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 that 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 fundamental, 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.

This paper addresses the following question which is of interest in designing efficient exclusive-use spectrum licenses sold through spectrum auctions. Given a system model in which customer demand, revenue, and bids of wireless operators are characterized by stochastic processes and an operator is interested in joining the market only if its expected revenue is above a threshold and the lease duration is below a threshold, what is the optimal lease duration which maximizes the net customer demand served by the wireless operators? Increasing or decreasing lease duration has many competing effects; while shorter lease duration may increase the efficiency of spectrum allocation, longer lease duration may increase market competition by incentivizing more operators to enter the market. We formulate this problem as a two-stage Stackelberg game consisting of the regulator and the wireless operators and design efficient algorithms to find the Stackelberg equilibrium of the entire game. These algorithms can also be used to find the Stackelberg equilibrium under some generalizations of our model. Using these algorithms, we obtain important numerical results and insights that characterize how the optimal lease duration varies with respect to market parameters in order to maximize the spectrum utilization. A few of our numerical results are non-intuitive as they suggest that increasing market competition may not necessarily improve spectrum utilization. To the best of our knowledge, this paper presents the first mathematical approach to optimize the lease duration of spectrum licenses.

The three-tier spectrum sharing framework (3-TSF) is a spectrum sharing model adopted by the Federal Communications Commission. According to this model, under-utilized federal spectrum like the Citizens Broadband Radio Service band is released for shared use where the highest preference is given to Tier-1 followed by Tier-2 (T2) and then Tier-3 (T3). In this paper, we study how a wireless operator, who is interested in maximizing its profit, can strategically operate as a T2 and/or a T3 user. T2 is characterized by paid but ”almost” guaranteed and interference-free channel access while T3 access is free but has the lesser guarantee and also faces channel interference. So the operator has to optimally decide between paid but better channel quality and free but uncertain channel quality. Also, the operator has to make these decisions without knowing future market variables like customer demand or channel availability. The main contribution of this paper is a deterministic online algorithm for leasing channels that has finite competitive ratio, low time complexity, and that does not rely on the knowledge of market statistics. Such algorithms are desirable in the early stages of the deployment of 3-TSF because the knowledge of market statistics may be rather inaccurate. We use tools from the ski-rental literature to design the online algorithm. The online optimization problem for leasing channels is a novel generalization of the ski-rental problem. We, therefore, make fundamental contributions to the ski-rental literature, the applications of which extend beyond this paper. We also conduct simulations using synthetic traces to compare our online algorithm with the benchmark and state-of-the-art algorithms.