From TV channels to mobile wireless

The Smith Institute verified the interconnected models and algorithms in the US’s so-called Broadcast Incentive Auction, which optimises and re-purposes the use of some of the most economically valuable parts of the radio frequency spectrum.

The problem

Radio spectrum auctions are a well-established mechanism of awarding spectrum to the ones who are willing to pay the most for it. Spectrum auctions are not new to the Smith Institute: we have been working on algorithmic verification of combinatorial clock auctions since Ofcom introduced this design to the European telecommunications industry in 2006.

More recently, the FCC (Federal Communications Commission), the US telecommunication regulator, has successfully implemented a visionary model and a ground-breaking mechanism of market exploration for the US 600MHz frequency band. In what is called the US Broadcast Incentive Auction (BIA), the FCC has designed an auction in which the spectrum for sale is not specified up-front but relies on the current broadcast users revealing their preferences for spectrum they are willing to release in return for different levels of payment. Then, this "relinquished" spectrum is put forward to be auctioned and assigned to the companies making the best offers for new uses of the frequencies. The value created is greatly boosted by “repacking” the spectrum that is retained for broadcast use. This spectrum repacking maximises the amount and the quality of spectrum that can be released for new uses, while protecting the coverage and service quality enjoyed by consumers of broadcast services.

The objective of the BIA was to repurpose spectrum from TV broadcast services to mobile services. The auction was in fact two auctions. In the Reverse Auction, TV stations indicated the amounts that they would be prepared to accept in financial compensation to move either to a lower TV band or to go off-air. In the Forward Auction, mobile network service operators placed bids for the amounts they would be prepared to pay for the repurposed spectrum. These auctions were interleaved in their implementation: they proceeded in stages, with each stage being targeted at repurposing a particular amount of spectrum, called the Clearing Target, representing the amount of spectrum available in the Forward Auction. If the pair of auctions did not cover its own costs (i.e. if the total amount bid in the Forward Auction was not sufficiently in excess of the amount that must be paid out in the Reverse Auction) then the whole process was repeated with a smaller Clearing Target. Each Clearing Target was determined through repacking the remaining broadcasters as tightly as possible, so maximising the value of the Forward Auction.

Bidding in the BIA started in March 2016 and concluded one year later, in March 2017. The Broadcast Incentive Auction is unlike any auction that has previously been attempted, and it is large by any measure: there were approximately 2,000 potential bidders in the Reverse Auction and spectrum was offered in more than 400 regions in the Forward Auction. Its value to the US economy will be measured in tens of billions of dollars. The value to the telecommunications sector itself is indicated by the total of winning bids in the Forward Auction, amounting to $19.6bn. Of this amount, more than $10bn is being provided to the broadcasters who relinquished spectrum or moved bands and more than $7bn directly to the US Treasury for deficit reduction. In addition, studies in other spectrum bands have consistently shown that the annual economic value accruing as consumer surplus to the end-users of repurposed spectrum is likely to be several times these amounts.

The solution

From the summer of 2015 and for the majority of 2016, the Smith Institute has provided extensive verification services to the FCC in the delivery of the BIA.

Our role has been to verify all the algorithmic components in the Auction System, and the interactions between them. Our comprehensive analysis addressed all three of the key aspects in the BIA:

  • Bidding systems.  Altogether, there are three bidding systems: one for the Reverse Auction, one for the Forward Auction allocations and one for the Forward Auction assignments.
  • Auction constraints.  TV stations have their coverage populations protected by the auction rules. These rules also control the interference between TV stations and mobile operators. They are implemented in the auction optimisations through constraints, which are derived from radio propagation models.
  • Optimisations.  As mentioned above, a Clearing Target establishes how much of the old TV band can be converted into mobile spectrum. The quality of this spectrum is determined by the interference from TV stations. The purpose of the optimisations is to repack the TV stations that remain on-air as tightly as possible, to maximize the quality of the new spectrum while protecting the coverage of the TV stations.

We worked creatively and independently by defining the testing specifications, constantly reviewing them as the Auction System evolved and creating test cases and scripts to cover all possible algorithmic aspects.

In such a large, critical project involving multiple groups of stakeholders and contractors, we worked in a flexible and agile way, by identifying issues for further investigation rapidly and reliably, by communicating conclusions clearly and promptly across different time zones, and by being ready to re-test the systems as soon as updates became available. We were also able to suggest improvements to the system implementation and optimisation models which contributed to the reliability and efficiency of the Auction System.

The two specific innovations in the BIA were the Reverse Auction Bidding System and the optimised repacking of broadcast stations. The bidders in the Reverse Auction, namely the TV stations, were generally new to auction participation. The bidding interface was therefore designed to be as simple as possible, with a small number of possible bids offered in each round, at specified bid amounts. These amounts on offer were generally different for different bidders, calculated through a sequence of detailed algorithms. One of the Smith Institute's project tasks was to verify these precise calculations and the process of communicating their results to bidders via the auction interface. The repacking algorithms consisted of a series of optimisations, designed to ensure that broadcasters’ interests were protected and that international agreements with Canada and Mexico were implemented, while maximising the value released by the overall process. The Smith Institute was key in the verification of the repacking software.

The benefit

The Smith Institute's contribution to the BIA project was targeted to the independent verification of all the algorithmic and optimisation components in the Auction System, and their interactions. In doing so, we contributed to the overall reliability and efficiency of the Auction System. Within the project, our role was critical: a flaw in any component of the system could have meant that the whole process failed.

The Smith Institute’s independent verification provided assurance on the correct operation of the Auction System to the FCC. We helped to de-risk the auction process and ensure that it met its objectives to create economic value.

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