This study presents models of an electro-hydraulic valve derived from physical principles and neural network techniques. Input-output models are constructed using experimental data from a hydraulic press machine in a steel manufacturing plant and as a plant of a closed loop system. The models are candidates for digital twins in the steel manufacturing plant. The physical model is derived based on fluid mechanics, fluid dynamics, and electronic principles. Two LSTM neural network models denoted NN1 and NN2 are employed for modeling the valve. The parameter estimation for each neural network model is conducted using distinct training datasets. This work compares the validation results of the models in the time and frequency domain. Both the physical model and NNs capture the main behavior of the valve. However, NNs have lower mean square error (MSE) compared to the physical model. NN2, trained the model using different operating conditions, is capable of modeling non-linearities (seen at high frequencies) and leakage effects of the system, that are not captured by NN1 and physical models. The fault caused by leakage is seen in the MSE vs cycles for the physical and NN1 models.

We consider backward crosstalk in 2 × 2 transmitters, which is caused by crosstalk from the outputs of the transmitter to the inputs or by the combination of output crosstalk and impedance mismatch. We analyze its impact via feedback networks together with third-order power amplifier non-linearities. We utilize the Bussgang decomposition to express the distorted output signals of the transmitter as a linear transformation of the input plus uncorrelated distortion. The normalized mean-square errors (NMSEs) between the distorted and desired amplified signals are expressed analytically and the optimal closed-form power back-off that minimizes the worst NMSE of the two branches is derived. In the second part of the paper, an achievable spectral efficiency (SE) is presented for the communication from this “dirty” transmitter to another single-antenna receiver. The SE-maximizing precoder is optimally found by exploiting the hardware characteristics. Furthermore, the optimal power back-off is analyzed for two sub-optimal precoders, which either do not exploit any hardware knowledge or only partial knowledge. The simulation results show that the performance of these sub-optimal precoders is close-to-optimal. We also discuss how the analysis in this paper can be extended to transmitters with an arbitrary number of antenna branches.

The effects of hardware-induced crosstalk in MIMO transmitters, subject to nonlinear power amplifier distortion, are considered in this paper. A methodology that provides tractable results and a clear understanding of the effects of crosstalk on transmitter performance is introduced and applied to different transmitter models. In particular, a physically motivated 2 × 2 MIMO transmitter model, which is subjected to input and output crosstalk, is studied in detail, as well as a behavior motivated transmitter model, which is subjected to linear crosstalk. For the latter structure, asymptotic results, when the number of transmitters tends to infinity, are derived. These results provide insight into different 1D and 2D transmitter structures in the massive MIMO scenario. The methodology provides tractable analytical results of the performance of the transmitter. It is shown that the transmitter crosstalk degrades the performance in terms of normalized mean squared error with 3 dB going from a 2 × 2 set-up to a 1D array of a massive amount of transmitters, and an additional 3 dB loss going from a 1D to 2D transmitter structure. Transmitter input power back-off optimization is further studied, with back-off determination that takes the effects of MIMO crosstalk into account in order to increase the energy efficiency of the transmitter.

The radio frequency transmitter is a key component in contemporary multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing systems. A detailed study of a 2×2 MIMO transmitter subjected to correlated input data streams, nonlinear distortion, thermal noise, and crosstalk is provided by stochastic modeling. The effects of correlated input streams, crosstalk, and nonlinearities are studied in detail and exemplified both by approximate expressions and numerical simulations. Key results include exact and approximate expressions for the normalized mean-squared error (NMSE) for systems with or without digital predistortion; the relationship between NMSE and the signal-to-noise-and-distortion ratio, the properties of the distortion noise, and a novel design for power amplifier back-off for MIMO transmitters subject to crosstalk. The theoretical derivations are illustrated by numerical examples and simulation results, and their relationships to the state-of-the-art research are discussed.

A digital predistortion (DPD) scheme is presented for non‐linear distortion mitigation in multi‐carrier satellite communication channels. The proposed DPD has a multiple‐input multiple‐output architecture similar to data DPD schemes. However, it enhances the mitigation performance of data DPDs using a multi‐rate processing algorithm to achieve spectrum broadening of non‐linear operators. Compared to single carrier (single‐input single‐output) signal (waveform) DPD schemes, the proposed DPD has lower digital processing rate reducing the required hardware cost of the predistorter. The proposed DPD outperforms, in total degradation, both data and signal DPD schemes. Further, it performs closest to a channel bound described by an ideally mitigated channel with limited maximum output power.