Mobile Phone Networks

What keeps your phone working as you walk around in a city is the solution to an invisible jigsaw puzzle whose pieces have to fit together just right. We found a new way to crack it.


When you cross a cell boundary, your phone has to be able to smoothly hand the service over from one base station to another. It uses different frequencies to tell the cells apart and thus avoids interference. The problem is that there are only a handful of such frequencies available. A network operator (such as Motorola) has to allocate them with great precision, essentially solving a tricky city-sized brainteaser for each new network.

In addition, the solutions found by Motorola did not remain usable for long. As new base stations were added to the network, the delicate balance of the frequencies was disrupted. Motorola’s only way to avoid interference was to carry out a laborious manual reset of all the frequencies periodically. This implied taking the entire network down, with the risk of a service interruption and the additional cost of buying replacement network capacity from competitors.

ThinkTank Maths (TTM) was offered the challenge of reformulating this difficult engineering problem mathematically. Expressing frequency allocation in terms of an intricate branch of pure mathematics allowed TTM to develop a method for dynamically re-setting the network. The solution involved changing the frequencies in a carefully computed sequence that avoided the need to take the network down, whilst still minimising interference.

In Motorola’s estimation, TTM’s solution led to an annual saving of several million pounds, along with a better quality of service for their customers. It’s easy to forget the formidable engineering challenges that have to be overcome, and the complex underlying mathematics, that make our phone calls possible in the increasingly convoluted communication network.


Mobile phone service providers require cellular towers to be deactivated for calibration and resynchronisation. Previous calibration methods required multiple neighbouring towers to be simultaneously deactivated, necessitating either service loss or purchasing of network capacity from competitors. ThinkTank Maths developed calibration procedures which allowed rolling deactivations, avoiding total network deactivation within a region.

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In Motorola’s estimation TTM’s solution led to an annual saving of several million pounds, along with improved quality of service for their customers.