# Auto-Encoder Learning-Based UAV Communications for Livestock Management
## 4 Results and Discussions  
This section presents the simulation results and discussions based on the performance metric. For performance evaluation, bit-error-rate (BER), \(\Pr(\hat{s}\
eq s)\) is used as a performance metric for assessing the efficacy of our proposed learning model. Figure 5 compares the BER performance of a communications system using uncoded QPSK (4, 4) and a Hamming (\(7\),\(4\)) code with the optimal maximum likelihood decoding (MLD) against the BER gained by the auto-encoder (\(7\),\(4\)) with different training samples and average fixed energy constraints. It can be seen that the performance of the auto-encoder trained with 25,000 training samples matches the Hamming (7, 4) maximum likelihood decoding scheme. We also observe that the auto-encoder's performance falls as the number of training samples decreases. We ensure that the system operates at a 7/4 communication rate for fair performance evaluation. This result reveals that the auto-encoder has learned the UAV and GCS information mapping (i.e., an encoder and decoder function) that achieves the same performance as the Hamming (7,4) code with MLD without prior knowledge. Figure 6 compares the BER produced when the input data are modulated with binary phase-shift keying (BPSK), QPSK and 8 PSK against the BER achieved by the trained auto-encoder with an average fixed energy constraint based on (2). Generally, the number of encoded bits depends on the number of encoded phases. The BPSK uses two distinct phases shifted by \(180^{0}\) compared to QPSK, which utilizes four phases to encode the data. Therefore, the QPSK transmits 2-bit data, twice the data transmitted by BPSK per symbol cycle. In contrast, 8 PSK uses eight phases, described by a 3-bit transmitting 3-bit symbols per cycle. Accordingly, while the uncoded QPSK (4, 4) produces a BER lower than the BPSK modulation scheme, the Hamming (7, 4) hard decision decoding scheme outperforms all three modulation schemes. Interestingly, the auto-encoder trained with QPSK and 8 PSK-modulated symbols performs better than all the baseline communication schemes. We have observed that the performance gap between the auto-encoders trained with QPSK and 8 PSK tends to close between 2 and4 dB SNRs. At these SNRs, the communication rate of the auto-encoder trained with QPSK-modulated symbols decreases; it is thus forced to learn a lower modulation scheme. Beyond the 4 dB SNR, a significant decline in BER  
Figure 4: UAV and GCS information communications system over wireless channel presented as an auto-encoder. is observed, suggesting that the auto-encoder trained with the 8 PSK modulation scheme learns to transmit more bits per symbol cycle. Figure 5: BER vs. SNR for the auto-encoder trained with different amounts of samples against various benchmark communication techniques. Figure 6: BER vs. SNR for the auto-encoder trained with 25,000 training samples using QPSK and 8 PSK modulation schemes against baseline modulation schemes. Figures 7 and 8 portray the effects of both fixed and varying SNR on the auto-encoder's performance. Figure 7 shows that the BER falls faster when the auto-encoder is trained with a fixed SNR and then saturates at the 25_th_ epoch. With this, a relatively small training effort is required for the auto-encoder to learn various communication schemes. However, when the auto-encoder is trained with a varying SNR from \(-4\) to 10 dB, the BER slowly decreases with the training epoch and finally saturates at the 10 th epoch, as shown in Figure 8. From these results, we can deduce that an auto-encoder trained with fixed SNR for end-to-end communications converges faster than the one trained with varying SNRs. To investigate whether the auto-encoder has learnt some communication schemes without prior knowledge of the channel model, we show the learned constellation representations \(\mathbf{x}\) of all messages for different values of \((n,k)\). Figure 9 depicts a typical \((2,2)\) system, which assembles rapidly to a classical QPSK constellation rotation.