2. PRELIMINARIES
The research efforts that proposed for the connectivity and coverage issues in WSNs are based upon a lot of theories and assumptions. The basic concepts of connectivity and coverage have an essential role in understanding this issue. In this section, we describe the notions of connectivity and coverage, the category of sensor nodes, sensing models and communication models.
2.1. Connectivity and coverage
The objective of deploying a WSN is to keep the FoI under strict surveillance and then forward the obtained information to a designated gateway/data sink. Hence, coverage and connectivity are the sufficient conditions for keeping the functionality of a WSN.
Since the data aggregated by a WSN has to be forwarded to the processing …show more content…
Communication model
Similar to the sensing model, multiple communication models also proposed to mathematically model the complex characteristics of the wireless communication channel. The simplest model is the protocol model in which two nodes can communicate with each other iff they locate in each other’s communication range Rc.
Further, in order to capture other disruptive physical characteristics of the wireless channel (e.g., the multiple path fading, and the interference, etc.) rather than only the diminishing effect of the transmission distance, the authors in [Gupta and Kumar 2000] modeled wireless channels incorporating these effects and called the model as signal-to-interference-plus-noise ratio (SINR) model ot the Physical model. Let Pti denote the transmission power of the node si in node set X . Then, by considering the ambient noise power level N0, the SINR of the received signal emitted by node si can be calculated by (4) where δmin is minimum acceptable SINR that necessary for node sj to achieve successful receptions and decoding. The signal power decays with distance is always assumed to be α > 2 [Gupta and Kumar …show more content…
Moreover, with similar assumptions, the authors in [Xue and Kumar 2004] showed that each node should be connected to Θ(logn) nearest neighbors for keeping the network connectivity. The critical conditions for the network asymptotically disconnected and the asymptotically connected are 0.074logn and 5.1774logn, respectively. Further, by considering the deterministically located unreliable nodes, the paper [Shakkottai et al. 2005] shows that, in a unit square area, the necessary and sufficient condition for the system to achieve both required connectivity and coverage is Rc2p(n) ∼ logn/n, where p(n) is the probability that a node is
The research efforts that proposed for the connectivity and coverage issues in WSNs are based upon a lot of theories and assumptions. The basic concepts of connectivity and coverage have an essential role in understanding this issue. In this section, we describe the notions of connectivity and coverage, the category of sensor nodes, sensing models and communication models.
2.1. Connectivity and coverage
The objective of deploying a WSN is to keep the FoI under strict surveillance and then forward the obtained information to a designated gateway/data sink. Hence, coverage and connectivity are the sufficient conditions for keeping the functionality of a WSN.
Since the data aggregated by a WSN has to be forwarded to the processing …show more content…
Communication model
Similar to the sensing model, multiple communication models also proposed to mathematically model the complex characteristics of the wireless communication channel. The simplest model is the protocol model in which two nodes can communicate with each other iff they locate in each other’s communication range Rc.
Further, in order to capture other disruptive physical characteristics of the wireless channel (e.g., the multiple path fading, and the interference, etc.) rather than only the diminishing effect of the transmission distance, the authors in [Gupta and Kumar 2000] modeled wireless channels incorporating these effects and called the model as signal-to-interference-plus-noise ratio (SINR) model ot the Physical model. Let Pti denote the transmission power of the node si in node set X . Then, by considering the ambient noise power level N0, the SINR of the received signal emitted by node si can be calculated by (4) where δmin is minimum acceptable SINR that necessary for node sj to achieve successful receptions and decoding. The signal power decays with distance is always assumed to be α > 2 [Gupta and Kumar …show more content…
Moreover, with similar assumptions, the authors in [Xue and Kumar 2004] showed that each node should be connected to Θ(logn) nearest neighbors for keeping the network connectivity. The critical conditions for the network asymptotically disconnected and the asymptotically connected are 0.074logn and 5.1774logn, respectively. Further, by considering the deterministically located unreliable nodes, the paper [Shakkottai et al. 2005] shows that, in a unit square area, the necessary and sufficient condition for the system to achieve both required connectivity and coverage is Rc2p(n) ∼ logn/n, where p(n) is the probability that a node is