Numerical optimisation methods for power consumption in multi-hop mobile phone networks

In recent years the importance of multi hop wireless networks has been growing mainly due to key factors such as: no backbone infrastructure or cost of installation are required and the network can be rapidly deployed and configured. A main problem in this kind of networks is to establish an efficient use of the power involved in the communication between network devices. In this dissertation, we present two different mathematical models which represent a multi hop wireless network: The first model considers the joint routing, scheduling and power control for TDMA/CDMA multi hop wireless network systems; minimising the used power to send messages through a multi hop wireless network. In this model we consider the scheduling of the message transmission. The scheduling is essential since it coordinates the transmission between devices in order to reduce the interference caused by the neighborhood devices and the background noise. Interference plays an important role in this kind of networks since the quality of service depends on it. We use two quality indicators: The Signal to Noise Ratio (SNR) and the Signal to Interference Noise Ratio (SINR). The second model considers the joint routing, power control for CDMA multi hop wireless network systems model in which we include two different filters: the Single User Matched Filter (SUMF) and the Minimum Mean Squared Error (MMSE), without considering the scheduling problem. The nature of the set of constraints inherent to both mathematical models is nonconvex, therefore we have a non convex optimisation problem. Since the problem is non convex, the obtained solutions are only local minimisers. We present and prove two theorems which, in general terms, state that at a local minimiser, the capacity over the links is fully exploited. We present different sets of experiments and numerical solution for both mathematical models