The aim of this PhD project is to investigate the design of algorithms for future wireless communication systems (Beyond 5G and 6G) that are enable by intelligent reflecting surfaces (IRS). IRS can improve communication coverage by reflecting incident electromagnetic waves from a base-station to a mobile user that cannot be reached directly, i.e., located in a non-line-of-sight shadowing zone. The IRS are constructed using low-cost passive antenna array elements that are controlled by the base-station using a low-cost microcontroller. The latter adjusts using feedback from the mobile user the phase shifts between antenna elements to control the reflecting signal beam and steer it to the desired direction. This PhD study will address IRS related challenges such as algorithms that optimize reflection, low-complexity channel estimation and feedback approaches, along with channel measurements, practical hardware constraints and integration in cellular architectures. The student will make use of the state-of-the-art lab facilities in the Department of Engineering at Nottingham Trent University and receive specialist training in simulation, theoretical analysis and measurement techniques.