## 4 Analysis of Results  
In this paper, we discuss the bit error rate (BER) and Q-factor performance of LUT-PS and the conventional constant composition distribution matching-based probabilistic shaping (CCDM-PS) scheme at an information entropy of 3.66 bits/symbol. The Q-factor is commonly used as a metric for evaluating system performance and serves as an effective indicator of signal quality. The Q-factor used in this paper is defined based on the error between the recovered received signal and the ideal transmitted signal. Specifically, Q is calculated as follows:  
\[Q=-20\cdot\log_{10}\left(\frac{\sqrt{\frac{1}{N}\sum_{i=1}^{N}|a_{i}-b_{i}|^{2 }}}{P_{ave}}\right) \tag{3}\]  
where \(a_{i}\) represents the normalized received symbols, \(b_{i}\) denotes the transmitted symbols, and \(P_{ave}\) is the target average power used as the normalization reference. A higher Q value indicates better signal quality with less distortion and noise. The distributions of LUT-PS and CCDM-PS are displayed in Figure 6. It can be observed that under the same conditions, the probability distributions of the two schemes differ. The CCDM-PS scheme focuses more on concentrating the constellation points in the innermost ring, while the LUT-PS scheme emphasizes reducing the probability that the constellation points will be found in the outermost ring. Figure 6: The distributions of LUT-PS and CCDM-PS. Figure 7 shows the simulation results for the BER and Q-factor versus the received optical power (ROP) of the UTC-PD for 400 GHz photonic terahertz OFDM signals under different schemes in the back-to-back (BTB) configuration without forward error correction (FEC). The ROP values used here are higher than those typically employed in conventional fiber-optic links because the photonic terahertz communication system simulated in this work adopts a receiver architecture that differs from traditional photodiode-based systems and can tolerate higher input power. It is clear from Figure 6(a) that the BER performance of the system is enhanced with the application of PS, and the degree of improvement becomes more obvious as the ROP values increase. When ROP is \(-\)0.64 dBm, the BER decreases from 1.2376 \(\times\) 10\({}^{-4}\) to 6.3256 \(\times\) 10\({}^{-5}\), representing a performance enhancement of 48.89%. In addition, the BER graph of LUT-PS basically coincides with that of CCDM-PS, indicating that their performances are comparable. Figure 6(b) illustrates the relationship between the Q-factor and the ROP. It reveals that the application of PS results in an approximate improvement of 0.93 dB in the Q-factor, and the results of the LUT-PS and CCDM-PS schemes are quite similar. By integrating Figure 6(a),b, it can be seen that the presented LUT-PS scheme can be on par with CCDM-PS in performance, demonstrating the feasibility of LUT-PS. Building upon the use of LUT-PS, we further investigate the performance of 5 Gbaud signal transmission over a 10 km fiber link with the application of the RBFNN nonlinear equalizer. The results were compared with those obtained using LUT-PS in combination with a decision feedback equalizer (DFE). The results are depicted in Figure 8, here Figure 7(a),b are the BER and Q-factor versus ROP, respectively. The images in Figure 7(c)-e, respectively, depict the received constellations of the traditional system, the system using LUT-PS and DFE (LUT-PS-DFE), and the system using LUT-PS and RBFNN (LUT-PS-RBFNN). As shown in Figure 7(a), LUT-PS improves the BER performance to a certain extent. Furthermore, compared to the system that does not use RBFNN, the BER performance of LUT-PS-RBFNN and LUT-PS-DFE shows further improvement, with both exhibiting similar enhancement. As ROP increases, the reduction in BER becomes more significant. When ROP exceeds \(-\)0 dBm, LUT-PS-RBFNN reduces BER by 81.45% compared to the conventional system, outperforming LUT-PS-DFE, which achieves a reduction of 67.54%. The red region in Figure 7(d),e represents the constellation diagrams after nonlinear equalization.