## 4 Experiments  
In this paper, we present experiments that were conducted on the proposed CO-IM-OFDM system, comparing it with existing traditional constellation mappings, including 16 APSK, 16 spiral, and 16 QAM. The training employed the Keras deep learning framework for network model construction, with the open-source library Sionna serving as the backend engine for link-level simulations. We also investigated the impact of different loss function weighting factors on the proposed scheme. The simulation configurations for the neural network-empowered constellation optimization design are shown in Table 1.  
Considering the CO-IM-OFDM system, index modulation corresponds to \(N_{g}=4\) and \(k=2\), and the other simulation parameters for CO-IM-OFDM are shown in Table 2.  
Figure 3 demonstrates the training results under different weighting factors. It can be observed that when communication performance is optimized (\(\alpha\to 0\)), the constellation exhibits a spiral-like structure to counteract signal-rotation-induced PN. Simultaneously, the inner and outermost constellation points maintain sufficient separation to preserve Euclidean distance uniformity under PA nonlinear distortion. Conversely, when sensing performance is prioritized (\(\alpha\to 1\)), the constellation approximates a constant-envelope structure where the signal's constant modulus property ensures stable sensing capabilities. However, this sensing-optimal configuration sacrifices amplitude diversity, a critical degree of freedom for information encoding, leading to degraded communication performance. This demonstrates an inherent deterministic-stochastic trade-off between communication and sensing objectives: communication-driven design requires maximized signal randomness to enhance information capacity, and sensing-driven design demands deterministic signal features to guarantee sensing reliability. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Configuration** \\ \hline Neural network architecture & \(2\times 16\) \\ \hline Parameter initialization & \(\Re(c(i)),\Im(c(i))\) of 16 QAM \\ \hline Training data & Random binary bit stream \\ \hline Optimizer & Adam optimizer \\ \hline Learning rate & 0.001 \\ \hline EDR for first-moment estimates & 0.9 \\ \hline EDR for second-moment estimates & 0.999 \\ \hline Small constant for numerical stability & \(1\times 10^{-7}\) \\ \hline Loss function & _Loss_ \\ \hline Batch size & 64 \\ \hline Training epochs & 30,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for constellation optimization. \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameter** & **Setting** \\ \hline FFT size & 128 \\ \hline OFDM symbol count & 64 \\ \hline PA model & Rapp model (\(P_{\text{asat}}=0.58\)) \\ \hline PN variance & 0.01, 0.1 \\ \hline Channel model & Rayleigh channel (path = 1, 10, 20) \\ \hline Training \(E_{b}/N_{0}\) range & 10–20 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameter configuration for CO-IM-OFDM. Figure 4 illustrates the results of balancing communication and sensing performance through weighting factor adjustment. The allocation of a weighting factor essentially represents a resource allocation trade-off, which is adjusted according to specific application scenarios. Through varying the weighting factor, we establish a constellation design framework and obtain the joint CRB-BER boundary for IM-OFDM under constellation optimization. Curve A represents the ideal state of the ISAC system, where both communication and sensing maintain optimal performance without mutual interference. However, this state is known to be unattainable. Curve B depicts the current baseline ISAC system state, which compromises partial communication performance to achieve sensing. This approach provides no additional performance gain and consequently causes performance degradation in the other objectives.