## 4 The Propose Transmission Optimization Algorithm
### The Implementation Scheme  
To implement the proposed CB transmission scheme of sensor nodes in CPSS, we present the message exchange process for communications. Then, the proposed algorithm can be implemented in a decentralized way. Let \(C_{Z}\) be collaborative node set with \(O\) social sensor nodes and \((M-O)\) physical nodes; our objective is to select a collaborative node set from \(M\) candidate nodes including social and physical sensor nodes. The detail implementation procedure is given as follows:  
**Step 1: Initialization.** Source node \(s\) sends the Initialization Messages to each node \(z_{m}\) (\(m=1,2,...,M\)) in the deployment area. Each node initializes its regret value by \(R_{i}^{a_{i}}(t,l)=0\) or \(R_{i}^{a_{i}}(t)=0\) with \(i\in\{1,2,\cdots,O\}\) and \(l=\{1,2,\cdots,S\}\), as well as the probability of action selection \(\mathcal{P}_{a_{i}}^{i}=1/2\). The iteration index is set to \(t=1\).  
**Step 2: Collect Node Information.** Source node \(s\) sends an Information Collection Message to each node \(z_{m}\) (\(m=1,2,...,M\)) in the deployment area. When a node receives the Information Collection Message, its sends the State Information Message including its node location, node ID, and current strategy as a response to source node. The source node saves the state information of all candidate nodes and broadcasts the information to each sensor node and then carries out the next step.  
**Step 3: Establish Collaborative Node Set.** Source node sends Node Selection Messages to all social and physical sensor nodes in transmission range of source node. When the sensor node \(z_{i}\) can receive the message, it selects an action \(a_{i}\) according to the probability of action selection and responds by an Action Selection Message. This step repeats until all neighbouring sensor nodes of the source node have responded. Then, the selected nodes use CB to transmit the State and Strategy Information to the intended BS.  
**Step 4: Calculate the Utility.** The intended BS calculates the utility according Equation (23). Then, the intended BS returns the result through an Utility Information Message to each collaborative node.  
**Step 5: Calculate Regret Value and Update the Probability of Action Selection.** Each node calculates the regret value based on the received utility using Equation (24). Then, the probability of action selection are updated using Equation (25).  
**Step 6: Update the Social Sensor Node Location.** The social sensor nodes update the current location information based on the social dynamic mobility.  
**Step 7: Repeat Iteration.** If the number of iterations is less than the maximum number, then \(t=t+1\) and return to Step 2. Otherwise, the learning process stops and go to the next step.  
**Step 8: Data Transmission.** Source node \(s\) broadcasts the Sensing Information Message to all collaborative nodes with \(c_{i}=1\). Then, each candidate node responds by a confirmation Message. Then, the phase synchronization and CB technique are used to send the data symbol to the intended BS. When the intended BS successfully receives the signal and the interference power at the unintended BS is lower than the required value, each collaborative node will implement the transmission of data symbol based on the current strategy.