## 4 Multi-Hop Data Forwarding Strategy Based on Annulus-Sectors
### Data Forwarding Strategy with the Help of the Candidate Cluster Heads  
It is obvious that in the annulus-sector of the \(k\)-th annulus, the number of nodes is the most, so \(\mathsf{o}\), in order to ensure that the buffer of the CH in the \(k\)-th annulus (i.e., \(c_{k}\)) does not overflow, the following requirement should be met during a round of data gathering. The buffer size is set to \(C^{\prime}\):  
\[l\times N_{k}\leq C \tag{26}\]  
In order to make full use of the storage space, the left and right side of Equation (26) are made equal in this paper. That is, the total amount of data collected by \(c_{k}\) is exactly equal to its buffer size at the end of a round of data collection. However, if \(c_{k}\) sends the \(C^{\prime}\) bits of data directly to \(c_{k-1}\) (the CH in the (\(k-1\))-th annulus) at this time, the buffer of \(c_{k-1}\) will overflow as \(l\times N_{k-1}\) bit of data has been stored. However, the buffer of each CCH in the RCCH where \(c_{k-1}\) is located at is empty right now. Thus, the CCH with the highest residual energy is selected as the next-hop receiver of \(c_{k}\). That is to say, in each RCCH of the (\(k-1\))-th annulus, there are two nodes responsible for data uploading. One is the CH (i.e., \(c_{k-1}\) in Figure 7, and another one is the CCH (i.e., node \(s_{k-1}\) in Figure 7. Similarly, in each RCCH, one CCH should be selected to receive and forward the data uploaded by the CH in the adjacent outer annulus. Therefore, for the RCCH in the \(i\)-th annulus, there are \(k-i+1\) nodes (one CH and \(k-i\) CCHs) need to send data to the corresponding nodes in the (\(i-1\))-th annulus, as shown in Figure 7. The specific steps of the data forwarding strategy are described as follows:  
1. For the RCCH in the \(i\)-th annulus (\(i<k\)), it is assumed that the nodes which are responsible for data forwarding have already been selected. The cluster head is defined as \(c_{i}\), and the other \(k-i\) forwarding nodes are denoted as \(c_{i,1}\), \(c_{i,2}\),..., \(c_{i,k-i}\), respectively, according to the load on them from high to low. 2. Then, \(c_{i}\) sends the \"request for data forwarding\" message to all the CCHs in the adjacent annulus-sectors of the \(i-1\)-th annulus. 3. After receiving this message, these CCHs return the reply messages with their residual energy information to \(c_{i}\), respectively. 4. After receiving all the reply messages, those \(k-i+1\) CCHs with the most residual energy are selected as the forwarding nodes. According to the residual energy ranking of them from high to low, they are denoted as \(c_{i-1,1}\), \(c_{i-1,2}\),..., \(c_{i-1,k-i+1}\). Then, \(c_{i-1,1}\), \(c_{i-1,2}\),..., \(c_{i-1,k-1}\) become the next-hop receivers of \(c_{i}\),\(2\),..., \(c_{i,k-i}\) respectively, while \(c_{i-1,k-i+1}\) is the next-hop receiver of \(c_{i}\). Figure 6: Analysis on the length of the communication radius. Thus, with the help of the CCHs, data packet loss due to buffer overflow could be avoided. In addition, the energy consumption of the CH and CCH could also be balanced to a certain extent. It is worth mentioning that, to implement this data forwarding strategy, the number of nodes in the RCCH of the (\(i-1\))-th annulus should be one more than those in the RCCH of the \(i\)-th annulus. According to Equation (15), it is known that this constraint can be met. In addition, it is not difficult to know from Equation (17) that if there are few nodes in the RCCH of the \(k\)-th annulus, in order to ensure the success of data forwarding, the value of \(k\) should be restricted. Considering the worst case, when there is only one node in the RCCH of the \(k\)-th annulus, the number of nodes in the RCCH of the (\(k-1\))-th annulus should be no less than two.