## 1 Introduction
For example, APSK, which is one kind of GS constellation point, has been adopted by the second-generation digital video broadcasting specification for satellite (DVB-S2) and approved by the consultative committee for space data systems (CCSDS) [13; 14]. Besides, post-equalization algorithms based on advanced digital signal processing (DSP) are proposed to mitigate linear and nonlinear distortions. At present, linear time-frequency domain equalization technology based on least mean square (LMS) [15], recursive least square (RLS) [16], direct decision least mean square (DD-LMS), zero-forcing [17] and other algorithms have been utilized in VLC systems, effectively eliminating linear distortion. In terms of nonlinear distortions, a series of nonlinear equalizers have also been proposed, such as Volterra series-based and Polynomial based algorithms [18]. Recently, artificial intelligence algorithms, especially neural networks (NN), are emerging as effective techniques to deal with nonlinear problems. Due to NN's universal approximation theorem, it is commonly used as a post-equalization algorithm in VLC systems. In [19], a Gaussian kernel-aided deep neural network (GK-DNN) equalizer was utilized to compensate for the high nonlinear distortion of underwater PAM8 VLC channels. In [20], [PERSON] et al. proposed a memory-controlled deep LSTM neural network post-equalizer for PAM-based VLC systems. In [21], a nonlinear resilient learning post-equalizer namedTFDNet was proposed. It exploits time-frequency image analysis, which considers the time and frequency domains simultaneously and is effective in tackling nonlinear distortions in UVLC systems. Except for equalizers, DNNs were recently used as a waveform to symbol converter, which could replace conventional demodulation, post-equalization, and down-sampling at the receiving end. In [22], a sparse data-to-symbol neural network (SDSNN) receiver is proposed for UVLC based on nonorthogonal multi-band CAP to mitigate ISI and inter-channel interference (ICI). In [23], a Neural-network-based waveform to symbol converter (NNWC) can directly convert the received multiband CAP waveform into quadrature amplitude modulation (QAM) symbols to simultaneously handle the ISI and ICI in a fiber-mmWave system. In [24], a DNN-based waveform to symbol decoder with three hidden layers was utilized in UVLC systems and achieved better communication performance than a traditional receiver. Moreover, neural networks are now becoming more and more popular in channel estimation [25] and end-to-end learning [26; 27]. In this paper, we first construct and optimize a traditional DNN-based waveform-to-symbol converter [24] to replace conventional demodulation, down-sampling and post-equalization at the receiving end in 64 QAM and 64 APSK UVLC systems based on CAP modulation. It is regarded as a benchmark that could increase signal Vpp dynamic range by 104% (from 250 mV to 511 mV) for 64 APSK and 181% (from 180 mV to 506 mV) for 64 QAM with 7% FEC of 3.8 \(\times\) 10\({}^{-3}\) as a BER threshold, compared with traditional CAP receiver. However, it comes at the cost of the high complexity of 26,210 trainable parameters. To achieve a better tradeoff between communication performance and computation complexity which is represented by total trainable parameters, we then innovatively propose a cascaded receiver consisting of a DNN-based waveform-to-symbol converter and modified NN-based DD-LMS. With fewer taps and nodes than the traditional converter, the front-stage converter could still mitigate the majority of ISI and signal distortions. Then modified NN-based DD-LMS is cascaded to improve communication performance by reducing phase offset, making received constellation points more concentrated and closer to standard constellation points. Compared with the traditional converter, the cascaded receiver could achieve 89.6% of signal Vpp dynamic range with 12.4% of complexity in the 64 APSK UVLC system.