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With a single radio and a single channel, it is difficult to provide reliable and timely communication in case of high data rate requirements because of collisions and limited bandwidth. Therefore, designing multi-channel based communication protocols is essential for improving the network throughput and providing quality communication services.
In (Cardei & Mihnea, 2014) we introduced a distributed algorithm for static channel assignment in a wireless sensor network in which the monitored area is divided into grids. This grid-based algorithm is robust to primary users but require the nodes to have GPS or other localization protocols. In (Cardei & Mihnea, 2013) we introduced a distributed algorithm that does not require nodes to know their location and which also provides robustness to primary users.
The centralized and distributed algorithms presented in (Zhao & Cao, 2012) require multiple negotiations between nodes and may require cascaded switching of multiple users. The proposed solutions outperform existing interference-aware approaches when primary users appear, and achieve similar performance at other times. Compared to existing channel assignment methods for multi-hop multi-radio networks (Subramanian, Gupta, Das, & Cao, 2008; Tang, Xue, & Zhang, 2005), the channels are carefully assigned so that the primary user’s appearance will not partition the network. The algorithms in (Zhao & Cao, 2012) are compared with INSTC (Tang, Xue, & Zhang, 2005).
Some papers use primary user behavior models but predictability is not always possible. Like in (Zhao & Cao, 2012), we do not assume a predictable primary user activity. But knowing the maximum number of channels that could be reclaimed simultaneously by primary users could help in choosing the best parameters for our algorithms.
In this paper we maintain the assumption from (Cardei & Mihnea, 2014) that the nodes are able to calculate their position using GPS or other localization protocols, see (Karl & Willig, 2005). Based on this information they can determine the grid cell they belong to. Each grid cell chooses a representative that will be used to communicate with the representatives of the neighboring cells (above, below, left and right). In Figure 1 the cell representatives are marked in grey.
Figure 1. Monitored Area Divided into Grids and Cells’ Representatives (Grey)
Suppose that the communication range of all the nodes is r, then the grid size is chosen to be d=r/
so that the representatives of any two neighboring cells can communicate directly. Channels are assigned only to the representatives and any other node in a grid cell uses one of its representative’s channels to communicate with it, using a communication range d
. Our network is assumed to be a dense network such that there is at least one node in each cell; therefore, each cell has a representative.
In this paper we do not focus on channel assignment like we did in previous research. Our goal is to study the network formed by representatives, a connected backbone that ensures communication between cells. We analyze the capacity of the representatives’ communication by considering the ideal case when these representatives form perfect grids.
We consider grids of nodes in which each node represents a device with only one radio. We first assume that the communication is unidirectional but later we also give formulas for bidirectional communication. In this paper the number of channels that we use is denoted by m.
In case of unidirectional communication, data is sent but there is no acknowledgment from the receiver that data was received. Bidirectional communication involves the fact that the receiver sends an acknowledgment message to confirm that the data was received or the fact that the two nodes initiate communication through the exchange of RTS/CTS messages.