## 4 Experiments
The closed region formed by Curves A and B represents the achievable integrated performance area, with the research goal being to approach the performance upper limit (Curve A). Curve C shows performance obtained through continuous weighting factor adjustment and the proposed end-to-end training. It can be observed that BER increases with \(\alpha\), while CRB decreases with \(\alpha\). The trained constellation diagram demonstrates performance gains compared to Curve B, approaching the theoretical upper limit. In practical scenarios, selecting an appropriate \(\alpha\) value yields a constellation tailored to the dominant system requirement. In detail, for applications predominantly considering sensing performance, such as autonomous driving, \(\alpha>0.5\) would be set; for prioritizing communication performance, such as end-to-end video transmission, \(\alpha<0.5\) would be set. This resource allocation problem depends heavily on the specific application context. We acknowledge that a more detailed investigation into optimal \(\alpha\) selection strategies would be a valuable point of focus for future research. Then, we provide simulation results under Gaussian channels and Rayleigh fading channels with different numbers of paths. By varying the number of multipath components as 1, 10, 20, and PN level as 0.01, 0.1, we simulated in different channel conditions. As shown in Figure 5, we simulated the CRB-BER joint performance under Rayleigh and AWGN channel conditions. It can be observed that all simulation curves exhibit a concave characteristic. This phenomenon indicates that in the trade-off between BER and CRB, the system achieves a significant improvement in communication reliability by sacrificing a small amount of sensing accuracy, thus obtaining performance gains. This concave trend is consistently present across all simulated channel conditions. In addition,  
Figure 3: The constellation under different weighting factors. as PN increases, the system performance deteriorates, with both endpoints of the curve, optimal communication and optimal sensing points, shifting back. This fully demonstrates that the proposed neural network architecture can adapt to different channel conditions and effectively achieve performance optimization in joint communication and sensing design. Next, the performance indicators, including BER, throughput, and CRB under various weight factors, as well as their variations with respect to SNR, are compared. The benchmark for comparison is based on traditional 16 QAM modulation. Figure 6 illustrates the BER performance curves under varying \(E_{b}/N_{0}\) and weight factors. For the traditional 16 QAM baseline, the BER decreases slowly at high SNR, remaining as high as \(10^{-1}\) at \(E_{b}/N_{0}=20\,\mathrm{dB}\). With the proposed algorithm, performance improves significantly as \(\alpha\) decreases. Specifically, when communication performance (\(\alpha=0\)) is prioritized, BER outperforms the baseline by approximately 10 dB under the same conditions, exhibiting a steep decline in high-SNR regions. Conversely, \(\alpha=1\) yields the worst BER due  
Figure 4: The CRB-BER joint performance of ISAC. Figure 5: The CRB-BER joint performance in different channel conditions. to the enforced constant-envelope constraint, demonstrating the limitation of deterministic signals on communication reliability. Figure 7 shows the CRB curves under varying \(E_{b}/N_{0}\) and weight factors. As SNR increases, the CRB decreases. When prioritizing communication performance, the proposed algorithm slightly underperforms compared to 16 QAM. However, in sensing-priority mode (\(\alpha=0.2\sim 1\)), the CRB decreases by 2\(\sim\)8% as the weight factor increases, indicating optimized parameter estimation accuracy through deterministic signal structures. Next, the performance of the constellation adapted for IM-OFDM via neural networks is compared with the existing constellations. We select 16 APSK, 16 QAM, and 16 spiral as algorithms for comparison.