Ex-Post Enforcement in Spectrum Sharing

It seems inevitable that future wireless systems will include shared spectrum. Shared spectrum can be viewed as a rearrangement of rights among stakeholders that will require enforcement. Demsetz indicates that enforcement is a key factor of any property rights management and Shavell argues that the timing of the enforcement action (ex-ante or ex-post) plays an important role. The emphasis in commercial-government sharing in the US has been on ex ante measures. It has been posited that a system built on efficient ex post enforcement would reduce the opportunity cost of the ex ante measures. Determining the role of ex post enforcement in a spectrum sharing scheme is of significant importance since spectrum sharing will inevitably result in interference events. We propose to evaluate the role of ex post enforcement by modeling how an ex post only enforcement scheme might work, and what the limits are on its effectiveness. In particular, there are a number of factors to consider, including the cost and time of adjudication as well as how well the penalty is calibrated to the value of the communication. To examine the role of ex post enforcement in a spectrum sharing regime, we study an ex-post-only regime. To determine whether (and when) this approach is superior to an ex ante approach, we build a model of a geographic region with geographically distributed secondary users and a single primary user. Aggregate signal power of the secondary users will be ‘measured’ at the primary user’s antenna. The number of excluded secondary users will be determined based on an ex ante approach that uses exclusion zones. We will plot the opportunity cost of the exclusion zones for varying values of secondary user communications. To evaluate ex post enforcement, we posit an adjudication system that penalizes the secondary user for each interference event received at the PU’s antenna. The penalty would be proportional to the lost value of reception by the PU. The SU optimizes their transmissions so that the net value of a sequence of transmissions is positive. There are a number of phenomena that we study in this scenario. First, as the value for SU transmissions increase, s/he may find it valuable to risk higher interference penalty by transmitting closer to the PU’s antenna. This results in dynamic and self-determined “exclusion zones”. We can also model the income stream to the PU; at some point, it may be more valuable for the PU to collect interference penalties than to operate their system in that location. The above approach assumes that adjudication is immediate and costless. To determine the bounds of adjudication costs, we determine the cost level that would result in a region that is equivalent to an exclusion zone in ex ante enforcement. Having achieved that, we reason about the effectiveness of ex post enforcement system and their technical requirements. Ex post enforcement must play a role in practical spectrum sharing systems. Despite this, it is not a topic that has attracted much attention in the research literature, with the notable exception of the work by Sahai and his co-authors (see, for example [6]). In this paper, we examine the behavior of a pure ex post enforcement system and compare it to pure ex ante approaches. The results of this study will help researchers develop feasible approaches to adjudication and will help policymakers balance the use of ex ante and ex post enforcement techniques in spectrum sharing regimes.