## 4 Experimental Results
(**i**,**ii**) show the constellation points of DNN converter and CAP demodulation in 64 APSK UVLC systems when data rate is 3.15 Gb/s, respectively. (**iii**,**iv**) show the constellation points of DNN converter and CAP demodulation in 64 QAM UVLC systems when data rate is 3.15 Gb/s, respectively. Figure 9: Phase Offset of DNN (32, 32, 32) with taps of 11 for (**a**) 64 APSK; (**b**) 64 QAM UVLC systems under different signal Vpp. (**i**,**ii**) show the movement vector of each constellation points’ center after NN-based DD-LMS for 64 APSK and 64 QAM systems when signal Vpp is 550 mV, respectively. the received constellation points are. The smaller ACSS is, the more concentrated the received constellation points are. ACSS can be expressed as,  
Figure 3:0  
where \(\mathbf{Y}_{ij}\) denotes the \(i^{th}\) point of \(j^{th}\) constellation points class and \(\mathbf{u}_{j}\) denotes the center of \(j^{th}\) constellation points class. The results of DNN (32, 32, 32), DNN (64, 64, 64) and DNN (96, 96, 96) with the taps of 11 are shown in Figure 3:1 The average distances and ACSS under different signal Vpp for 64 APSK UVLC systems are demonstrated in Figure 10a,b, respectively. It can be seen that after using NN-based DD-LMS, the average distance and ACSS both become smaller almost under every signal Vpp, which indicates that symbol decision would be more accurate after modified DD-LMS. The details of the 64 constellation points' class for the 64 APSK system are shown in Figure 10i,ii, where blue and brown columns represent the results of the front-stage DNN converter with or without NN-based DD-LMS, respectively. The experimental results are similar for the 64 QAM system, which are provided in Figure 10c,d. In summary, NN-based DD-LMS could improve communication performance by reducing phase offset, making constellation points more concentrated and closer to standard constellation points. Then the communication performance of the cascaded receiver we proposed is presented in Figure 11a-d with 7% FEC of \(3.8\times 10^{-3}\) as a BER threshold, compared with traditional CAP demodulation and typical DD-LMS. Figure 11a shows that in 64 APSK UVLC systems, the BER of using a DNN converter is much lower than traditional CAP demodulation in the high-power region. The red line represents the traditional DNN converter we optimize, and it achieves the best communication performance. When reducing the taps from 19 to 11, the communication performance becomes worse due to remaining ISI and signal distortions, in which the dynamic range is 475 mV. After using typical DD-LMS or NN-based DD-LMS, BER performance is enhanced. Furthermore, using modified NN-based DD-LMS could achieve better performance than typical DD  
Figure 3:2 (**a**) The average distance between the center of received constellation points’ class and standard constellation points for 64 APSK systems; (**b**) ACSS for 64 APSK systems; (**c**) the average distance for 64 QAM systems; (**d**) ACSS for 64 QAM systems. LMS due to the usage of Adam optimizer. In Figure 11b, cascaded receivers consisting of DNN converters with different complexity and NN-based DD-LMS are investigated in 64 APSK systems. The traditional DNN converter we optimize has the largest dynamic range of 511 mV. When reducing the taps from 19 to 11, the dynamic range of the DNN converter with NN-based DD-LMS is 497 mV. Continuing to reduce the complexity, the BER performance is slightly worse. The dynamic range of signal Vpp is 481 mV for DNN (64, 64, 64) with NN-based DD-LMS and 458 mV for DNN (32, 32, 32) with NN-based DD-LMS. The trend is similar for 64 QAM in Figure 11c,d. The BER performance and trainable parameters that represent the complexity of different receivers for 64 APSK and 64 QAM systems are compared in Tables 1 and 2, respectively. Ratio* represents the ratio between signal Vpp dynamic range (mV) and total trainable parameters.