# Acoustic Backscatter Communication and Power Transfer for Batterless Wireless Sensors
## 4 Evaluation
### Backscatter Communication
#### 4.4.1 Sdr Pipeline  
We first analyze the characteristics of the backscatter channel in the test structure. Figure 14 shows in the top graphs the SNR for different carrier frequencies. It can be seen that the SNR fluctuates by more than 20 dB within a few hundred hertz. Remarkably, in our measurements, the distance between the reader and tag transducer was small: the 3 m channel has even higher peak SNRs than the 2 m channel. To provide a detailed evaluation of a diverse range of channels, we pick three distinct carrier frequencies for each distance for further evaluation. In Figure 14 (bottom), the impulse responses for the selected channels are shown. We observe that all channels exhibit extended reverberation for about 10 ms. However, channel impulse responses vary strongly with carrier frequency. Hence, SNR alone is likely unsuitable for estimating a carrier frequency's communication reliability. The recorded impulse responses are available for download in Supplementary Material Data S2. Figure 12: The power consumption of the tag MCU with different oscillators. External crystal oscillators at equivalent frequencies consume significantly more power than the low-power internal oscillator. The backscatter modulation itself only consumes around 20 uW. Figure 13: The evaluation setup on a 3.5 m steel beam (not to scale). We use two different channels with lengths: 2 m and 3 m.  
Next, we transmitted 250 messages through each channel for each selected frequency and decoded them using our SDR pipeline, as described in Section 3.4, using the internal oscillator at the tag once and the more stable external oscillator once. The modulation scheme was 4-PSK at a symbol rate of 1000 symbols per second, yielding a total data rate of 2 kbit s\({}^{-1}\). Each packet contained 200 payload bits. First, we investigate if the more complex receiver with phase and timing error tracking is advantageous. Therefore, we decode all messages without tracking, i.e., only estimating CFO and STE from the preamble and assuming it is constant throughout the whole message. We then use the DPLLs for tracking the CFO and STE dynamically. The packet error rates (PER) displayed in Figure 14(a) reveal that nearly all packets are decoded correctly, even without error tracking when using the stable external oscillator. However, nearly 25% of the packets contain errors when using the internal oscillator. DPLLs enable error-free reception of all packets in both cases. Figure 14: SNR over the raw signal and after equalizing the received messages in 2 and 3 channels. Figure 15: Tracking phase and timing errors with a PLL improves the packet error rate drastically when using the unstable internal oscillator (**a**). When using a PLL, internal and external oscillators perform similarly, and all messages are received and decoded correctly in the channels under test (**b**). The switch used to decouple the harvester from the modulator circuit does not significantly impact output SNR (**c**). All recorded messages are available in Supplementary Material Data S1. We then compute the SNR of the equalizer output as  
\[\text{SNR}_{\text{out}}=10\log_{10}\left(\frac{\sum_{k}x_{k}^{2}}{\sum_{k}(y_{k}- x_{k})^{2}}\right), \tag{17}\]  
where \(x\) is the original transmission sequence, and \(\hat{y}\) is the equalizer's output. Figure 14 displays the deviation of output errors. The results show that the instability of the internal oscillator can be mitigated successfully when using the PLLs. The equalizer output's SNR with the internal oscillator is comparable to the one with the external oscillator. Notably, the results for the different channels are very similar, even though the SNR of the received signal varies by more than 10 dB between the channels. However, when comparing internal and external oscillators, note that the underlying channels are unequal. Even when the same nominal carrier frequency has been configured, the CFO of up to 70 Hz causes the internal oscillator to use a slightly shifted frequency band.