The main focus of this thesis is to develop and investigate a new possible solution for compensation of in-phase/quadrature-phase (I/Q) impairments and power amplifier (PA) nonlinearity in wireless transmitters using accurate, low complexity digital predistortion (DPD) technique. After analysing the distortion created by I/Q modulators and PAs together with nonlinear crosstalk effects in multi-branch multiple input multiple output (MIMO) wireless transmitters, a novel two-box model is proposed for eliminating those effects. The model is realised by implementing two phases which provide an optimisation of the identification of any system. Another improvement is the capability of higher performance of the system without increasing the computational complexity. Compared with conventional and recently proposed models, the approach developed in this thesis shows promising results in the linearisation of wireless transmitters. Furthermore, the two-box model is extended for concurrent dual-band wireless transmitters and it takes into account cross-modulation (CM) products. Besides, it uses independent processing blocks for both frequency bands and reduces the sampling rate requirements of converters (digital-to-analogue and analogue-to-digital). By using two phases for the implementation, the model enables a scaling down of the nonlinear order and the memory depth of the applied mathematical functions. This leads to a reduced computational complexity in comparison with recently developed models. The thesis provides experimental verification of the two-box model for multi-branch MIMO and concurrent dual-band wireless transmitters. Accordingly, the results ensure both the compensation of distortion and the performance evaluation of modern broadband wireless transmitters in terms of accuracy and complexity.