### 2.1. Ant System and Optimization

In ant colony optimization (ACO), a colony of artificial ants is used to construct solutions guided by the pheromone trails and heuristic information [15]. ACO was inspired by the foraging behavior of real ants. This behavior enables ants to find the shortest paths between food sources and their nest. Initially, ants explore the area surrounding their nest in a random manner. As soon as an ant finds a source of food, it evaluates the quantity and quality of food and carries some of this food to the nest. During the return trip, the ant deposits a pheromone trail on the ground. The quantity of pheromone deposited, which may depend on the quantity and quality of the food, will guide other ants to the food source. The indirect communication between the ants via the pheromone trails allows them to find the shortest path between their nest and food sources. This functionality of real ant colonies is exploited in artificial ant colonies in order to solve optimization problem [15, 16].

### 2.2. Cost Function for Cluster

In the traditional clustering routing protocol, the radar node chooses to join the cluster head whose signal is strongest, according to the signal received from cluster head. However, it does not consider the residual energy of cluster head. Obviously, the structure of this cluster is irrational. To comprehensively consider the distance between the radar node and its cluster head, the residual energy of cluster head, and to further optimize the structure of cluster, we define the cost function for cluster, which is based on radio-free space path loss model. The radar node computes the values of cost function for clusters between it and cluster head, and chooses to join the cluster head whose values are maximum, so this structure of cluster will be able to better balance the network energy consumption.

In radar sensor network, the radar node transmits the radio in free space. The path loss model [17] is as follows:

where is radar node's transmission power, is the radar node's received power, is distance between radar node and , and and are antenna gain of receiving antenna and transmitting antenna, respectively. is the wavelength of carrier. is the path loss exponent which indicates the rate at which the path loss increases with distance; is the close-in reference distance which is determined from measurement close to the radar node transmitter.

Suppose transmission time, then sending energy and receiving energy. Formula (1) can be transformed by multiplying time, then

From (2), the receiving energy of receiving radar node is proportional to the transmission energy of transmission radar node; it inverses to the distance between and*.* Therefore, based on (2), we refer to ACO and define the cost function for a cluster as follows:

where is set of cluster head, are distance between radar node and cluster head , and is residual energy of cluster head , is adjustable weight of distance.

Clearly, the values of are proportional to the residual energy of cluster head and reverses to the distance between the radar node and cluster head. When is larger, not only the radar node is closer to its cluster head, but also the residual energy of this cluster head is greater. Hence, the node should choose to join the cluster head whose values of are maximum. Obviously, the cluster formed by this method, and not only the residual energy but also the energy attenuation of data transmission are taken into account.

### 2.3. Distance Pheromone

The location information of radar node's neighbor significantly influences the selection of cluster head for next round. When the distance between radar node and its neighbors is shorter, the aggregation of this radar node is larger, because this radar node is cluster head, and the cluster head is closer to its cluster members. The energy consumption of network can be reduced effectively. Referring to the pheromone model [3] of ant colony algorithm, we define the distance pheromone as follows:

where is distance volatile factor, , and , , is the distance between radar nodeand radar node , NBR is the neighbors' set of , is the number of neighbors, and is the distance between all cluster members and cluster head; is the distance between radar node and its cluster head, is adjustable weight of distance.

From (4), the value of is proportional to the average distance between radar node and its neighbors. A small value of indicates that the radar node aggregation is big, which brings that a great probability of this radar node is selected as cluster head.

### 2.4. Energy Pheromone

In addition, the residual energy of radar node's neighbor also significantly influences the selection of cluster head for the next round. The higher the residual energy of the radar node is, the greater will be the probability of selecting this radar node as a cluster head. If this radar node is selected as the cluster head, it can afford the energy dissipation of collection data, fusion data in the cluster, and sending data to the base station. Referring to the pheromone model [3] of ant colony algorithm, the energy pheromone is defined as follows:

where is energy volatile factor, , is the residual energy of radar node ; is the initial energy of radar node , is the residual energy of all cluster members which cluster node belongs to. is the adjustable weight of energy.

From (5), the larger the residual energy of the node is, the bigger is. As a result, the energy of radar node volatile is smaller, and the probability of selecting this radar node as the cluster head is greater.

### 2.5. Cluster Head Selection Function

According to the transition probability [3], the ant selects next node (cluster head for next round) from this node (cluster head for this round). In order to select cluster head for next round effectively, we comprehensively consider the residual energy and aggregation of radar node (energy pheromone and distance pheromone). The novel transition probability is defined as follows:

where cluster is a set of cluster members, and is the probability values of radar node , which is decided by the residual energy and aggregation of radar node. The radar node is selected as the cluster head for next round, whose value of is maximum. and are the adjustable weights of and , respectively. The selection of cluster head is related with and*.* A higher value ofincreases the chance for an ant to choose the radar node with more residual energy as the cluster head. A higher value ofincreases the chance for an ant to choose the radar node with bigger aggregation as the cluster head. Hence, the different cluster head is selected by dynamically changing the values ofand*.* When an RSN is not stable (the radar nodes move, so the distance between radar nodes is variable), a lower value ofand higher value ofare generally preferred. This is because the distance pheromone has become more important for the cluster head selection. As an RSN becomes stable, a higher value ofis preferred. This is because a higher value ofmeans energy pheromone has become more important for the cluster head selection.