBm. Interestingly, for the second harmonics (400 MHz and 440 MHz), the products of the frequency separation of the two signals (20 MHz), and the fifth-order intermodulation distortions (IMD5,160 MHz and 260 MHz) were suppressed.