# Backscatter Communications: Inception of the Battery-Free Era--A Comprehensive Survey
## 4 BackCom: Signal Processing and Detection
### Signal Detection in BackCom
#### 4.2.2 Non-Coherent Detection  
Non-coherent detection in BackCom does not need phase information for the detection of signals. Therefore, this detection technique can be used in different scenarios in which phase information cannot be extracted easily. [PERSON] et al. studied the fundamentals of various aspects of non-coherent Amb-BackCom systems [84]. They utilized the joint probability distribution function (PDF) of the received signals for the computation of the maximum likelihood detector. Figure 17 shows the decision regions for the non-coherent joint energy detector, which has four decision regions: \(R_{1}\)-\(R_{4}\). The notation \(Z_{k}\) and \(Z_{k-1}\) are notations referred to below as signal energies, and \(T_{h}\) is considered the detection threshold. * Decision Region \(R_{1}\) would be selected if \(Z_{k-1}\leq T_{h}\) and \(Z_{k}\leq T_{h}\), and the \(k-th\) symbol sent by the tag would be decided as \(\hat{d}_{k}=0\). * Decision Region \(R_{2}\) would be selected if \(Z_{k-1}>T_{h}\) and \(Z_{k}>T_{h}\), and the \(k-th\) symbol sent by the tag would be decided as \(\hat{d}_{k}=0\). * Decision Region \(R_{3}\) would be selected if \(Z_{k-1}\leq T_{h}\) and \(Z_{k}>T_{h}\), and the \(k-th\) symbol sent by the tag would be decided as \(\hat{d}_{k}=1\). * Decision Region \(R_{4}\) would be selected if \(Z_{k-1}>T_{h}\) and \(Z_{k}\leq T_{h}\), and the \(k-th\) symbol sent by the tag would be decided as \(\hat{d}_{k}=1\). Figure 16: The Structure of Coherent Correlation Receiver with Four Correlators and Two Pairs of Complex Channel Gains. The detection schemes for Amb-BackCom are highlighted next. [PERSON] et al. considered a transmission model for signal detection in Amb-BackCom [65]. The authors designed an algorithm to derive two closed-form detection thresholds. Similarly, another algorithm based on the detection of three states of backscattered signals considered a positive phase backscatter, a negative phase backscatter, and non-backscattered signals for Amb-BackCom [72]. Later, a joint-energy detector was designed to derive detection thresholds for Amb-BackCom signals [84]. This work also suggested a simple blind method for the practical implementation of detectors to obtain necessary parameters. [PERSON] et al. solved the issue of the error floor in conventional energy detection created by the direct link interference in BackCom [85]. Moreover, they proposed a likelihood ratio dependent detector and a beamforming assisted energy detector for BackCom symbol detection, in the presence of channel state information. Likewise, the problem of uplink detection for the Amb-BackCom system was considered in a one-reader-one-tag scenario [67]. Theoretical models for two detectors were designed to address the problem of uplink detection. One detector obtains a minimum BER, while the other attains equal BER in detecting \"0\" and \"1.\" Meanwhile, the thresholds are derived for both detectors in addition to similar BER expressions. Signal detection for Amb-BackCom is focused on examining the corresponding BER performance [86]. Authors formulated a theoretical system model to design a data detection approach with channel state information (CSI). Similarly, a flicker detector uses per symbol in-band BackCom while using a residual channel of WiFi packets [87]. [PERSON] et al. suggested a semi-coherent manchester detector and a non-coherent manchester detector [88]. These detectors could decode the manchester-coded and differential manchester-coded information, respectively. Later, the signal detection problem in the cooperative receiver was addressed for Amb-BackCom. The recovery of signals from ambient devices in addition to RF sources is shown in [89]. [PERSON] et al. solved the signal detection problem with differential modulation for the Amb-BackCom system [90]. They designed a suboptimal detector by integrating an approximate threshold for detection and derived relative BER expressions.