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PhD Studentship - Riemann-Hilbert problem and algebro-geometric approach in optical communications (Leverhulme Trust Project)

Engineering and Applied Science - Studentships

Location:  Aston University Main Campus
Basis:  Full Time
Closing Date:  23.59 hours GMT on Thursday 31 October 2019
Reference:  R190172

Applications are invited for a three year prestigious cross-sectoral Postgraduate studentship supported the School of Engineering and Applied Science through Leverhulme Trust project RPG-2018-063 “Riemann-Hilbert problem and geometric approach in optical communications”, to be undertaken within the Aston Institute of Photonic Technologies (AIPT) at Aston University.  The successful applicant will join an established theoretical/experimental group working on the applications of the nonlinear Fourier transform (inverse scattering method) and the Riemann-Hilbert problem-based signal processing methods, for the sake of fibre nonlinearity mitigation in optical transmission systems and the investigation of paradigm-shifting approach for the next generation extra-high-capacity optical networks. The project requires the student to be proficient in contemporary nonlinear mathematical physics/applied mathematics, the knowledge of scientific programming, and implies the intensive interaction with mathematicians and theoretical physicist. 

The Aston Institute of Photonic Technologies pursues a diverse range of device-and-system-level topics at the leading edge of technology.  Our belief is that the understanding and mastering of nonlinear physical systems have a huge potential to enable a new generation of advanced engineering concepts. Our research typically resides at the interface between fundamental nonlinear science, including physics and mathematics, and practical applications in fibre optics and photonics in general. The key research areas of the Institute include nonlinear optics and related math-physical methods, inverse scattering methods for signal processing and nonlinearity mitigation, high-speed optical transmission and processing, in fibre-based optical devices and components, etc.

The position is available to start in September/October 2019 (subject to negotiation)


The successful candidates will be employed on a full-time basis with a competitive salary in accordance with the Aston University regulations and the personal circumstances of the applicant. 

PhD studentship bursary

This studentship includes a fee bursary to cover the home/EU fees. Applicants from outside the EU may apply for this studentship but will need to pay the difference between the ‘Home/EU’ and the ‘Overseas’ tuition fees, the difference currently being £12,573 p.a. in 2019/20.

Confirmation that this funding support is in place for the full duration of the PhD studentship will be required as part of the application process. 

Background of the Project

This project is aimed at developing the theoretical base for fundamentally new, paradigm-shifting transmission and signal processing methods based on the essentially nonlinear principles and advanced contemporary mathematical theory describing the noise-perturbed nonlinear signal evolution down the optical fibre links. 

Optical fibre systems form the backbone of the global telecommunication networks that underpin Internet, broadband communications and digital economy. However, the growth of the Internet-based activities and the rapid proliferation of bandwidth-hungry on-line services (e.g. Internet of Things) have resulted in the ever-escalating pressure on the speed and quality of information flows interconnecting network participants. Hence, the contemporary communication systems are facing an increasing challenge to provide more and more line capacity. We will apply modern mathematical tools, such as the Riemann-Hilbert (RH) factorisation problem, for the design of new highly efficient approaches to signal processing and transmission in nonlinear fibre channels. 

Objective I. Theoretical approach. There are several possible ways for the effective adaptation of the Riemann-Hilbert problem solution specifically for the tasks of the optical communications. Within the Riemann-Hilbert problem-based approach, the information is mapped onto the parameters of finite-genus solutions of the master equation governing the light propagation inside the optical fibre – the celebrated integrable nonlinear Schrödinger equation. These parameters comprise the “gap ends” defined in the complex plane of the spectral parameter, and the associated phases. The paramount feature of this type of modulation is that the evolution of these parameters is linear while the signal propagates through the truly nonlinear fibre medium. The first task within the project will be to define the ranges of parameters and the types of nonlinear data modulation that could provide the best effectiveness of the communication system functioning (the highest data rate within the allowed spectral band, i.e. the maximal spectral efficiency). In turn, the system proposed must be resilient to the realistic corruptions occurring in fibre systems: optical noise, nonzero gain-loss profile, higher order terms, and other. Further, we plan to extend this approach for the two-component integrable generalisation of the channel model – the Manakov system. 

Objective II. Numerical approach. The applications to such a highly demanding field as optical communications requires our developing efficient, fast, stable, easily-controllable and reliable numerical methods for the digital signal processing used in the optical transmission system. The existing numerical algorithms for the computation of Riemann-Hilbert problem solution, however, have been developed with disregard to the aforementioned efficiency requirements. Thus, we need further modification and improvement of the existing methods and investigation of the new updated algorithms for the Riemann-Hilbert problem-based signal processing, which are able to respond to the challenges posed by the transmission application. The project implies the development of fast and parallelisable methods for the Riemann-Hilbert problem solution and for the recovery of modulated nonlinear spectral parameters at the receiver side. 

Within this project, the student will work on the theoretical development of new coding and modulations techniques, as well as on the development of related numerical algorithms, for the Riemann-Hilbert problem-based optical transmission systems, under the supervision of world-class mentors: Prof. S. Turitsyn (AIPT, main supervisor), and Dr Y. Prylepskiy (AIPT), in collaboration with Prof. D. Shepelskiy (Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine). The student will also benefit from cross-disciplinary collaboration with world-known experts in nonlinear mathematical physics, signal processing and optical communication in academia and industry, including University College London and Cambridge University.

Person Specification

We are looking for candidates with exceptional skills in mathematical and/or theoretical physics, or applied mathematics, with the accent on nonlinear systems and inverse scattering methods. Preferred skill requirements include experience in scientific programming and computing, nonlinear systems and their numerical analysis, integrable systems, inverse scattering, Riemann-Hilbert problem.  Knowledge in either the theory of integral and/or differential equations, information and communication theory, or machine learning methods, is an asset. Applicants with a Master of Science degree in Applied Mathematics, Theoretical Physics, or equivalent, are especially encouraged to apply. The successful applicant should have a first class or upper second class honours degree or equivalent qualification in mathematics, physics, or engineering.  

Additional Requirements:

1. Academic Entry Requirements

You should have been awarded, or expect to achieve, a first or upper second class Honours degree or equivalent qualification in mathematics, physics, or engineering. Preferred skill requirements include experience in nonlinear systems, inverse scattering methods, integral and differential equations, knowledge of scientific programming and computing, optics, communications. If your qualification are from an overseas institution please provide transcripts of the marks you have already achieved with your application

2. English language

For applicants from non-English speaking countries, it is necessary to have taken either the Test of English as a Foreign Language (TOEFL) or the British Council IELTS test (taken no more than two years before the start date of your course):

  • TOEFL IBT: 93 (23 in Writing, 19 in Speaking, 18 in Reading and 19 in Listening) 
  • IELTS:   6.5 (6.0 in Writing, Speaking, Reading and Listening).
  • Pearsons English language test: 63 with no less than 57 in each band

Further information can be found at

The online application form, reference forms and details of entry requirements are available here

Applications must also be accompanied by a research proposal giving an overview of the main themes of the research, and explaining how your knowledge and experience will benefit the project.

Details of how to write your project proposal are also included in the How to Apply section.

For informal enquiries about this project and other opportunities within the AIPT, contact Professor Sergei Turitsyn by email:

If you require further information about the application process please contact the Postgraduate Admissions team at

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Further particulars and application forms are available in alternative formats on request i.e. large print, Braille, tape or CD Rom.

If you have any questions, please do not hesitate to contact HR via






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