Fast multi-dimensional array processing

About the Project

About the Programme

SPADS trains the next generation of UK defence engineers in cutting-edge and generation-after-next technologies in the areas of artificial intelligence, sensing and processing, and hardware design.

Through this training, which is co-designed with our industry and government partners, you will over four years become a highly qualified professional engineer, develop the solid technical foundations and skills required to work within multidisciplinary projects, as well as critical regulation and security knowledge to work with national and international companies.

The programme is based in Edinburgh and is delivered jointly by the University of Edinburgh and Heriot-Watt University. All students graduate with a joint degree awarded from both universities.

The project

This project is in collaboration with Thales UK and aims to new computationally efficient algorithms for large multi-dimensional array processing.

Objectives:

1. Develop new fast beamforming algorithms and adaptive array processing techniques using advances in fast Fourier integral operators and randomized algorithms
2. Build applications using these techniques for high-dimensional wideband sensor array processing problems, e.g. requiring the simultaneous processing of range, doppler, azimuth, elevation and frequency, in challenging acoustic and/or radar domains.
3. Explore the performance trade-off between accuracy and computational efficiency.

Description:

This project requires a student with a high level of mathematics or numeracy.

Large scale, multi-dimensional array processing problems, e.g. simultaneously processing range, doppler, azimuth, elevation and frequency, are ubiquitous in radar and sonar sensing, and it is essential to keep the computation to a minimum in order to process the outputs in a timely manner. For narrowband uniformly spaced linear arrays fast transforms such as the FFT can be exploited. However, dealing with large wideband non-uniform arrays remains a major challenge.

This project will develop novel fast array processing algorithms for statistical estimation and beamforming based on two recent developments in signal processing and related mathematics. The first is the construction of fast Fourier integral operator approximations [1,2,3,4], that can provably approximate the Fourier integral to a given level of accuracy in O(n.log(n)) while accommodating different sampling/physical geometries. The second is efficient fast randomized algorithms for solving large least square problems [5,6] that offer the potential for novel beamforming solutions [7]. The project will explore how these ideas can be integrated to develop novel efficient array processing solutions to tackle challenging sonar and RF array processing problems and to assess their performance trade-off between accuracy and computation.

To Apply: How to apply | SPADS CDT

Equality, diversity and inclusion

The programme aims to promote a culture of inclusion and diversity. In this context, we particularly welcome applications from women and other under-represented groups in science, technology, engineering, and mathematics (STEM).

Funding Notes

We are pleased to announce that we are part of the TechExpert pilot offering tax free stipends of £31,000 for students entering in session 2026/27 eligible for home fee status.

International students will receive a tax free stipend, for 2025/26 this was £23,112.

Full funding is available for this position.

As part of your funding package you will also a generous research training and support grant (RTSG).