## 2 Related Works
### Non-EH Clustering Routing Protocols
#### 2.1.2 Uneven Clustering Routing Protocols  
Uneven clustering routing protocols are divided into single-hop and multi-hop clustering routing protocols, depending on whether they can address inter-cluster routing issues.  
1. In single-hop uneven clustering routing protocols, CHs far away from the sink will consume more energy to transmit their data, which will result in imbalanced energy consumption among nodes. In [22; 23], the size of the cluster radius is determined by Equation (1). Candidate CHs are chosen based on the number of accessible channels, and those with substantial residual energy within the cluster radius are elected to become CHs [22]. In [23], an uneven clustering protocol is put forward based on particle swarm optimization, which seeks to minimize energy expenditure within clusters. This is achieved by implementing a multi-objective function encompassing residual energy of nodes, neighboring node count, and proximity to the sink for CHs selection within a defined circular coverage area. Additionally, it proposes two fitness functions to determine the optimal location of CHs within the circular area for comprehensive network coverage. \[R_{c}=\left(1-c\frac{d_{\max}-d(i,sink)}{d_{\max}-d_{\min}}\right)R_{c}^{0},\] (1) where \(R_{c}^{0}\) signifies the maximum competitive radius, and \(c\) denotes the uneven clustering constant. \(d_{max}\) and \(d_{min}\) represent the maximum and minimum Euclidean distancesfrom all nodes to the sink, respectively, with _d_(_i_,_sink_) indicating the Euclidean distance from candidate CH \(i\) to the sink.
2. Multi-hop uneven clustering routing protocols can balance the energy consumption among CHs by controlling cluster radius, thereby extending the network lifespan. Reference [24] considers the nodes' residual energy when selecting candidate CHs and uses ant colony optimization to search for inter-cluster paths, which lightens the load on CHs, and the cluster radius is also determined by Equation (1). Reference [25] further factors in the residual energy of nodes, the number of neighbors, and the probability of idle channels when calculating the cluster radius. Protocols [24; 25] offer an improvement in balancing energy consumption and prolonging network lifetime compared to uniform clustering protocols, but the precise value of \(c\) is not tailored to the specific network configurations. In [26], an algorithm is presented that leverages grid clustering for efficient multi-hop routing, with the explicit goal of minimizing energy consumption. The algorithm considers various parameters including network area, node location, and node energy, and introduces communication nodes to alleviate the burden of inter-cluster communications in multi-hop routing protocols. Our previous work [27] designs a multi-hop uneven clustering routing protocol for CRSNs based on intra-cluster SWIPT (S-MUCRP). It establishes criteria for selecting CHs and relay nodes based on an energy level function, assessing nodes' transmission capabilities by considering both energy availability and spectrum access, thereby facilitating the selection of qualified CHs and relay nodes for improved energy equilibrium and network connectivity. While uneven clustering protocols have successfully tackled issues related to energy holes and hot spots, they have not yet rectified the fundamental limitation of energy scarcity in sensor nodes.