1. Birmingham,15 th April 2010 1 Mathematics and Telecommunications – aspects from an operator’s perspective Michael Walker President of the IMA Vodafone Professor Telecommunications, Royal Holloway, University of London, and Visiting Professor University of Surrey HoDoMS Meeting 2010, Birmingham, 15th April 2010

2. 2 Contents IMA news Telecoms and Maths Users’ needs Terminal Customer propositions Service Enabling Connectivity Access Spectrum and regulation

3. Birmingham,15 th April 2010 3 IMA News (1) IMA and NUMS IMA 96% in favour of merger with LMS Council accepts LMS democratic decision Council continues to embrace the vision set out in the NUMS consultative report University Liaison Peter Rowlett peter.rowlett@ima.org.uk £400 grants available for any university maths society –http://www.ima.org.uk/student/index.htmlhttp://www.ima.org.uk/student/index.html IMA / Greenwich Undergraduate conference –6 February 2010, with thanks to Tony Mann and Noel Anne Bradshaw Free eStudent membership for 2011

4. Birmingham,15 th April 2010 4 IMA News (2) CMath Teach –Launched December 2009 Maths Careers website –mathscareers.org.uk –launched December 2009 –greatly improved resource for students –themes - I love maths; environment; health and society; business and money; entertainment; science and engineering; sport –11-14,14-16,16-19, undergraduates, graduates, adults, teachers Essential Modern Mathematics Research – Case Studies –To show to politicians and scientists the great benefit of current and recent mathematics research –Nigel Peake to co-ordinate –Two versions: politicians and scientists –Call for topics and experts –Working with EPSRC

5. Birmingham,15 th April 2010 5 Maths and telecoms – a rich history Seminal papers of Shannon –A mathematical theory of communications, Bell Syst Tech J 27, 1948 –Communication theory of secrecy systems, Bell Syst Tech J 28, 1949 Compression coding Error correcting codes –geometry, groups and combinatorics Cipher systems –symmetric cryptography and information theory –public key cryptography and number theory and complexity theory IEEE Transactions on Information Theory Users’ needs Customer propositions Service Enabling Connectivity Access Spectrum and regulation

6. Birmingham,15 th April 2010 6 Mobile communications

7. Birmingham,15 th April 2010 7 The Internet information, entertainment, publishing, communications and social interaction PersianBlog.Com

8. Birmingham,15 th April 2010 8 Access Tomorrow Multi-service platforms Content Services Yesterday Vertical services Mobile Fixed Data Net Fixed Telephony WLAN Services Transport, Switching & Access Networks Content Services Environment IP Multi-Services network Convergence of telecoms and the web

9. Birmingham,15 th April 2010 9 Problems of networks Sharing resources –radio frequency spectrum management Interference management –maximising capacity and coverage of radio access network –diversity coding and MIMO: quaternions and Cayley numbers Designing and managing networks for IP data traffic Securing the cloud How can mathematics help? –Don’t expect well formulated mathematical problems Users’ needs Customer propositions Service Enabling Connectivity Access Spectrum and regulation

10. Birmingham,15 th April 2010 10 Propagation characteristics – 3G extension bands @ 2.6 GHz and digital dividend UHF @ 800Mhz UHF 3G extension band

11. Birmingham,15 th April 2010 11 Economics of spectrum

12. Birmingham,15 th April 2010 12 Spectrum auctions Allocation by auction Gradual move to lighter regulation – –may permit change of use –may be traded  Usage defined by regulators  Allocation by “Beauty Contest”  Barrier to new entrants multi-round, multi-object simultaneous auctions designed to increase competition as well as achieve maximum prices combinatorial auctions bid strategies – and what is the best outcome

13. Birmingham,15 th April 2010 13 Coverage and capacity improvement Relaying - fundamental work by Kumar on ad-hoc and sensor networks distributed MIMO –mathematics of MIMO elaborated by Calderbank and others –but not yet for distributed MIMO Backhaul infrastructure Between sites Terminal jointly detected by 3 base stations

14. Birmingham,15 th April 2010 14 Designing IP data networks

15. Birmingham,15 th April 2010 15 The chaotic nature of IP traffic optimisation of data rates –nature of traffic –type of device optimisation of routing –early breakout –edge caching excessive usage offload multi-dimensional optimisation

16. Birmingham,15 th April 2010 16 The reason why these problems are important for operators Costs Time VoiceData Revenue Traffic Diverging expectations for traffic and revenue growth