Multiple-input multiple-output (MIMO) technology will continue to play a vital role in next-generation wireless systems, e.g., the fifth-generation wireless networks (5G). Large-scale antenna arrays (also called massive MIMO) seem to be the most promising physical layer solution for meeting the ever-growing demand for high spectral efficiency. Large-scale MIMO arrays are typically deployed with high integration and using low-cost components. Hence, they are prone to different hardware impairments such as crosstalk between the transmit antennas and power amplifier (PA) nonlinearities, which distort the transmitted signal. To avert the performance degradation due to these impairments, it is essential to have mechanisms for predicting the output of the MIMO arrays. Such prediction mechanisms are mandatory for performance evaluation and, more importantly, for the adoption of proper compensation techniques such as digital predistortion (DPD) schemes. This has stirred a considerable amount of interest among researchers to develop new hardware and signal processing solutions to address the requirements of large-scale MIMO systems. In the context of MIMO systems, one particular problem is that the hardware cost and complexity scale up with the increase of the size of the MIMO system. As a result, the MIMO systems tend to be implemented on a chip and are very compact. Reduction of the cost by reducing the bill of material is possible when several components are eliminated. The reuse of already existing hardware is an alternative solution. As a result, such systems are prone to excessive sources of distortion, such as crosstalk. Accordingly, crosstalk in MIMO systems in its simplest form can affect the DPD coefficient estimation scheme. In this thesis, the effect of crosstalk on two main DPD estimation techniques, know as direct learning algorithm (DLA) and indirect learning algorithm (ILA), is studied. The PA behavioral modeling and DPD scheme face several challenges that seek cost-efficient and flexible solutions too. These techniques require constant capture of the PA output feedback signal, which ultimately requires the implementation of a complete transmitter observation receiver (TOR) chain for the individual transmit path. In this thesis, a technique to reuse the receiver path of the MIMO TDD transceiver as a TOR is developed, which is based on over-the-air (OTA) measurements. With these techniques, individual PA behavioral modeling and DPD can be done by utilizing a few receivers of the MIMO TDD system. To use OTA measurements, an on-site antenna calibration scheme is developed to individually estimate the coupling between the transmitter and the receiver antennas. Furthermore, a digital predistortion technique for compensating the nonlinearity of several PAs in phased arrays is presented. The phased array can be a subset of massive MIMO systems, and it uses several antennas to steer the transmitted signal in a particular direction by appropriately assigning the magnitude and the phase of the transmitted signal from each antenna. The particular structure of phased arrays requires the linearization of several PAs with a single DPD. By increasing the number of RF branches and consequently increasing the number of PAs in the phased array, the linearization task becomes challenging. The DPD must be optimized to results in the best overall linear performance of the phased array in the field. The problem of optimized DPD for phased array has not been addressed appropriately in the literature. In this thesis, a DPD technique is developed based on an optimization problem to address the linearization of PAs with high variations. The technique continuously optimizes the DPD coefficients through several iterations considering the effect of each PA simultaneously. Therefore, it results in the best optimized DPD performance for several PAs. Extensive analysis, simulations, and measurement evaluation is carried out as a proof of concept. The different proposed techniques are compared with conventional approaches, and the results are presented. The techniques proposed in this thesis enable cost-efficient and flexible signal processing approaches to facilitate the development of future wireless communication systems.