# Adaptive Linearization for the Sub-Nyquist Photonic Receiver Based on Deep Learning
## 2 Materials and Methods  
A proof-of-concept experimental setup based on the sub-Nyquist photonic receiving system is illustrated in Figure 1. The optical source was a self-developed mode-locked fiber (MLL) laser, based on a semiconductor saturable absorption mirror with long-term stability. The optical pulse width was 247 fs and the spectral width was 10.10 nm. The MLL was amplified by an erbium-doped fiber amplifier (EDFA) (Accelink, EDFA array series, Wuhan, China) with an output power of 20 dBm. The RF signals modulated the MLL through a Mach-Zehnder intensity modulator (MZM) (iXblue, MXLN-40, Paris, France), and the frequency modulation range of the RF signal was up to 40 GHz. Subsequently, the photoelectric conversion process was carried out by an encapsulated high-speed positive -intrinsic-negative (PIN) photodetector (PD) (Bonphot Optoelectronics, PD03, Suzhou, China). The output down-converted RF signals were amplified by a tailor-made wideband low-noise amplifier (YQAMP01040, LNA), and then the high-frequency components were filtered out by a low-pass filter (LPF). The receiving signals were sampled and observed by a 20 GS/s Oscilloscope (Rohde & Schwarz, RTO2044, Muenchen, Germany). After the analog-to-digital process, the digital signals were processed by digital signal processing (DSP), and then fed into the deep learning (DL) module, where the signals polluted by multi-source distortions could be automatically linearized. The down-conversion principle of receiving signals with deep learning-assisted linearization is shown in Figure 1 as well. In the frequency domain, the mode-locked laser was performed as an optical frequency comb (OFCs) with a repetition rate of ~1030 MHz. The Nyquist zone was expressed from 1 to N with a frequency width of 515 MHz. To maximize the down-conversion efficiency, the RF signals were copied to every optical frequency comb through the MZM with dual-sideband modulation mode. After the propagation through optical fibers, the loaded RF signals beat with the near combs in the photoelectric conversion process. The copies of down-converted RF signals, harmonic distortions, and intermodulation distortions emerged via direct detection through PD. Subsequently, the high-frequency components were filtered by the low-pass filter, and all the frequency components falling into the first Nyquist zone could be sampled by a low-speed ADC. Ultimately, the harmonics and intermodulation distortions were suppressed by the deep learning method. As deep learning is a data-driven approach, the appropriate dataset generation provided for training and testing is essential. The datasets were derived from the down-converted duplicates of single-tone sinusoidal signals, dual-tone sinusoidal signals, wireless communication signals, and linear frequency modulation (LFM) radar signals. The single-tone and dual-tone sinusoidal signals were generated by a microwave analog signal generator (Sinolink Technologies, SLFS-440D, Beijing, China) with various frequencies (0-40 GHz) and amplitudes (0 dbm-20 dbm). The wireless communication signals were generated and transmitted from a universal software radio peripheral (USRP) (National Instruments, USRP-2794, Austin, TX, USA) with multiple modulation formats and carrier frequencies (0-6 GHz). The LFM signals were generated by an Arbitrary Waveform Generator (Tektronix, AWG5202, Tokyo, Japan). To produce the training targets (reference data) for the deep neural network, the acquired receiving raw digital signals were preprocessed using digital signal processing (DSP) filtering algorithms in the time domain. Afterward, every processed reference signal and the raw signal were dominated as a pair of reference/raw data. All the reference/raw data pairs constructed the total datasets. As shown in Figure 2, the deep learning module was divided into two processes: training and testing. Correspondingly, the datasets were randomly split into training datasets and testing datasets, with a ratio of 0.2 without overlap (169 samples for training and 47 samples for testing).