# Efficient FPGA Implementation of an ANN-Based Demapper Using Cross-Layer Analysis
## 5 Results and Discussion
### Performance Demonstration  
To demonstrate the performance of our AE implementation, we show how the receiver can adapt to a varying phase offset of the channel. Therefore, we train the AE for a standard AWGN channel with zero phase-offset. Afterward, the trainable receiver is implemented in hardware, and we modify the channel conditions by changing the phase offset of the channel model by drawing from a uniform distribution from \(-\pi\) to \(\pi\) for an \(E_{b}/N_{0}\) of 2 dB. Subsequently, fine-tuning of the receiver is applied by retraining for the new channel characteristics. It is to note that phase offset is a simple example of the adaptability of our architecture; in theory, it can also adapt to more complex channel fluctuations which will be further explored in future work. Figure 10 shows the convergence of the demapper ANN for the described scenario, including the BERs of the different phase offsets, the average BER and the baseline BER corresponding to an AWGN channel without phase offset.  
Figure 9: Latency, power and energy on Ultra96-V2.  
It can be seen that for all phase offsets, the BER of the demapper ANN converges to that of the baseline. The convergence process is nonlinear, the gain is the highest for the first iterations and it decreases during the training. For instance, the average BER is reduced by a factor of 2.2 during the first 200 iterations. For small phase offsets of \(\pm 0.63\), 200 iterations are even enough to approach the baseline BER. Figure 10 provides a first step towards connecting the communication layer to the hardware layer which will be described in more detail in Section 5.5.  
In Figure 11, the average BER of the training process for multiple phase offsets is plotted over different SNRs for various number of training iterations. This illustrates how the convergence varies for different SNRs.  
The gap between the baseline AWGN channel and the average BER of the phase offset channel is fairly small for low SNRs after training for an appropriate number of iterations. This gap increases for larger SNRs. The behavior can be explained by the fact that for high SNRs, the target BER is much lower, and therefore, small fluctuations of the learned decision regions (DRs) from the optimal ones are directly reflected in the BER. This problem can be solved by reducing the learning rate of the AE for higher SNRs with the drawback of an increased convergence time.  
It is worth mentioning that in Figure 11, we do not intend to show the communication performance on the system-level. Since our work focuses on the implementation of the  
Figure 11: BER over SNR for different number of training iterations.  
Figure 10: Convergence of phase offset for \(E_{b}/N_{0}=2\).  
trainable demapper, we are evaluating the performance of this block, without including post-processing steps (channel decoding and soft-decisions) that are necessary to improve the BER of the overall system. As shown, with higher number of iterations, we are getting the same performance as the conventional technique. However, the main goal at this stage is to have a deeper look at the interrelations between the different layer's parameters, i.e., the number of iterations needed for convergence with respect to a system performance metric which is the BER in our case for different SNRs.