## 4 Conclusions and Future Work
### Pros and Cons of the Proposed Symbolic Model  
We next summarize in Table 1 the advantages and disadvantages of our model, and detail a few real case studies that can greatly benefit from symbolic modelling.  
To highlight the benefits of the proposed symbolic modelling, we consider three real case studies where it can be applied to significantly improve the outcomes:  
Case Study 1: Adaptive Receiver Design in Urban Mobile Environments [22]: In a scenario where a telecom research lab is developing adaptive NOMA receivers for 5G/6G small cell deployments in dense urban areas where multipath fading and user mobility introduce severe synchronization challenges. This symbolic model can simulate irregular QAM constellations and their sensitivity to impairments (e.g., timing offsets, carrier frequency drift) across multiple users in varying channel conditions. This helps design and test adaptive synchronization blocks and equalizers in the receiver chain. This way, early-stage development and theoretical validation are accelerated without relying on hardware prototypes, and labeled synthetic data for training AI-based adaptive receivers can be generated.  
Case Study 2: Synthetic Data Generation for Deep Learning in NOMA Detection [23]: A use case where a university research group is building a deep neural network for blind symbol classification in a NOMA uplink, aimed at improving multi-user detection using AI instead of classical SIC. The symbolic framework can rapidly simulate thousands of irregular constellation configurations and modulation impairments under various signal-to-noise ratios (SNRs), thereby facilitating the generation of high-quality training datasets for supervised learning. This removes dependency on hardware-based data collection, ensuring full control over ground-truth parameters while enabling large-scale, diverse dataset creation in a reproducible and low-cost environment.  
Case Study 3: SDR System-Level Testing for Mission-Critical Internet-of-Things (IoT) Networks [24]: An industrial R&D team is building a custom SDR-based NOMA transceiver  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Pros** & **Cons** \\ \hline Intuitive representation of irregular NOMA constellations and symbol decision regions & Symbolic computations can be slower for large-scale system-level simulations \\ \hline Enables generation of synthetic training datasets for machine learning models & Requires symbolic math expertise for effective customization \\ \hline Easily modifiable for testing different modulation, synchronization, and pulse shaping schemes & Limited support for real-time testing without external SDR integration \\ \hline Provides analytical insight into signal behavior under modulation impairments & May not capture full non-linear effects of analog RF front-ends without additional modeling \\ \hline Supports rapid prototyping and algorithm validation in Wolfram language & Wolfram environment may not be as widely adopted in communication system prototyping \\ \hline Facilitates SDR implementation by bridging high-level theory and practical system behavior & Less suited for integration with traditional SDR toolchains (e.g., GNU Radio) without export \\ \hline \hline \end{tabular}
\end{table}
Table 1: Advantages and disadvantages of the proposed symbolic model.  
for low-latency, mission-critical IoT applications (e.g., factory automation), where several sensors communicate concurrently with a base station under tight spectral and power constraints. The proposed symbolic model allows pre-deployment validation of the modulation design (e.g., pulse shaping, spectrum usage, constellation overlap) to predict and avoid potential impairments such as inter-symbol interference or spectral leakage. This can have an extended impact as the framework ensures that signal processing algorithms are well-optimized before porting to SDR platforms, saving prototyping time and improving signal quality under constrained resources.