# Blockchain-Based Licensed Spectrum Fair Distribution Method towards 6G-Envisioned Communications
## 3 BEAST System Model
### System Process
### Incentive Mechanism

#### 4.3.1 Incentive Mechanism for Spectrum Users

In the PoT mechanism, there is no need for the nodes to calculate the hash puzzles. Therefore, how to generate a new block is a crucial issue in the proposed consensus mechanism. The block can be constrained as a fixed size of transactions. The nodes can generate new blocks only if they have collected certain transactions. In the traditional public blockchain consensus process, the miners will receive a certain quantity of transaction fees as rewards for mining the block successfully. Miners in Ethereum will obtain a _gas_ reward for collecting transactions through a smart contract. Thus, to actively participate in the PoT consensus further, the leader and the validator should be paid an extra trust reward. In order to encourage users to follow the spectrum usage rules, a trust value module is embedded in the proposed PoT consensus method. Apart from the rewarding _gas_, the

Figure 3: PoT consensus process. reward also includes the trust value. This trust-based incentive mechanism can effectively defend against a block withholding attack and deprivation of the incentives. The trust value reward is calculated with the following formulations [27]. \[T_{reward}=\frac{Count_{reward}}{\frac{C_{reward}}{C_{duration}}\bullet\frac{TV_ {i}}{Trust_{MAX}}\bullet E_{block\_max}},\text{ if }T_{reward}>1,\text{ then }T_{reward}=1 \tag{3}\]

\[TV_{i}=TV_{i}+\frac{(1-T_{reward})(Trust_{MAX}-TV_{i})}{d},d\geq 1 \tag{4}\]

Assume that the number of the registered miners on the consortium blockchain is \(n_{\text{miner}}\). And \(C_{duration}=2\bullet n_{\text{miner}}\) represents a certain number of blocks before the present moment. \(Count_{reward}\) is the number of blocks that a miner generated within the reward cycle \(C_{reward}\). \(E_{block\_max}\) is the expected maximum number of blocks generated with a miner with the maximum trust value in a competition cycle, \(C_{duration}\). The rewarded trust value is set to 0 when the expected maximum number of blocks is reached. Generally, \(E_{block}\) should be set large enough, so that it will not go to the most extreme situation that results in a block-accounting balance between miners. Otherwise, block generation will be very difficult, and further limits the speed of spectrum accessing. For different selection functions, the divisor \(d\) can be differently set to optimize the consensus protocol. For a block withholding attack, the corresponding malicious miner should be penalized; the penalty function of the miner \(n\) is expressed as follows:

\[E_{penalty}=\frac{Count_{penalty}}{\frac{C_{penalty}}{C_{duration}}\bullet \frac{TV_{i}}{Trust_{MAX}}\bullet E_{block\_min}},\text{ if }E_{block\_min}>1,\text{ then }E_{block\_min}=1 \tag{5}\]

\[TV_{i}=TV_{i}-\frac{(1-E_{penalty})TV_{i}}{d},d\geq 1 \tag{6}\]

where \(Count_{penalty}\) is the number of blocks that a miner generated within the penalty cycle \(C_{penalty}\), and \(C_{penalty}=2\times C_{duration}=4\times n_{\text{miner}}\). \(E_{block\_min}\) is the expected minimum number of blocks generated with a miner with the maximum trust value in a competition cycle, \(C_{duration}\). The aim of introducing this adaptive parameter is that if a miner can generate blocks satisfying the minimum expected number in a period of time, the miner will not be penalized, otherwise it will be deducted a corresponding trust value according to the percentage of completion. \(Trust_{MAX}\) is the top limit for the trust value; in this way, the trust value will not grow infinitely. #### 4.3.2 Incentive Mechanism for Spectrum Providers

In an actual scenario, there is usually more than one MNO belonging to different telecom operators in the \(ISA1\). Nowadays, the spectrum users tend to embed two Subscriber Identity Module (SIM) cards in smart devices. More and more smart devices support choosing telecom operators intelligently and accessing the idle spectrum provided with corresponding MNOs.