Wireless communications technology enables us to seamlessly access many multimedia services, e.g., stored multimedia (e.g., video on-demand), live streaming (e.g., Internet live sport networks, Internet radio stations), and realtime interactive streaming (e.g., online games, video conference, e-education), etc. As such, wireless communications technology has rapidly gained a crucial role and become an important aspect of life. There is a strong, credible body of evidence, suggesting that mobile network operators are facing many formidable tasks but exciting areas of endeavour. Of most concern is the increase in ever-growing wireless/mobile devices and the huge demand in data rates associated with this. It is predicted that the number of mobile-connected devices will exceed 11.5 billion by 2019 (nearly 1.5 mobile devices per capita), which poses a huge traffic demand for ubiquitous communications. On the one hand, it is anticipated that we will witness an up to 10000- fold growth in wireless data traffic by the year 2030, and that of the UK alone is projected to increase between 23-fold and 297-fold over the period 2012-2030. The future 5G cellular network is expected to achieve as much as 1000 times data rate relative to its current 4G counterpart. On the one hand, as many as 50 billion devices will be connected to the Internet by 2020 request seamless connectivity and mobility. Data rates are projected to increase by a factor of ten every five years, and with the emerging Internet of Things (IoT) predicted to wirelessly connect trillions of devices across the globe, without novel approaches, future mobile networks (5G) will grind to a halt unless more capacity is created. One of the most attractive solutions is the implementation of ultra-dense networks constituted by the combination of macro-cells and small-cells and exploited the emerging technologies of millimetre wave (mm-wave) frequency bands, large-scale antennas arrays. But while these enabling technologies constitute one of the most attractive approaches, i.e., ultra-dense cellular networks, to improving the capacity and coverage of wireless systems, the "ultra-dense" aspect poses fundamental challenges, which urgently require solutions. Most importantly, the tool of system-level performance evaluation and optimization is very essential for telecommunication service providers. However, it is usually conducted by relying on numerical simulations, which are often time-consuming and even extremely difficult in the context of 5G ultra-dense networks. At present, no sound but essential mathematical methodologies towards the design of practical communication protocols and transmission techniques for ultra-dense heterogeneous cellular networks are available. Motivated by this lack of tractable solution, this research project proposes a mathematical model to take into account the practical aspects of 5G ultra-dense networks, i.e., highly dense distribution, dynamic random topologies, and heterogeneous interference. The unique feature of the project is to augment the recent advances in mathematics, random process, and signal processing theory involved by both base stations and mobile devices in ultra-dense cellular networks for recovering the transmitted voice, data, video, etc. This allows us to integrate interference management between large and small cells along with a large number of transmit/receive antennas and higher transmission bandwidth in mm-wave frequency bands. These include the development of new theoretical framework that is informed by the limitations of a practical system not currently considered in the context of "extremely dense networks" of current cellular systems.

We investigate mathematical models of computation, which is a necessary precondition to understand and explain the behaviour of AI systems and other computer programs. Cyber-physical systems increasingly affect most aspects of our lives: they are used in pacemakers, manage factory supply chains, trade in stocks and autonomously pilot modern planes and cars. Software deficiencies can have serious economic and life-threatening consequences. While traditional methods of testing and simulations can be effective for finding errors, they are hopelessly inadequate for showing their absence. A more promising approach is to use mathematical arguments to prove that a system behaves as intended, in all possible situations. Verification is the area of research based on this idea. It is truly interdisciplinary and has fascinating connections to Artificial Intelligence, Discrete Mathematics and Software Engineering. To prove the correctness of some system one starts with a formal model of the system itself as well as a specification that defines what correctness means. In model-checking, for instance, we model systems as a finite-state machine and the specifications as temporal logic formulae. Correctness then ammounts to the fact that the finite-state machine satisfies the formula, which can often be verified automatically. Naturally, there are many different ways to formalize systems and specifications, and some formalisms are more expressive than others. Current methods are very good at analysing models with only finitely many internal configurations, such as microchips or hardware drivers. However, if we move to more expressive models we quickly go beyond the reach of known techniques or even cross theoretical limits. At this point the research frontier is on so-called infinite-state models, which enable us to argue directly about unbounded quantities such as realtime constraints, recursion depth or simultaneous user requests. For example, imagine a network server that can receive any number of requests concurrently and which should eventually respond to all of them. The total number of requests is not determined in advance and so it is necessary to incorporate it into the model, which consequently has infinitely many possible internal configurations. However, we do have good finite representations, such as Counter Machines or Pushdown Automata, that can be used in such situations. The result is a trade-off between the expressibility of these formalisms and the feasibility of their verification. A key mathematical tool for correctness checks and decision making in the presence of environmental uncertainty are games between antagonistic players, who try to cause and prevent errors, respectively. Closely related formalisms are used in Economics, Biology, Chemistry and other sciences, in the form of Markov Chains and Markov Decision Processes. Correctness here corresponds to the existence of winning strategies, which tell their player how to move in order to secure a win. Winning strategies are important not only because they act as correctness certificates but also because they can often be directly translated into executable code. Our research seeks to understand more general, infinitary strategies, which are often necessary for realistic specifications. We will investigate the mathematical structure, internal complexity, and thus the cost of winning strategies. Advancing our understanding of strategies promises to yield better finite representations, which in turn makes it easier to verify that winning strategies exist (checking correctness) as well as automatically generating and executing them. Our research leads to a deeper understanding of the nature of computation and decision making and provides new and improved methods for automated program verification.

The emerging theory of negative imaginary systems is attracting increasing interest amongst control systems researchers because it captures a wide range of practical problems. Negative imaginary dynamics often arise as a simple fundamental consequence of Newton's second law of motion. Often control systems performance can be significantly improved, despite demanding robustness requirements and difficult dynamics, by directly exploiting system properties. The study of negative imaginary systems can lead to potential improvements in several engineering fields including areas of advanced technology such as nano-positioning systems, control of multi-agent dynamical systems, distributed network control, mechatronics and robotics among others. This work will develop new results in the theory of negative imaginary systems. These results will underpin controller design methods and controller tuning guidelines for this class of systems. The developed methodologies will be applied to several specific benchmark applications and case studies. Wide dissemination of the advantages of the negative imaginary concepts will be a key aspect of this work.

Wireless power transfer (WPT) via radio-frequency (RF) radiation has long been regarded as a possibility for energising low-power devices in the internet of things. It is, however, not until recently that WPT has become recognised as feasible, due to reductions in power requirements of electronics. Far-field WPT using RF could be used for long range power delivery to increase user convenience. In the same way as wireless disrupted communication, WPT using RF is expected to disrupt the delivery of energy. The real challenge with far field WPT is to find ways to increase the DC power level at the energy harvester output without increasing the transmit power, and to ensure that sufficient range between transmitter and receiver can be achieved. The project relies on the observation that far-field WPT RF-to-DC conversion efficiency is a function of the rectenna design but also of its input waveform. A proper design of far-field WPT therefore requires a complete transmitter-receiver optimization rather than just the receiver (rectenna) design. Unfortunately state of the art waveforms have been shown partially disappointing for far-field WPT. The fundamental question behind the project is "can we design a disruptive but practical WPT transceiver architecture to make wireless power transfer a reality at distances of tens (if not more) of meters within regulated transmit power levels?" This visionary project, conducted at Imperial College London, will uniquely leverage signal processing tools to tackle a problem commonly investigated by the RF community. Motivated by recent results by the PI and Co-I and leveraging a unique set of complementary skills on multi-antenna signal processing (Clerckx) and WPT/rectenna design (Mitcheson), the project will design and show the feasibility of a disruptive M2WPT architecture based on optimized, adaptive and reliable large-scale multi-antenna multi-sine waveforms for single-user and multi-user scenarios, and identify its potential for far-field WPT. Thinking big, we advocate in this project that M2WPT will be to WPT what massive MIMO is to communication. M2WPT will enable highly efficient far-field WPT delivering sufficient power at long range for a wide range of applications. To put together this novel M2WPT solution in a credible fashion, this project focuses on 1) designing and modelling the energy harvester, 2) designing large-scale multi-sine multi-antenna waveforms for single and multi-user scenarios, 3) demonstrate the feasibility through experiment and measurement. The project will be performed in partnership with two leaders in equipment manufacturing and WPT standardization (Toshiba and Keysight), two well-established academic/research centres active in WPT (KULeuven and Eindhoven/IMEC) and the UK Office of the Chief Science Adviser. The project demands a strong and inter-disciplinary track record in microwave theory and techniques, circuit design, optimization theory, multi-antenna signal processing, wireless communication and it is to be conducted in a unique research group with a right mix of theoretical and practical skills. With the above and given the novelty and originality of the topic, the research outcomes will be of considerable value to transform the future of wireless networks supplied by remote wireless charging and give the industry a fresh and timely insight into the development of highly efficient remote wireless charging, advancing UK's research profile of wireless power in the world. Its success would radically change the design of radiative WPT, have a tremendous impact on standardization, and applications in a large number of sectors including building automation, healthcare, telecommunications, ICT, structural monitoring, consumer electronics.

This proposal starts with the notion that, when considering future visual sensing technologies for next-generation Internet-of-Things surveillance, drone technology, and robotics, it is quickly becoming evident that sampling and processing raw pixels is going to be extremely inefficient in terms of energy consumption and reaction times. After all, the most efficient visual computing systems we know, i.e., biological vision and perception in mammals, do not use pixels and frame-based sampling. Therefore, IOSIRE argues that we need to explore the feasibility of advanced machine-to-machine (M2M) communications systems that directly capture, compress and transmit neuromorphically-sampled visual information to cloud computing services in order to produce content classification or retrieval results with extremely low power and low latency. IOSIRE aims to build on recently-devised hardware for neuromorphic sensing, a.k.a. dynamic vision sensors (DVS) or silicon retinas. Unlike conventional global-shutter (frame) based sensors, DVS cameras capture the on/off triggering corresponding to changes of reflectance in the observed scene. Remarkably, DVS cameras achieve this with (i) 10-fold reduction in power consumption (10-20 mW of power consumption instead of hundreds of milliwatts) and (ii) 100-fold increase in speed (e.g., when the events are rendered as video frames, 700-2000 frames per second can be achieved). In more detail, the IOSIRE project proposes a fundamentally new paradigm where the DVS sensing and processing produces a layered representation that can be used locally to derive actionable responses via edge processing, but select parts can also be transmitted to a server in the cloud in order to derive advanced analytics and services. The classes of services considered by IOSIRE require a scalable and hierarchical representation for multipurpose usage of DVS data, rather than a fixed representation suitable for an individual application (such as motion analysis or object detection). Indeed, this is the radical difference of IOSIRE from existing DVS approaches: instead of constraining applications to on-board processing, we propose layered data representations and adaptive M2M transmission frameworks for DVS data representations, which are mapped to each application's quality metrics, response times, and energy consumption limits, and will enable a wide range of services by selectively offloading the data to the cloud. The targeted breakthrough by IOSIRE is to provide a framework with extreme scalability: in comparison to conventional designs for visual data processing and transmission over M2M networks, and under comparable reconstruction, recognition or retrieval accuracy in applications, up to 100-fold decrease in energy consumption (and associated delay in transmission/reaction time) will be pursued. Such ground-breaking boosting of performance will be pursued via proof-of-concept designs and will influence the design of future commercial systems.