## 2 Related Work  
The Power and Spectrum Allocation Technique is one of the key technologies in cognitive radio technology. Reference [7] proposed a spectrum allocation scheme considering cognitive user mobility. In the same environment, cognitive users were able to access more spectrum when mobile, achieving good results in practical commercial applications. However, fairness among nodes was not extensively addressed. Reference [8] proposed a dynamic spectrum allocation algorithm that achieves on-demand allocation of spectrum resources, significantly improving fairness. However, this algorithm did not consider the issue of channel power interference in strong interference environments, making it suitable only for professional wireless radio systems with higher transmission rates. Reference [9] employed a Cournot game model that optimized the spectrum allocation for licensed users, demonstrating that reducing spectrum similarity would decrease the amount of spectrum leased by primary users. However, this algorithm treated all secondary users as a collective entity and did not deeply consider the issue of mutual interference among secondary users in terms of transmission power. Reference [10] introduced a bandwidth allocation scheme based on false alarm, determining perception cycles based on the Nash equilibrium, and allocating a spectrum bandwidth based on false alarm performance, effectively reducing energy consumption. Reference [11] proposes a multiuser OFDM subcarrier, bit, and power allocation algorithm to minimize the total transmit power. This is achieved by assigning each user a set of subcarriers and by determining the number of bits and the transmit power level for each subcarrier. However, this algorithm is only applicable to terrestrial wireless networks. Thus, it can be seen that spectrum allocation and power control are key technologies in cognitive radio (CR) to enhance spectrum utilization. The underwater acoustic cognitive network is proposed based on the above cognitive radio technology. CR technology based on spectrum allocation and power control is still an effective means to improve the utilization of spectrum, but due to the complexity of the underwater environment, the above technology needs to be improved before it can be applied. Based on game theory and OFDM modulation technology, literature [12] proposes a distributed power distribution algorithm to maximize the performance of each user through a non-cooperative game. However, because this algorithm does not provide channel state and node exchange information, it can not improve the performance and reliability. Literature [13] divides a channel into different cells and obtains a more accurate CSI based on the channel state information feedback by time-varying channels through self-learning. However, this algorithm can only achieve a higher throughput than traditional frequency multiplexing without considering propagation delay and resource allocation, which has great limitations. Based on the theory of a non-cooperative game,literature [14] proposes a CSI acquisition scheme with an instantaneous adaptive power allocation strategy. The forgetting factor is introduced into the power allocation algorithm, thus, improving the adaptive power allocation performance of multi-user communication in underwater acoustic channels. However, this algorithm does not consider the impact of sensor networks on marine mammals. Literature [15] proposed an environmentally-friendly channel allocation scheme. On the basis of locating marine mammals, transmit power and available channels were jointly allocated to competing users, which avoided the interference of artificial sensors on marine mammals and improved the network capacity. However, there was no further study on related issues such as channel transmission rate.