# Nonlinear Distortion Cancellation using Predistorter in MIMO-GFDM Systems
## 1 Introduction
Generally, there are four types of techniques which may be used to overcome nonlinear distortion in the multicarrier system. These include decreasing input back-off (IBO) [19], linearization of the HPA [20], a PAPR reduction approach [12], and signal reconstruction on the receiver side by estimating nonlinear noise and eliminating it with an iterative algorithm to eliminate the probability of error [21]. However, there limited studies that examine the effects of nonlinear distortion and techniques to overcome distortion in GFDM. A study that discusses the performance of Long-Term evolution (LTE) MIMO downlink systems in various fading environments has been carried out [22]. Research on GFDM MIMO has been carried out on the time-reversal space-time coding technique, Alamouti space-time coding, and spatial multiplexing, among others [23; 24; 25]. The detection system on GFDM MIMO using expectation propagation and near-maximum likelihood [25] has also been investigated. Additionally, the following studies have also been carried out: the implementation of the \(2\times 2\) MIMO transceiver GFDM for the 5G [26], the effects of nonlinear distortion on MIMO GFDM [18], and nonlinearity research on the space-time coding (STC) MIMO system using the Saleh model [27], where the HPA of each branch is assumed to have the same nonlinear characteristics and the parameters are considered known at the receiver side. However, based on the central limit theorem and for large subcarrier values, nonlinear distortion can be considered as a complex Gaussian process [28]. For MIMO systems, each user operates with multiple antennas and therefore the identical HPA assumptions are more realistic [11]. The techniques meant to overcome nonlinear distortion may be carried out on the transmitter or receiver sides. Predistorters are designed to model the inverse of a nonlinear HPA response and are often applied to the transmitter side for systems with a single transmitting antenna (SISO or SIMO system), though they may also be applied to MIMO systems [29] Two methods--DLA and ILA--may be compared to eliminate crosstalk on digital predistorters in the MIMO system where it is applied to each HPA separately [30]. On a large scale, antenna transmitter beam-forming has been investigated with the hybrid digital predistorter linearization method [31]. To date, no research has investigated the technique of overcoming nonlinear distortion in MIMO-GFDM systems. The contributions of this paper are as follows:  
1. This study investigates the effect of HPA nonlinearity on MIMO-GFDM systems and derives the new signal-to-noise (SNR) ratios in the scenario of a nonlinear MIMO-GFDM system. The HPA is characterized using amplitude and phase distortion curves known as AM/AM and AM/PM curves and modeled using the famous Saleh model [32]. This is an empirical model used in the literature because of the simplicity of parameter extraction obtained using direct measurements. 2. The study applies a predistorter algorithm meant to linearize HPAs at MIMO-GFDM. This approach is called \"local linearization\" and is used to obtain a distortion-free signal at the output of each HPA. For simplicity, it is assumed each of the HPAs in all branches of the sender have the same nonlinear characteristics. Furthermore, to simplify the model, the HPAs are presumed to be modeled using the Saleh model. The idea of modifying the MIMO-GFDM system to obtain distortion-free signals is investigated [13; 33]. 3. The main contribution is to investigate predistorter, which can linearize nonlinear distortion in MIMO-GFDM transmitters. The predistorter proposal with local linearization in GFDM MIMO uses a point to point scenario. The results are supported by Matlab simulation of the MIMO-GFDM system in the Additive White Gaussian noise (AWGN) channel. This application requires changes on the transmitter side (i.e., at the base station on cellular networks) and not on the receiver.