Wireless systems have become an inevitable part of modern technologies serving humankind. The rapid growth towards large dimensional systems, e.g. 5th generation (5G) technologies, incurs needs for improving the performance of the systems and considering aspects to make them as far as possible environmentally friendly in terms of power efficiency, cost, and so on. One of the key parts of every wireless communication system is the radio frequency (RF) power amplifier (PA), which consumes the largest percentage of the total energy. Hence, accurate models of RF PAs can be used to optimize their design and to compensate for signal distortions. This thesis starts with two methods for frequency-domain characterisation to analyse the dynamic behaviour of PAs in 3rd-order non-linear systems. Firstly, two-tone signals superimposed on large-signals are used to analyse the frequency-domain symmetry properties of inter-modulation (IM) distortions and Volterra kernels in different dynamic regions of RF PAs in a single-input single-output (SISO) system. Secondly, three-tone signals are used to characterise the 3rd-order self- and cross-Volterra kernels of RF PAs in a 3 × 3 multiple-input multiple-output (MIMO) system. The main block structures of the models are determined by analysing the frequency-domain symmetry properties of the Volterra kernels in different three-dimensional (3D) frequency spaces. This approach significantly simplifies the structure of the 3rd-order non-linear MIMO model.

The following parts of the thesis investigate techniques for behavioural modelling and linearising RF PAs. A piece-wise modelling technique is proposed to characterise the dynamic behaviour and to mitigate the impairments of non-linear RF PAs at different operating points (regions). A set of thresholds decompose the input signal into several sub-signals that drive the RF PAs at different operating points. At each operating point, the PAs are modelled by one sub-model, and hence, the complete model consists of several sub-models. The proposed technique reduces the model errors compared to conventional piece-wise modelling techniques.

A block structure modelling technique is proposed for RF PAs in a MIMO system based on the results of the three-tone characterisation technique. The main structures of the 3rd- and higher-order systems are formulated based on the frequency dependence of each block. Hence, the model can describe more relevant interconnections between the inputs and outputs than conventional polynomial-type models.

This thesis studies the behavioural modelling and compensation techniques in both the time and the frequency domains for RF PAs in a 3 × 3MIMO system. The 3D time-domain technique is an extension of conventional 2D generalised memory polynomial (GMP) techniques. To reduce the computational complexity, a frequency-domain technique is proposed that is efficient and feasible for systems with long memory effects. In this technique, the parameters of the model are estimated within narrow sub-bands. Each sub-band requires only a few parameters, and hence the size of the model for each sub-band is reduced.