# Acoustic Backscatter Communication and Power Transfer for Batterless Wireless Sensors
## 3 Materials and Methods
### Packet Structure  
Our packet structure consists of three parts: First, a synchronization sequence, where the tag generates the same symbol for multiple symbol periods. This sequence is designed to be long enough to yield a steady state despite the Inter Symbol Interference (ISI), allowing the receiver to roughly estimate the CFO and signal amplitude required for robust preamble  
Figure 6: The signal is filtered and demodulated in hardware to remove the carrier frequency at the reader. Afterward, a bandpass filter removes the self-interference, only leaving the backscattered signal. Figure 7: In the backscatter radio, the CFO and Symbol Timing Error (STE) stem from a mismatch in the same pair of clocks. detection. The second part is the preamble, where we employ a 13-symbol barker sequence. Finally, the actual symbols are sent. Different modulation orders may be used to achieve higher data rates or more robust signal detection, depending on the SNR of the channel. In this work, we have only investigated 4-PSK as a modulation scheme. Software-Defined Receiver  
After sampling, the signal is transformed into a baseband in software by digitally multiplying it with a sine of the same frequency. By choosing a sampling rate of \(4f_{i}\), the transformation to complex baseband samples with an in-phase component \(y_{1}\) and a quadrature component \(y_{\text{Q}}\) is  
\[y_{1}[i] =(-1)^{i+1}y[2i] \tag{7}\] \[y_{\text{Q}}[i] =(-1)^{i}y[2i+1]. \tag{8}\]  
Finally, this resulting signal has a sampling rate of \(2\cdot f_{i}\) and can be further downsampled to a multiple \(L\) of the symbol rate \(f_{\text{m}}\). Due to the previously described clock instability, three errors may arise in the baseband signal--CFO, Phase Offset (PO), and STE. We apply standard techniques from software-defined radio receivers, using DPLLs to track and correct these errors. The whole reception process consists of the three stages shown in Figure 8. First, in the _carrier detection stage_, the receiver detects the presence of the signal by a signal power threshold. Once the threshold has been exceeded, this stage also uses the recorded samples to perform a rough CFO and signal amplitude estimation. The CFO estimate \(\hat{f}_{\text{CFO}}\) is important because the preamble can not be detected reliably when the CFO is large. At the same time, the signal is scaled to unity power for each message, as the optimal gains and parameters for DPLLs in subsequent stages depend on the signal amplitude \(\hat{a}\). For the detection and compensation of timing errors, we need to oversample the signal with a multiple \(L\) of the symbol rate. In the _preamble detection_ stage, the receiver corrects the incoming samples by phase-shifting and scaling them with the estimated errors. It then searches for the start of a message by correlating it with the preamble. Once a peak in the correlation exceeds a fixed threshold, the start of the message is detected. In the following _symbol decoding_ stage, the DPLLs track the phase and timing errors during the message. The detected preamble is used to estimate the initial CFO and STE \(\alpha\) for DPLL initialization. Second, we also use the preamble to train the equalizer. As the preamble is used for parameter estimation and  
Figure 8: The SDR pipeline has three stages: Carrier detection, preamble detection, and symbol decoding. CFO \(\hat{f}_{\text{CFO}}\), phase error \(\hat{\phi}\), and TE \(\beta\) must be estimated and tracked throughout the message. equalizer training, its length is crucial. A longer preamble increases the accuracy of the estimated parameters and equalizer weights but also adds overhead and keeps the tag active without transmitting any payload. In the last stage, the data symbols are decoded. At the input of the stage, the signal is scaled and phase-shifted to compensate for CFO and PO. Then an interpolator corrects the STE. The samples are subsequently equalized with a decision feedback equalizer to remove ISI. Finally, a symbol decision is performed.