## 2 Preliminaries and Related Works
### Link Correlation Reasoning and Measurement  
Previous works have concluded that link correlation is greatly affected by shadow fading and interference [13; 21]. If two nodes have similar signal strengths and interference, they are more likely to receive/lose packets at the same time. As a result, the link correlation between the two links would more likely be strong. Data transmission rate and packet length: With the above two factors, however, we can still not decide the link correlation. The reason is that the underlying interference and noise are varying, and the data transmissions capture only part of the interference and noise. For example, of two links \(A\to B\) and\(A\to C\), when there is an interfering source (e.g., WiFi AP) near \(B\) and \(C\), it is more likely that the two links have similar packet losses and are thus highly correlated. However, the two links may also be independent if the transmissions from \(A\) happen at the whitespace of WiFi communication. We can see that the interference and noise captured by the packet transmissions (the interference and noise covered by grey parts) essentially decide the link correlation. To decide the interference and noise fractions captured by the packet transmissions, clearly, the packet length and transmission rate are the two important factors (it is worth noting that in many WSN-based applications, data packets are transmitted with fixed data rate [1]). To more clearly illustrate the impact of the two factors, we use a simple example with one sender and two nearly-placed receivers. Nearly-placed receivers have similar signal strength, noise and interference. The sender keeps broadcasting packets, and we study the link correlation between the two links. As depicted in Figure 1, the x-axis denotes time, and the y-axis denotes the environmental interference. The grey blocks denote packet transmissions. PTD denotes the packet transmission duration, which is determined by the packet length. PTI means packet transmission interval. We can see that the three packets capture different fractions of interference, resulting in certain link correlation values. As a result, Packets 1 and 3 are more likely to be lost at the receivers, while Packet 2 is more likely to be independently received/lost at different receivers. The reason is that interference during Packet 2's transmission is low, while the interference during Packets 1 and 3 is high. Clearly, different PTIs and PTDs will lead to different captured interference and noise, resulting in different link correlations. Beacon-based correlation measurement (BCM) has two main drawbacks in capturing the link correlation (_i.e._, the data packet reception/loss correlation). First, from the above observation, beacons have different packet lengths and transmission rates than data packets, capturing different interference patterns with data packet transmissions. Thus, interference that has a large impact on data packet reception/loss correlation may not be captured by the beacons. Second, even the captured interference is similar, since the beacons' packet lengths are different from the data packets, the reception of beacons and data packets will be different. Existing works have concluded that with the same signal-to-interference and noise ratio (SINR), short packets are more likely to be correctly received [22]. Figure 1: An example to illustrate the impacting factors of link correlation. PTD, packet transmission duration; PTI, packet transmission interval. Therefore, a data packet loss may be misestimated as a reception using a beacon message, which further yields errors for estimating data packet reception/loss correlations. Statistical approach: A simple improving approach is to simply use data receptions/losses for measuring link correlation, in which the link correlation is calculated based on the historical traces of packet receptions and losses. However, since link correlation is often used for routing decisions, the desired link correlation should combine long-term stable behavior, as well as short-term behavior.