# Adaptive Linearization for the Sub-Nyquist Photonic Receiver Based on Deep Learning
## 3 Results and Discussion
Figure 6a displays the measured powers of the folded third-order intermodulation distortion (IMD3), the fifth-order intermodulation distortion (IMD5), and the sum-frequency sidebands as a function of the input RF powers, with and without deep learning-assisted signal linearization. Owing to the deep learning method, the suppression of the IMD3 could be realized up to 28.9 dB, and the suppression of the IMD5 could be realized up to 21.3 dB. Meanwhile, the suppression of the sum frequency (420 MHz) could be realized up to 44.1 dB. It was demonstrated that the Resnet could automatically recognize the dual-tone signals and suppress the stray components, except for signals at one time without any prior knowledge. The third-order-spurious-free dynamic range (\(SFDR_{2/3}\)) is generally an essential evaluation criterion of the photonic link, which can be calculated in the format distributed in Equation (10). The \(OIP_{3}\) is the output cut-off point of the third-order nonlinear distortion component, and \(N_{0}\) is the output noise of the link normalized in 1 Hz. \[SFDR_{2/3}=\frac{2}{3}(OIP_{3}-N_{0}) \tag{10}\]  
By varying the input RF powers, both the powers of the target intermediate frequency (IF) and IMD3 sidebands were monitored and dominated the major powers. Figure 6b depicts the comparison of the \(SFDR_{2/3}\) with and without the deep learning method. The slope for the third-order-inter-modulation component was 3. The measured raw noise floor was \(-\)133 dBm/Hz, which was reduced to \(-\)148 dBm/Hz after the deep learning processing. The \(SFDR_{2/3}\) was improved from 96.92 dBm \(\cdot\) Hz\({}^{2/3}\) to 115.08 dBm \(\cdot\) Hz\({}^{2/3}\), which indicated that the \(SFDR_{2/3}\) enhancement was 18.16 dBm \(\cdot\) Hz\({}^{2/3}\). It should be noted that the current \(SFDR_{2/3}\) was also restricted by the quantization noise of the electrical ADC, which cost a lot in hardware upgrade. Figure 7a,b show the effects of signal linearization testing on wireless communication quadrature phase-shift keying (QPSK) signals. The carrier frequency of the testing example  
Figure 6: (**a**) Measured sum frequency (420 MHz), third-order intermodulation (180 MHz), and fifth-order inter-modulation (160 MHz) components versus the input RF powers with and without the proposed deep learning-assisted method. (**b**) The comparison of the third-order-spurious-free dynamic range (\(SFDR_{2/3}\)) with and without the deep learning-assisted method. The black and blue solid line represents the \(SFDR_{2/3}\) before and after the linearization, respectively. of the QPSK signal was 0.14 GHz. It was confirmed that the deep Resnet model delineated the compelling generalizing capacity on wideband wireless communication signals. In detail, it is observed that the burr noises were eliminated in the time domain waveforms in Figure 7a. In Figure 7b, the \(SSR\) was improved from 25.67 dB to 65.46 dB on wideband communication QPSK signals, realizing an improvement of 39.86 dB. Specifically, the second harmonics (280 MHz) and third harmonics (420 MHz) were almost eliminated. The noise floor dropped by about 15 dB, which improved the \(SNR\) without any loss of the intensity of the signals. Besides, LFM radar signals with wide bandwidth were also exploited to validate the proposed model. The testing LFM signal was centered at 50 MHz with a bandwidth of 80 MHz. As with the other kinds of signals, it is observed that the burr noises were eliminated in the time domain waveforms in Figure 7c. In Figure 7d, the \(SSR\) was improved by about 25.39 dB. At the same time, the noise floor dropped by about 15 dB.