Low-Complexity Digital Predistorter for MIMO Transmitters with Nonlinear Crosstalk

In this paper, we evaluate the effect of applying peak-to-average power ratio (PAPR) reduction and digital pre-distortion (DPD) on two types of radio frequency power amplifiers when an orthogonal frequency division multiplexing (OFDM) signal is used. The power amplifiers under test are a standard class-AB amplifier and a Doherty amplifier. The PAPR reduction methods are based on a state-of-the art convex optimization formulation and on the standard clipping and filtering technique. The DPD method consists of modeling the behavior of the power amplifier using a parallel Hammerstein model, and then extracting the inverse parameters based on the indirect learning architecture. To achieve better DPD performance, extracting the DPD parameters based on multiple-step iterations is investigated. The cases where PAPR reduction and DPD are applied separately and combined are studied and investigated. Power amplifier figures of merit are evaluated. Good performance is shown when combining both pre-processing techniques up to a certain operating point where DPD performance deteriorates due to generation of strong peaks in the signal. In addition, a difference in the power amplifier behavior is reported and analyzed.

Power amplifier (PA) nonlinearities and the digital predistortion (DPD) required for linearization are modeled at baseband using the memoryless polynomial, memory polynomial, and pruned Volterra series. The sampling requirements for the nonlinear basis waveforms created from a band-limited signal are determined as a function of the polynomial order. A Gaussian approximation of the channel filtering is used to make the mathematical analysis tractable. For the memory polynomial and pruned Volterra series cases, the spacing between memory taps, referred to as the delay offset, is selected to trade off model accuracy and the condition number of the coefficient estimation. Examples are provided showing how to select the appropriate delay offset for a memory-based amplifier model and its effect on the DPD performance. A pruned Volterra series is proposed, which demonstrates improved DPD performance compared with the memory polynomial.

<span lang="EN-US">In this paper, a low-complexity model is proposed for linearizing power amplifiers with memory effects using the digital predistortion (DPD) technique. In the proposed model, the linear, low-order nonlinear and high-order nonlinear memory effects are computed separately to provide flexibility in controlling the model parameters so that both high performance and low model complexity can be achieved. The performance of the proposed model is assessed based on experimental measurements of a commercial class AB power amplifier by applying a single-carrier wideband code division multiple access (WCDMA) signal. The linearity performance and the model complexity of the proposed model are compared with the memory polynomial (MP) model and the DPD with single-feedback model. The experimental results show that the proposed model outperforms the latter model by 5 dB in terms of adjacent channel leakage power ratio (ACLR) with comparable complexity. Compared to MP model, the proposed model shows improved ACLR performance by 10.8 dB with a reduction in the complexity by 17% in terms of number of floating-point operations (FLOPs) and 18% in terms of number of model coefficients.</span>

Digital predistortion (DPD) of a phased array requires that multiple transmit paths must be measured by a feedback (FB) receiver (Rx), This paper proposes a simplified FB architecture to be used for phased array DPD. A single FB line collects the waveform samples from the parallel paths to the FB Rx. The gain and phase of the common FB line is obtained by comparing the FB outputs to over-the-air (OTA) measurements. The overall DPD training is done by collecting the PA outputs with the common FB line, post-equalizing them to model the main lobe waveform and combining them to create the object used for array DPD. The DPD performance was verified by OTA measurements with 5GNR waveform and 28 GHz 8-path phased array transmitter. The DPD trained through the local FB line with the proposed calibration method achieved < -45dB ACPR which was close to OTA DPD performance.

This paper expounds a complexity-reduced generalized memory polynomial (CR-GMP) model for multi-band power amplifier (PA) digital predistortion (DPD). First, PA block diagrams characterizing the behavior of PAs under multi-band stimulus are proposed. Second, CR-GMP forward models are derived from the feedback block diagrams of the PA, driven with both dual- and tri-band signals, leading to a general formulation for PAs driven with multi-band signals. The resulting models are used to linearize two PAs driven with dual- and tri-band signals. The proposed CR-GMP models are compared to a dual-input digital predistortion (2D-DPD) model and a triple-input digital predistortion (3D-DPD) model and show similar linearization performance while requiring fewer coefficients. Due to the presence of cross terms in the dual-band CR-GMP formulation, the proposed model is robust against time-delay misalignment between dual-band signals, whereas the 2D-DPD is not. With a reduced number of coefficients and the presence of cross terms, the proposed CR-GMP models represent excellent candidates for the linearization of highly nonlinear PAs driven with multi-band signals.

Digital Predistortion (DPD) improves power amplifier efficiency and reduces energy consumption in wireless networks. Recent advancements have produced new DPD models for dual-band transmission, but overlapping signal harmonics complicate implementation. Fixed-point precision issues on FPGAs can affect performance during hardware realization. This work optimizes PA and DPD modeling using a twodimensional Harmonic Memory Polynomial (2D-HMP) model and ridge regression to minimize large coefficients, allowing shorter fixed-point word lengths. This approach reduces the size of multipliers and adders, improves DSP utilization, and decreases memory and power consumption, making DPD more efficient and scalable for FPGA systems.

This paper investigates the issue of high complexity of digital predistortion for the nonlinear distortion introduced due to crosstalk in addition to the nonlinear distortion generated by a power amplifier (PA) in 2 × 2 MIMO transmitters. This paper proposes a less complex, novel model for digital predistortion (DPD) for linearizing multiple-input multiple-output (MIMO) transmitters. This model is constructed by taking account of both linear and nonlinear crosstalks, along with the fact that the nonlinearity generated due to crosstalk would be lesser than the nonlinearity already available due to PA. For proof-of-concept, it is shown for two different scenarios that proposed model provides similar linearization performance as compared to 2 × 2 PH model with less number of coefficients.

This paper reports a novel digital predistortion (DPD) scheme for concurrent tri-band power amplifier (PA). The proposed three-dimensional tri-band DPD is based on the analysis of crosstalk between the fundamental frequencies, their harmonics and intermodulation products due to the nonlinearity exhibited by the tri-band PA. The DPD performance is validated using a broadband PA driven concurrently with LTE, WIMAX, and WCDMA signals centered at 2.14 GHz, 2.425 GHz, and 2.655 GHz, respectively.

This letter proposes a stable-sample-level (SL)-based digital predistortion (DPD) technique for 2-D phased array with fixed-position over-the-air (OTA) feedback (FB) to overcome significant SL fluctuation when the beam is steered. It is achieved by optimizing the phase of the beamformer based on the DPD requirement, which can control the SL at a given value without affecting the main lobe of radiation pattern, relaxing the requirement of FB dynamic range. The radiation pattern and DPD performances are measured on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> phased array at 26 GHz. The measured results show that the proposed method can realize the stable SL with good DPD performance.

In this article, we study digital predistortion (DPD)-based linearization with a specific focus on millimeter-wave (mmW) active antenna arrays. Due to the very large-channel bandwidths and beam-dependence of nonlinear distortion in such systems, we present a closed-loop DPD learning architecture, lookup table (LUT)-based memory DPD models, and low-complexity sign-based estimation algorithms such that even continuous DPD learning could be technically feasible. To this end, three different learning algorithms-sign, signed regressor, and sign-sign-are formulated for the LUT-based DPD models such that the potential rank deficiencies, experienced in earlier methods, are avoided while facilitating greatly reduced learning complexity. The injection-based LUT DPD structure is also shown to allow for low numbers and reduced dynamic range of the involved LUT entries. Extensive RF measurements utilizing a state-of-the-art mmW active antenna array system at 28 GHz are carried out and reported to validate the methods, incorporating very wide channel bandwidths of 400 and 800 MHz while pushing the array close to saturation. In addition, the processing and learning complexities of the considered techniques are analyzed, which, together with the measured linearization performance figures, allows to assess the complexity-performance tradeoffs of the proposed solutions. Overall, the results show that efficient mmW array linearization can be obtained through the proposed methods at very low complexity.

In this paper, a new model which is called a pruning general memory polynomial (PGMP) model is introduced to solve the conflict between model precision and complexity in DPD research. The new model eliminates those items which have little effect to output signal from the expression of the traditional general memory polynomial (GMP) and obtain a new model expression which has similar performance with the PGMP model and similar coefficient number with the memory polynomial model. The experiment result shows that the new DPD model exhibits a very good performance and its ACPR of output spectrum is 5dB better than that of MP model.

Digital predistortion (DPD) is known as an efficient solution to suppress nonlinear distortion of power amplifiers (PAs) in wireless transmitters to achieve both high linearity and power efficiency. In multiple input and multiple output (MIMO) applications, the power gains of multiple transmitting channels are usually different. Meanwhile, the channel crosstalk cannot be ignored, given the isolations between the physical channels are limited. Accordingly, the linearization performances of the conventional DPD methods are usually degraded. In this article, we propose a novel DPD method for MIMO transmitters, where both the crosstalk and different power gains of multiple channels are considered. In this method, the expected predistorted signals, which would be used to train the DPD model, are firstly obtained by an iterative algorithm derived from the contraction mapping theorem. Then, the coefficients of a MIMO-DPD model are extracted by fitting the DPD model to the obtained predistorted signal. Experimental results verify that the extracted coefficients can achieve an improved linearization performance for the MIMO transmitter with crosstalk between the channels, especially in the case where the channel gains are different. Specifically, for a $2 \times 2$ MIMO transmitter with -20 dB crosstalk and 1.2 dB difference between the two channel gains, the proposed DPD improves the adjacent channel power ratio (ACPR) from -31.4 dBc to -47.1 dBc, which outperforms the conventional DPD by 6.8 dB.

Radio over Fiber (RoF) fronthaul system linearization has become much more important due to the distortions produced by the optical link between the Baseband Unit (BBU) and the Remote Radio Head (RRH) in a Cloud Radio Access Network (C-RAN) architecture. Its main disadvantage is that in a real scenario the output signal may be far a few kilometers. Along the literature, digital predistortion (DPD) on RoF mobile fronthaul architectures considers an ideal feedback link, but in a real scenario the captured output signals at the BBU side are affected by the RoF feedback effects. In a first place, we evaluate the effects of this feedback loop on the downlink RoF predistorter. Then, we propose and experimentally demonstrate the use of a postdistorter on the feedback RoF in order to compensate its effects. This feedback RoF link can be accomplished in the same optical link by means of wavelength division-multiplexing (WDM). Experiments are carried out with a 20MHz-LTE downlink signal (16QAM) at 2.65 GHz within the Band 7 of the LTE standard. The DPD performance has been tested in an intensity modulation/direct detection (IM/DD) RoF mobile fronthaul system. Experimental results reveal that with a properly feedback RoF postdistortion it is possible to achieve Adjacent Channel Power Ratio (ACPR) and Error Vector Magnitude (EVM) values in the downlink RoF system close to the results with an ideal feedback link.

Optimization of digital predistortion models for RF power amplifiers using a modified differential evolution algorithm

This paper proposes a near-field dual-polarized feedback (NFDPF) technique for tracking real-time status and improving linearity of 5G RF-beamforming millimeter-wave (mm-wave) phased array. The feedback signal captured by NFDPF can be used for array self-calibration and digital predistortion (DPD). A 2×2 dual-polarized 24.25-27.5-GHz phased array prototype with integrated NFDPF is designed for validation of the scheme. Using NFDPF, four RF chains of dualpolarizations are calibrated which is similar to far-field (FF) calibration. Furthermore, the DPD is applied to validate the performance of feedback structure. Experimental results show that the adjacent channel power ratio (ACPR) and normalized mean squared error (NMSE) can be improved from -40dBc and 28dB to -51dBc and -40dB respectively, which is close to the performance of FF DPD.