Optimal Joint Partitioning and Licensing of Spectrum Bands in Tiered Spectrum Access under Stochastic Market Models

We consider the problem of partitioning an entire band into M channels of equal bandwidth, and then further assigning these M channels into $P\leq M$ licensed channels and M-P unlicensed channels. Licensed channels can be accessed both for licensed use and opportunistic use while unlicensed channels can be accessed only for opportunistic use. The access to licensed channels follows a tiered structure, where licensed use has a higher priority than 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 entire bandwidth? This abstract problem is highly relevant in practical scenarios, e.g., in the context of partitioning the recently proposed Citizens Broadband Radio Service band. If M is too high (low), it may decrease (increase) spectrum utilization due to limited (wastage of) channel capacity. If P is too high (low), it will not incentivize the wireless operators who are primarily interested in licensed (unlicensed) channels to join the market. These trade-offs are captured in the optimization problem which is modeled as a two-stage Stackelberg game consisting of the regulator and the wireless operators. We design an algorithm to solve the Stackelberg game in order to find the optimal M and P. We use this algorithm to obtain interesting numerical results that suggest how the optimal values of M and P change with different market settings.