The part of the UHF band occupied by TV is getting smaller. The economic benefits of using the UHF band for mobile operators rather than TV, together with technology improvements, mean an increased amount of content can be broadcast on less spectrum. Over the last decade, what is considered as the “beachfront spectrum” has been cleared of TV and transferred to mobile 100 MHz. At the moment, Europe is undergoing a clearing and transition of the 700 MHz band, while the US and Canada are clearing 600 MHz as a result of the FCC’s Broadcast Incentive Auction.

Optimal transitioning in the UHF band

When preparing the clearing of a band, a new channel assignment for the TV broadcasters is needed that frees up spectrum for mobile operators. With a channel assignment in place, the costs of implementing the assignment and the transition from old to new can be determined alongside understanding the level of consumer education needed (e.g. retuning, new set-top boxes, new technology, new services, etc.) and finally how long the process will take. The transition can be a slow-moving procedure. For example, the clearing of the 600MHz band in the US is estimated to last 36 months. The duration is largely determined by the complexity of the transition from the old assignment to the new, e.g. by how many temporary channels are needed.

What if it was possible to shorten the transition time, at a lower cost and with less consumer impact, just by choosing the final channel assignment in a clever way? The Smith Institute believes that with mathematics, operations research and advanced algorithms, this is achievable.

The potential for interference between two broadcasters can cause dependencies between the stations regarding the order in which the transition from the old assignment to the new is organised. These dependencies can form chains which will determine that order. However, these chains can be complex and hence complicate the transition process. Furthermore, the chains can close on themselves, which means loops form that require each station to transition before the next station in the loop. This makes the new channel assignment impossible to implement without the use of temporary channels or raising the interference threshold to break the loop. Both operations will have impacts on consumers and be expensive, either in terms of equipment costs associated with changing channel twice at the same location, or lost revenue from consumers experiencing TV interference.

With mathematical optimisation techniques, an algorithm that can generate the best new channel assignments can be created. This means channel assignments that reduce the need for temporary channels and simplify the daisy-chains to minimise costs and consumer-impact, are the easiest to implement.

Finding a channel assignment satisfying all the interference constraints is like trying to spot a galaxy in the night sky, it’s not too difficult with a telescope. Finding the best channel assignments is like finding a star with an Earth-like planet orbiting it. There is an astronomical set of possible channel assignments to consider so it is not possible to check them all individually. With luck one of the best assignments can be found by chance, but it is more likely that a completely new set of tools to find them will be needed.

The Smith Institute believes that these tools are mathematical optimisation and advanced algorithms, paired with engineering data and propagation models. With these tools multiple different scenarios with different objectives can be explored at the same time. A channel assignment produced manually by humans can take one, at most two, objectives into consideration at a time but there is no way of knowing whether the assignment found is optimal.

Having an efficient way to generate the best channel assignments will allow multiple scenarios for assignments and transitions to be explored and enable decisions about the final channel assignment to be based on evidence.

These optimisation techniques are not only relevant to the UHF band but could also be applied in any other spectrum band, such as those occupied by mobile, satellite or radar. Therefore, mathematics and operations research will continue to have a big role to play in spectrum management to make evidence-based decisions.