## 2 Related Work  
### Overview of Wireless Radio Link Models  
A lot of existing works are based on the Boolean disk model, as illustrated in Figure 1(a). Two nodes are either connected or disconnected depending on the transmitter-receiver distance and the disk radius. Recent works [2, 13] argue that the real characteristics of low-power wireless links differ greatly from the ideal model especially in their unreliability and asymmetry. Some studies have improved the disk model and consider the shadowing effect. The radiation pattern is squeezed and stretched as shown in Figure 1(b). It is proved in [14] that irregular radio patterns can achieve connectivity more easily if they can maintain an average number of functioning connections. The two models above are basically deterministic either with assured transmission or assured probability of transmission within the communication range. However, several studies [2, 13, 15-19] have pointed out that the communication range of a wireless node cannot be specified and they propose to use probabilistic link model, as shown in Figure 1(c) (the sickness of the line represents the probability of connection), instead of deterministic model. It is found that the successful transmission probability at agiven distance \(s\), namely \(P(s)\), is a non-monotonically decreasing function to \(s\). \(P\) relies not only on the distance \(s\) between two nodes but various parameters such as the channel parameters like the path loss exponent, the shadowing variance and the degree of irregularity (DOI) [16], the radio parameters including modulation, encoding, output power, receiver noise and frame size. The third link model discussed above is supported by many experimental studies and significantly affects networks behavior. [PERSON] _et al._ have identified in [2] the existence of three distinct reception regions in wireless links: connected, transitional and disconnected. The transitional region is relatively large in size and is characterized by high variance in reception rates and asymmetric connectivity. In a typical sensor networks, a large number of links (even higher than 50%) can be unreliable because of the transitional region. [PERSON] _et al._[17] provide a wealth of empirical data from studies of large scale, dense wireless network, which demonstrate that even a simple flooding algorithm entails complex behavior under unreliable links. [PERSON] _et al._[16] find that radio irregularity has a significant impact on the routing protocols in wireless sensor networks, especially location-based routing, such as geographic forwarding. All these research results lead us to stress the need for realistic link models for wireless sensor networks. Several recent studies have proposed communication models based on empirical data and analyzed related phenomena for more accurate evaluation of upper-layer protocols. [PERSON] _et al._[2] present a simple synthetic link model to generate data under specific radio and environment based on an assumption of Gaussian distribution of the packet reception rate for given transmitter-receiver distance. These synthetic traces are used for simulation of passive link estimators that snoop traffic over the channel and estimate link qualities. [PERSON] _et al._[15] study the relationships between location and communication properties using non-parametric statistical techniques. They provide a probability density function that completely characterizes the relationship and develop a series wireless network models that produce networks of arbitrary size with empirical observed properties. The accuracy of their models is evaluated through a set of communication tasks like connectivity maintenance and routing. [PERSON] _et al._[18] propose link inefficiency as a cost metric based on detailed observations of link quality variation and explore how link inefficiency can be measured in energy efficient way. They find that only a few measurements of the channel are sufficient to obtain a good estimate of the cost metric. Figure 1: Different kinds link models.