The energy used to power cellular communication networks has grown immensely in recent times due to the increased human reliance on the wireless transmission of data. This has led to increased energy consumption of cellular networks, intensified by the advent of the Fifth Generation (5G) communication standard. In order to improve the energy efficiency of current and future cellular communication genera- tions, the reasons why and how to reduce the power consumption without affecting performance is an important area of research. Power Amplifiers (PAs) are responsible for a considerable percentage of the power inefficiencies in Radio Frequency (RF) transmitters. There is a trade-off in the topol- ogy of PA architectures between linearity and efficiency. However, to maintain both high efficiency and linearity external linearisation procedures can be implemented digitally. Digital Predistortion (DPD) has been demonstrated as a suitable linearisa- tion solution of PAs that enables the retention of high efficiency and signal linearity. However as the carrier frequencies and bandwidths of the power amplifiers increase along with the introduction of multi-antenna base stations, new research and im- plementation obstacles emerge regarding efficiency, estimation and computational complexity of traditional DPD methodologies. This thesis contributes to the advancement of PA models, DPD function estima- tion process in terms of accuracy and robustness, and finally dimension reduction of specific DPD functions. These novel developments are cultivated with the afore- mentioned energy targets of 5G transmission and reception taken into consideration. Four novel contributions are presented in this thesis. The four contributions are related to publications listed in the Introduction of this thesis. The focal point of work presented is optimisation of techniques for PA modelling and linearisation. The first novel contribution was enhancing a specific learning adaption, Recursive Least Squares, with improved robustness. An elegant early stopping criterion was established to minimize both time taken to train model coefficients and model ac- curacy. The next novel contribution was a new strategy for DPD to combat the presence of multi-collinearity, and further reduce computational cost. The next contribution is related to the calculation of the limits to which modern communication signals can be down-sampled before use in calculating DPD coefficients , regardless of the DPD function used. The final contribution is that of a novel methodology for calculating a common set of coefficients suitable for behavioural model and DPD coefficient estimation for any modulated signal. Native features of the testbench were used and the structures implemented employed hardware resources commonly found in Field Programmable Gate Arrays (FPGAs).