Research Initiation Award Grant: Study of Satellite Radio Resource Management by Differential Game Models

研究启动奖为历史悠久的黑人学院和大学的初级和职业生涯中期教师提供支持，这些教师正在建立新的研究计划或重新定向和重建现有的研究计划。预计该奖项有助于进一步提高教师的研究能力和有效性，改善所在机构的研究和教学，并让本科生参与研究经验。授予克拉夫林大学的奖项可能在许多领域产生更广泛的影响。该项目的目标是研究卫星通信系统中的最优控制策略，以便在竞争的用户终端之间分配功率，这些用户终端共享一个频率选择性干扰信道，并将竞争有限的无线电资源；以及通过让本科生参与数学建模来提高大学的教与学。由于系统的竞争性和动态性，将利用微分博弈(DG)模型来求解最优控制策略。该动态博弈的主要内容如下：在频率选择性高斯干扰信道模型中，系统中有K个发射机和K个接收机。每个发送器和接收器对将被视为用户或玩家。整个频段被分成N个频段。在频率区间f中，玩家k以某种功能的模式分配能量，这被称为玩家k的控制。通过这种控制，如果将干扰视为噪声，则在时间t处能够实现的数据速率播放器k是时间的函数。玩家k的目标是在特定的时间间隔内最大化数据增益，该时间间隔是该时间间隔内数据速率函数的积分。系统的动力学是信道增益的变化率，它是控制和噪声的函数。因此，所有玩家都被组合在一个相同的动态系统中，使用他们的控件来实现他们自己的数据需求。在玩家之间不存在协作的假设下，构造了一个非合作的微分博弈模型来求解每个玩家的最优功率分配策略。此外，还将针对不同类型的竞争研究合作竞争模型和分级竞争模型。对DG模型的最优性条件进行了数学分析。将开发数值方法来求解模型。该项目的更广泛影响将是直接向卫星通信控制器提供功率分配策略设计，并推广为求解DG模型而开发的解决方法，并提高微分博弈模型的适用性。该项目将与明尼苏达大学数学及其应用研究所合作进行。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to Claflin University has potential broader impacts in a number of areas. The goal of this project is to study optimal control strategy in satellite communication system to allocate power among competing user terminals, who share a frequency-selective interference channel, and would be competing for limited radio resources; as well as to enhance teaching and learning at the university by involving undergraduate students in mathematical modeling. Differential game (DG) models will be used to solve for optimal control strategies, because of special features of the system - competitive and dynamical. The major components of this dynamic game are as follows: In a frequency-selective Gaussian interference channel model, there are K transmitters and K receivers in the system. Each transmitter and receiver pair will be viewed as a user or a player. The whole frequency band is divided into N frequency bins. In frequency bin f, player k allocates power in a pattern of some function, which is referred to as player k's control. With this control, if treating interference as noise, the data rate player k can achieve at time t is a function of time. Player k's objective is to maximize the data gain in a specific period of time interval, which is an integration of the data rate function over this time interval. The dynamics of the system is the rate of change of channel gain, which is a function of controls and noises. Thus, all players are combined in a same dynamic system, using their controls to realize their own data needs. Under the assumption of nonexistence of collaboration between players, a non-cooperative differential game model will be constructed to solve for optimal power allocation strategy for each player. Furthermore, cooperative and hierarchical competition models will also be studied for different types of competition. Mathematical analysis will be conducted to analyze the optimality condition of DG models. Numerical methods will be developed to solve models. The broader impacts of the project will be to directly supply satellite communication controllers with a power allocation strategy design, and to generalize solution methods developed for solving DG models and improve applicability of differential game models. This project will be conducted in collaboration with the Institute for Mathematics and its Applications at the University of Minnesota.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.