## 5 The Detail of Our Protocol  
In this section, we will describe the detail of our protocol. We call it Multi-hop Energy Neutral Clustering (MENC). As shown in Figure 3, the procedure of MENC consists of a one-time initialization phase and many repeated rounds that can be further divided into topology formation phase and steady-state phase. The duration of each round is just the minimum network data transmission cycle \(T\). During each round, sensor nodes in every unit will be re-grouped into several clusters. In addition, a cluster consists of one CH and some cluster member nodes. Since a cluster member node consumes less energy than it can harvest during each round, its accumulated residual energy will reach a certain threshold after several rounds (energy accumulation cycle), and then it has the eligibility to be selected as a CH. Since the units closer to BS have more clusters, the nodes in these units have shorter energy accumulation cycle and smaller energy threshold. For any node in unit \(i\) (\(1\leqslant i\leqslant m\)), its energy accumulation cycle is \(n_{i}.T\), since it serves as the CH once every \(n_{i}\) rounds. In addition, based on Equations (16), (18) and (26), its energy threshold \(ETh_{i}\) can be calculated as follows:  
\[ETh_{i}=Ech_{i}=n_{i}TP_{e}-\left(n_{i}-1\right)Ecm_{i} \tag{40}\]  
where \(Ech_{i}\) is the average energy consumed by a node in unit \(i\) when serving as a CH; \(n_{i}\) is the average number of sensor nodes per cluster in unit \(i\); \(T\) is the minimum network data transmission cycle; \(P_{e}\) is energy harvesting rate; and \(Ecm_{i}\) is the average energy consumed by a non-cluster head node in unit \(i\) to transmit data to its corresponding CH.  
In the initialization phase, BS broadcasts a message with different power level \(Lev_{i}\) (\(1\leqslant i\leqslant m\)) corresponding to the outer radius \(R_{i}\) (\(1\leqslant i\leqslant m\)) of each unit. In addition, this message includes the minimum network data transmission cycle \(T\), optimal number \(m\) of units, cluster numbers  
Figure 3: Time line denoting the procedure of MENC.  
\(c_{i}\) (\(1\leq i\leq m\)), average numbers \(n_{i}\) (\(1\leq i\leq m\)) of sensor nodes per cluster and energy thresholds \(ETn_{i}\) (\(1\leq i\leq m\)). A sensor node only receives the message broadcasted by BS with the lowest power level and determines which unit it belongs to based on this message. In addition, this node also estimates its distance to BS according to the received signal strength. CHs in each unit will be selected in the topology formation phase, and each one in unit \(i\) (\(1<i\leq m\)) will select a routing head from the CHs in unit \(i\) - 1. All CHs act as a routing backbone and cooperatively transmit data to BS. Based on this backbone, each sensor node will begin to transmit its sensing data to BS during the steady-state phase. To avoid the conflict of signals on the wireless channel, each CH creates an individual time division multiple access (TDMA) schedule for its cluster members. Every cluster member node transmits its sensing data to the CH in its own time slot and goes dormant during other time slots. Once a CH has received the data from its member nodes, it aggregates this with its own data by adopting data compression techniques and then transmits the data to its routing head or BS using a randomly selected code division multiple access (CDMA) code.  
In the rest of this section, we will give the detail of topology formation phase which includes clusters formation and routing heads selection. In addition, the pseudo code of the topology formation phase is shown in Figure 4.