The indirect learning architecture (ILA) is the mostused methodology for the identification of Digital Pre-distorter (DPD) functions for nonlinear systems, particularly for high power amplifiers. The ILA principle works in black box modeling relying on the inversion of input and output signals of the nonlinear system, such that the inverse is estimated. This paper presents the impact of disturbances, such as noise in the DPD identification. Experiments were performed with a state-of-art Doherty power amplifier intended for base station operation in current telecommunication wireless networks. As expected, a degradation in the performance of the DPD (measured innormalized mean square error (NMSE)) is found in our experiments. However, adjacent channel power ratio (ACPR) can be a misleading figure of merit showing improvement in the performance for wrongly estimated DPD functions.

The paper presents a method for modeling strongnonlinear effects in power amplifiers based on the principlesof density estimation. The static nonlinear transfer function isobtained by averaging measured data. The performance obtainedwith density estimation is similar to the one using high ordernonlinear static polynomial models. The benefit of consideredmethod over the ones using polynomial models is that the formerestimates blindly the structure of the transfer function and doesnot suffer from numerical instabilities.

A general description of nonlinear dynamic MIMO systems, given by Volterra series, has significantly larger complexity than SISO systems. Modeling and predistortion of MIMO amplifiers consequently become unfeasible due to the large number of basis functions. We have designed digital predistorters for a MIMO amplifier using a basis pursuit method for reducing model complexity. This method reduces the numerical problems that appear in MIMO Volterra predistorters due to the large number of basis functions. The number of basis functions was reduced from 1402 to 220 in a 2x2 MIMO amplifier and from 127 to 13 in the corresponding SISO case. Reducing the number of basis functions caused an increase of approximately 1 dB of model error and adjacent channel power ratio.

In this paper a synthetic vector network analyzing measurement system is presented. The system is based on a hardware set-up, including a signal generator and a vector signal analyzer, with the vector network analyzing functionality implemented in the software. The measurements of the proposed system demonstrated comparable performance in terms of accuracy and speed compared with a modern traditional vector network analyzer, but it is more flexible due to its inherent software implementation. The proposed system’s ability to measure nonlinear phenomena is addressed and discussed, and some preliminary results are given.

A technique to extend the effective measurement bandwidth of a non-coherent vector receiver is presented. This bandwidth extension technique relies on the use of a pilot signal (known a priori), which is added on the signal of interest and is measured in a single receiver. Compared to other bandwidth extension techniques referred as stitching techniques, the proposed approach avoids error propagation in the measurement bandwidth and simultaneously enables the measurement of signals that do not contain energy in certain spectral bands.

The pilot signal is created in digital stages, which tackles to large extent the requirement of the a priori knowledge of this signal. Further, the pilot signal is designed to minimize estimation errors of the proposed technique, providing enhanced performance. It is analytically shown that the error incurred by the proposed method is always lower than the error from the measurement noise.

Measurement results show the method functionality with an error in the range of −50 dB of the signal measured. Finally, the usefulness of the proposed technique is illustrated by measuring the input and output of an amplifier with dynamic range in excess of 80 dB over 290 MHz using an 18 MHz bandwidth receiver. This measurement could not have been performed by existing stitching techniques.

This paper analyzes the effects of load impedancemismatch in power amplifiers which linearity has been enhancedusing various digital predistortion (DPD) algorithms. Two different power amplifier architectures are considered: a class AB and a Doherty amplifier and three model structures for the DPD model are compared: memoryless polynomial (MLP), general memory polynomial (GMP) and Kautz-Volterra functions (KV). This paper provides a sensitivity analysis of the linearized amplifiers under load mismatch conditions and reports the performance when dynamic parameter identification for the DPD is used to compensate for the changes in the load impedance. In general,power amplifiers linearity is sensitive to load impedance mismatch. Linearity may degrade as much as 10 dB (in normalized mean square error) according to the magnitude and the phase of the reflection coefficient provided by the load impedance. However, depending on the amplifier design, the sensitivity toload impedance mismatch varies. While the Doherty amplifier studied show significant linearity degradations in the in-band and out-of-band distortions, the out-of-band distortions of the studied class AB were less sensitive to the load impedance mismatch. In adaptive DPD schemes, the performance obtained in the MLP model does not benefit from the updating scheme and the performance achieved is similar to a static case, where no updates are made. This stresses the memory requirements in the predistorter. When employing the GMP and the KV models in an adaptive DPD scheme, they tackle to a larger extent the linearity degradations due to load impedance mismatch.

A non-parametric technique for modeling the behavior of power amplifiers is presented. The proposed technique relies on the principles of density estimation using the kernel method and is suited for use in power amplifier modeling. The proposed methodology transforms the input domain into an orthogonal memory domain. In this domain, non-parametric static functions are discovered using the kernel estimator. These orthogonal, non-parametric functions can be fitted with any desired mathematical structure, thus facilitating its implementation. Furthermore, due to the orthogonality, the non-parametric functions can be analyzed and discarded individually, which simplifies pruning basis functions and provides a tradeoff between complexity and performance. The results show that the methodology can be employed to model power amplifiers, therein yielding error performance similar to state-of-the-art parametric models. Furthermore, a parameter-efficient model structure with 6 coefficients was derived for a Doherty power amplifier, therein significantly reducing the deployment’s computational complexity. Finally, the methodology can also be well exploited in digital linearization techniques.

Aiming to reduce the power/mass requirements in satellite transponders and toreduce mission costs, joint amplification of multiple-carriers using a singleHigh-Power Amplifier (HPA) is being considered. In this scenario, a carefulinvestigation of the resulting power efficiency is essential as amplification isnonlinear, and multicarrier signals exhibit enlarged peak-to-average power ratio.Thus, operating the amplifier close to saturation vastly increases signal distortionresulting in a severe degradation of performance, especially for higher ordermodulations. This paper proposes a reduced-complexity digital pre-distortion(DPD) scheme at the transmitter and a corresponding equalizer (EQ) at thereceiver to mitigate these nonlinear effects. Scenarios include both the forward aswell as the return links. In particular, the paper exploits the MIMO Volterrarepresentation and builds on a basis pursuit approach using a LASSO (leastabsolute shrinkage and selection operator) algorithm to achieve an effienct basisrepresentation, avoiding large computational complexity, to describe the selectionof pre-distorter/ equalizer model. The work further compares and contrasts thetwo mitigation techniques taking various system aspects into consideration. Thegains, in performance and amplification efficiency, demonstrated by the use ofDPD/ EQ motivate their inclusion in next generation satellite systems.