## 6 Numerical Results
### Performance in the Symmetric Networks  
The theoretical and experimental BER performances of the proposed JSCC-IA schemes with identical and different propagation delays for the (4 \(\times\) 4, 1) [10] network are provided and compared with those of the conventional IA scheme in Figure 4.  
From the results, it can be seen that the experimental BER agrees very well with the theoretical one, verifying the analytical BER expressions in Section 4. For the JSCC-IA scheme with the same propagation delay, the experimental BER becomes zero when \(E_{b}/N_{0}\) is larger than 10 dB due to the finite length of the simulation messages. It is expected that the performance of the traditional IA  
Figure 4: The average theoretical and experimental BER performances of the conventional IA scheme and the JSCC-IA schemes with identical/different propagation delays in the (4 \(\times\) 4, 1) [10] symmetric networks. system is significantly degraded by the strong interference that cannot be mitigated only by the spatial adjustment. The average BER of the conventional IA scheme stays at a very high level, and can only reach the level of \(10^{-3}\) at \(E_{b}/N_{0}=14\) dB, which is certainly inadequate for the practical requirements. However, when the code domain is introduced, there is a substantial improvement in the error performance. In the JSCC-IA system with identical propagation delay, the BER can be suppressed to the level of \(10^{-5}\) only at \(E_{b}/N_{0}\) of 4 dB. The BER of the JSCC-IA scheme decreases rapidly with the raise in \(E_{b}/N_{0}\), and the theoretical value can reach the degree of \(10^{-16}\) at \(E_{b}/N_{0}\) of 14 dB. For the JSCC-IA system with different propagation delays, the performance might be degraded by the various delays, and the associated BER becomes higher. In spite of this, its performance is still much superior to that of the conventional IA system, with BER of \(10^{-5}\) at \(E_{b}/N_{0}\) of 8 dB. To further evaluate the performances in the large-scale WSNs, the scenarios with even more users are considered, and the experimental BER in the (\(4\times 4\), \(1\))\({}^{20}\) network is presented in Figure 5. As the number of users is much larger than that the conventional IA scheme can accommodate, the average BER of the conventional IA scheme stays around the high level of \(10^{-1}\). On the contrary, the JSCC-IA scheme can suppress the BER to a much lower level. Considering the \(E_{b}/N_{0}\) of 8 dB, the associated BER is \(10^{-7}\) and \(10^{-4}\) for the JSCC-IA schemes with identical and different propagation delays, respectively. When \(E_{b}/N_{0}\) increases, the proposed scheme can achieve even better BER. Aside from the single DoF circumstance, we progress to a more complicated double data streams situation, and the performances in the (\(6\times 6\), \(2\))\({}^{18}\) network are depicted in Figure 6. The BER of the conventional IA system still stays at the unacceptable high value of \(10^{-1}\), and does not show significant improvement with the raise in \(E_{b}/N_{0}\). On the other hand, the proposed JSCC-IA scheme exhibits much better BER than the conventional IA system. For the scenario of identical propagation delay, the BER decreases dramatically with the rise in \(E_{b}/N_{0}\), and reaches the level of \(10^{-9}\) at \(E_{b}/N_{0}=6\) dB. Although the performance of the JSCC-IA scheme with different propagation delays is inferior to that with the same delay, it still shows good performance, with BER of \(10^{-5}\) at 4 dB. Therefore, simulations validate  
Figure 5: The average experimental BER performances of the conventional IA scheme and the JSCC-IA schemes with identical/different propagation delays in the (\(4\times 4\), \(1\))\({}^{20}\) symmetric networks. the application of JSCC-IA in multi-data-stream networks. Consequently, the proposed JSCC-IA scheme exhibits an implicit advantage over the conventional IA system in term of BER performance.