We consider the problem of partitioning a spectrum band into M channels of equal bandwidth, and then further assigning these M channels into P licensed channels and M-P unlicensed channels. Licensed channels can be accessed both for licensed and opportunistic use following a tiered structure which has a higher priority for licensed use. Unlicensed channels can be accessed only for opportunistic use. We address the following question in this paper. Given a market setup, what values of M and P maximize the net spectrum utilization of the spectrum band? While this problem is of fundamental nature, it is highly relevant practically, e.g., in the context of partitioning the recently proposed Citizens Broadband Radio Service band. If M is too high or too low, it may decrease spectrum utilization due to limited channel capacity or due to wastage of channel capacity, respectively. If P is too high (low), it will not incentivize the wireless operators who are primarily interested in unlicensed channels (licensed channels) to join the market. These tradeoffs are captured in our optimization problem which manifests itself as a two-stage Stackelberg game. We design an algorithm to solve the Stackelberg game and hence find the optimal M and P. The algorithm design also involves an efficient Monte Carlo integrator to evaluate the expected value of the involved random variables like spectrum utilization and operators' revenue. We also benchmark our algorithms using numerical simulations.

中文翻译：

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随机市场模型下的分层访问中的最佳频谱划分和许可

我们考虑将频带划分为相等带宽的M个信道，然后将这些M个信道进一步分配给P个许可信道和MP个非许可信道的问题。按照具有较高优先级的分层结构，可以访问许可通道以进行许可使用和机会使用。未经许可的通道只能用于机会性访问。我们在本文中解决以下问题。在给定市场设置的情况下，M和P的哪个值可使频谱的净频谱利用率最大化？尽管此问题具有根本性质，但在实际应用中（例如，在对最近提议的“公民宽带无线电服务”频段进行分区的情况下）具有高度相关性。如果M太高或太低，分别由于有限的信道容量或由于信道容量的浪费，它可能降低频谱利用率。如果P太高（太低），将不会激励主要对非许可信道（许可信道）感兴趣的无线运营商加入市场。这些折衷体现在我们的优化问题中，该问题表现为两阶段Stackelberg游戏。我们设计了一种算法来解决Stackelberg博弈，从而找到最优的M和P。该算法设计还涉及有效的Monte Carlo积分器，以评估涉及的随机变量（如频谱利用率和运营商的收入）的期望值。我们还使用数值模拟对算法进行基准测试。它不会激励那些对无执照通道（有执照通道）主要感兴趣的无线运营商加入市场。这些折衷体现在我们的优化问题中，该问题表现为两阶段Stackelberg游戏。我们设计了一种算法来解决Stackelberg博弈，从而找到最优的M和P。该算法设计还涉及有效的Monte Carlo积分器，以评估涉及的随机变量（如频谱利用率和运营商的收入）的期望值。我们还使用数值模拟对算法进行基准测试。它不会激励那些对无执照通道（有执照通道）主要感兴趣的无线运营商加入市场。这些折衷体现在我们的优化问题中，该问题表现为两阶段Stackelberg游戏。我们设计了一种算法来解决Stackelberg博弈，从而找到最优的M和P。该算法设计还涉及有效的Monte Carlo积分器，以评估涉及的随机变量（如频谱利用率和运营商的收入）的期望值。我们还使用数值模拟对算法进行基准测试。该算法设计还涉及一个高效的蒙特卡洛积分器，以评估涉及的随机变量的期望值，例如频谱利用率和运营商的收入。我们还使用数值模拟对算法进行基准测试。该算法设计还涉及一个高效的蒙特卡洛积分器，以评估涉及的随机变量的期望值，例如频谱利用率和运营商的收入。我们还使用数值模拟对算法进行基准测试。