An optimization approach to the economics of efficient multi-tiered spectrum sharing

Abstract

The Three-Tier Spectrum Sharing Framework (3-TSF) is a spectrum sharing model adopted by the Federal Communications Commission which operates in the 3.5 GHz spectrum band. 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 and then Tier-3. In this thesis, we study how a wireless operator, who is interested in maximizing its profit, can strategically operate as a Tier-2 and/or a Tier-3 user. Tier-2 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 thesis 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 thesis. We also conduct simulations using synthetic traces to compare our online algorithm with the benchmark and state-of-the-art algorithms.

In 3-TSF, the channels are leased to Tier-2 users through spectrum auctions. The duration of spectrum leases plays a crucial role in determining utilization of the spectrum bands. To the best of our knowledge, optimizing the duration of spectrum leases is an unexplored problem. In Chapter 3, we study the problem of optimal duration of spectrum leases but a simpler setup where channels are allocated for exclusive-use only. Specifically, we consider the following problem. 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, for e.g. 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 our problem as a two-stage Stackelberg game consisting of the regulator and the wireless operators and design efficient algorithms to find the Nash equilibrium of the entire game. These algorithms can also be used to find the Nash 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. 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 thesis presents the first mathematical approach to optimize the lease duration of spectrum licenses.

Chapter 4 of our thesis is motivated by how the 3.5 GHz band for 3-TSF is partitioned into channels and how those channels are further partitioned for licensed and unlicensed use. Motivated by 3-TSF, we consider the problem of partitioning an entire bandwidth into M channels of equal bandwidth and then further partitioning these M channels into P<=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 follow a tiered structure where licensed use has higher priority than opportunistic use. We address the following question in this thesis. Given a market setup, what value of M and P maximizes the net spectrum utilization of the entire bandwidth? This problem is highly relevant in 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 licensed channels (unlicensed channels) to join the market. These tradeoffs are captured in our optimization problem which manifests itself 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. The algorithm design also involves an efficient Monte Carlo integrator to evaluate expected value of the involved random variables like spectrum utilization and operators revenue. We use this algorithm to obtain interesting numerical results which suggest how the optimal value of M and P changes with different market settings.

In the recent years, the Federal Communication Commission has adopted several regulatory initiatives to encourage multi-tiered spectrum sharing over the TV-Band, AWS-3 band and the 3.5 GHz band. However, regulatory reforms are not enough for the success of multi-tiered spectrum sharing. From the inception of this paradigm, it was clear that for it to work, the requirements of various stakeholders like the regulator and the wireless operators need to be met. Satisfying such requirements involves solving various techo-economic optimization problems. In this thesis, we focus on three such optimization problems; online algorithm for leasing channels in multi-tiered spectrum sharing market, optimizing duration of spectrum leases to maximize spectrum utilization, and optimally partitioning a spectrum band to maximize spectrum utilization. The first problem is from the perspective of the wireless operators while the second and the third problem is from the perspective of the regulator.

Radio spectrum is the natural resource behind various wireless services we enjoy these days. However, radio spectrum is a limited resource. With exponential rise in wireless data traffic, we have saturated certain frequency bands which has lead to spectrum scarcity. However, other frequency bands, specially the ones allocated for federal use, are highly underutilized. In order to improve spectrum utilization, the concept of spectrum sharing has been proposed in which a spectrum band is shared among multiple entities of spectrum market at a granular time scale. Many different approaches of spectrum sharing, especially primary-secondary model, has received a widespread attention. In primary-secondary model, primary users have priority access rights to a spectrum band while the secondary users can use the spectrum band, provided that they are not degrading the performance of the primary users. The primary-secondary model is a specific case of multi-tiered spectrum sharing model with only two tiers.