Modern cellular radio systems such as 4G and 5G use antennas with multiple elements, a technique known as MIMO, and the intention is to increase the capacity of the radio channel. 5G allows even more possibilities, such as massive MIMO, where there can be hundreds of elements in the transmit antenna, and beam-forming (or beam-steering), where the phase of the signals fed to the antenna elements is adjusted to focus the signal energy in the direction of the receivers. However, this technology poses some difficult optimization problems, and here mathematicians can contribute. In this talk I will explain the background, and then look at questions such as: what is an appropriate objective function?; what constraints are there?; are any problems of this type convex (or quasi-convex, or difference-of-convex)?; and, can big problems of this type be solved in real time?
Further Information
A discussion session will follow the workshop and those interested are invited to stay in the meeting for the discussions.