# Performance Analysis of Two-Hop mmWave Relay Nodes over the 5G NR Uplink Signal
###### Abstract
In conclusion, the combination of relay node co-operative networks and MIMO in mmWave bands emerges as an optimal solution to address the requirements of 5G network deployments. Our investigation team has been deeply studying the co-operative networks in this context; in [17], a MIMO relay node co-operative system based on Software Defined Radio (SDR) and Matlab\({}^{\text{TM}}\) software is implemented over the downlink LTE signal. Additionally, ref. [18] implements a link-level co-operative simulator for the study of mmWave MIMO RNs over the downlink 5G signal. However, the implementation of the mmWave MIMO RN co-operative network over 5G uplink has not been studied and evaluated yet. Therefore, in this work, we consider the first step to the implementation of mmWave MIMO co-operative network for the 5G uplink signal. Motivated by the described issues, in this paper, an mmWave MIMO 5G relay node co-operative system over a 5G uplink through Matlab\({}^{\text{TM}}\) and Simulink\({}^{\text{TM}}\) tools has been implemented and evaluated. In this paper, the major contributions are summarized as follows:  
* A link-level co-operative simulator for an uplink two-hop network using out-band 5G RNs at mmWave frequency and with MIMO capabilities is proposed and implemented. * In the proposed co-operative system, the 5G NR signal features, UL-SCH transport channel coding, and PUSCH generation were implemented, which fulfilled the requirements of the NR uplink 3 GPP. * Decode-and-Forward (D&F) protocols taking into account the channel knowledge with a Perfect Channel Estimation (PCE) and Least Square (LS) estimator were developed. Additionally, both structures implement the Minimum Mean Square Error (MMSE) equalization technique. Furthermore, analytical expressions for the D&F strategy of the proposed uplink co-operative network were derived. * An Amplify-and-Forward (A&F) strategy has been developed. Furthermore, system models for both A&F and D&F relaying strategies of the proposed uplink mmWave MIMO relay node co-operative network with a real-world focus have been derived. * In addition, the authors focus on the study in an indoor-to-outdoor scenario, using the 64-QAM and 256-QAM modulation schemes. Additionally, extensive simulations were taken into account and carried out with the Mathlab\({}^{\text{TM}}\) and Simulink\({}^{\text{TM}}\) tools, considering the non-linearity of mmWave subsystems. The rest part of this paper is structured as follows. Section 2 provides the system model and basic assumptions, in which uplink mmWave A&F and uplink mmWave D&F relays are introduced. In Section 3, the link-level co-operative simulator, topology, channel model, and mmWave transceptor are explained. The simulation results and performance evaluation are presented and discussed in Section 4. Finally, the conclusions are drawn in Section 5. _Notation:_ Boldface lower and upper case symbols represent vectors and matrices, respectively. \((\cdot)^{\mathrm{H}}\) denotes the Hermitian transpose of a vector or a matrix. \(||\cdot||_{\mathrm{F}}\) is the Forbenius norm and \(N\sim(m,\sigma^{2})\) describes a complex Gaussian random variable with mean \(m\) and variance \(\sigma^{2}\).