## 1 Introduction  
In recent years, optical wireless communication (OWC) has become a big focus of next-generation 6G communication [1]. As a branch of it, free-space optical communication (FSO) has many advantages such as easy deployment, high bandwidth and strong security. However, in practical applications, geometric loss, pointing error, atmospheric attenuation and turbulence effects will affect the signal transmission, and the atmospheric turbulence is particularly obvious. These effects will cause the signal to produce more serious distortions. In addition, the transmission of carrierless amplitude and phase modulation (CAP) signals in FSO channels is prone to producing obvious nonlinearity effects and inter-symbol interference (ISI), which seriously limit the transmission efficiency of the transmitted information. Many digital signal processing techniques have been proposed to solve this problem [2]. The neural network technology in machine learning is an efficient and accurate equalization technology because of its strong approximation ability and the excellent characteristics whereby it can be processed directly from end to end without starting from theory [3]. It can effectively approximate the transmission function of the backlight channel and offset the nonlinear effect. However, choosing which network to use as an equalizer is often a big problem, because both the accuracy and processing rate should be taken into account. Recurrent neural networks (RNNs) (our study used GRU, a type of RNN) show excellent performance in eliminating nonlinear distortion due to their excellent properties for timing processing [4; 5; 6]. However, because of its recursive structure, it is difficult to realize parallel processing, resulting in a poor processing rate as an equalizer. Using CNNs, which have a structure that is easy to parallelize, the speed can be greatly improved, but the accuracy is not so ideal [7]. How to balance accuracy and speed was the focus of this research. We introduce a new way to balance the excellent characteristics of GRUs for timing and the parallelization of CNNs for speed improvement: knowledge distillation (KD). KD is a method of transferring a more complex teacher model to a relatively simple student model, which can approximate or exceed the performance of the teacher model, and enjoy the speed increase from the simplified structure [8]. KD can use the structure of CNNs for parallelization, and it can also allow the CNN to absorb the recognition of time sequence information brought by the GRU. KD in the past usually distills the same kind of network, from complex to simple, but there are few studies on this kind of cross structure at present [9]. In this study, the method of distilling across the network structure was adopted so that the student network CNN can have the advantages of both types of networks and improve the speed by using parallelization rather than reducing the computational complexity. In this way, the CNN equalizer after KD from the biGRU can be used to quickly and accurately complete the signal recovery work in the hardware. In particular, in bandwidth-limited systems like the one in our experiments, a network architecture that can be quickly trained for minimalist deployment is cost-effective. In this work, we accomplished the following:  
1. We propose a solution using KD to distill the biGRU-based equalizer to obtain a network structure that can be parallelized. We transfer the knowledge that can recognize temporal signals from the teacher model based on the biGRU to the student model 1D-CNN, which can be processed in parallel, so that the student model also has the ability to recognize temporal information [10]. We compare the biGRU, 1D-CNN after KD and 1D-CNN without KD in terms of Q-factor and equalization velocity. The experimental data showed that the Q-factor of the 1D-CNN increased by 1 dB after KD learning from the biGRU, and KD increased the RoP sensitivity of the 1D-CNN by 0.89 dB on the HD-FEC threshold of \(1\times 10^{-3}\). 2.