Power Ratio Error Research Articles

Dynamical Embedding of Single-Channel Electroencephalogram for Artifact Subspace Reconstruction.

This study introduces a novel framework to apply the artifact subspace reconstruction (ASR) algorithm on single-channel electroencephalogram (EEG) data. ASR is known for its ability to remove artifacts like eye-blinks and movement but traditionally relies on multiple channels. Embedded ASR (E-ASR) addresses this by incorporating a dynamical embedding approach. In this method, an embedded matrix is created from single-channel EEG data using delay vectors, followed by ASR application and reconstruction of the cleaned signal. Data from four subjects with eyes open were collected using Fp1 and Fp2 electrodes via the CameraEEG android app. The E-ASR algorithm was evaluated using metrics like relative root mean square error (RRMSE), correlation coefficient (CC), and average power ratio. The number of eye-blinks with and without the E-ASR approach was also estimated. E-ASR achieved an RRMSE of 43.87% and had a CC of 0.91 on semi-simulated data and effectively reduced artifacts in real EEG data, with eye-blink counts validated against ground truth video data. This framework shows potential for smartphone-based EEG applications in natural environments with minimal electrodes.

On the Viability of Using a Subset of Transmitter- Observation Receivers for Training a Common DPD in Fully Digital MIMO Transmitters

This letter lays the foundation for reducing the required number of transmitter-observation receivers (TORs) for training digital predistortion (DPD) in fully digital massive multiple-input, multiple-output (MIMO) transmitters. Specifically, it investigates the viability of applying the same, common set of DPD coefficients to linearize all RF chains in fully digital massive MIMO transmitters. First, it is shown that if all RF chains are operated at the same output power, the common set of DPD coefficients can be found by simply averaging the coefficients obtained by training each RF chain on its own. This suggests that only a few chains may be needed for training provided the chains are a representative sample. Experimental results are then conducted where one and three chains are used for training. It is found that when training for one chain, significant variations in normalized mean square error (NMSE) and adjacent channel power ratio (ACPR) of up to 9 dB across the chains are realized. For training with three chains, the common set of DPD coefficients can reduce the variation to 1–2 dB. Finally, after over-the-air (OTA) combining, excellent linearization performance is found for three chains.

Power Amplifier Linearization in the Presence of Crosstalk and Measurement Noise in MIMO System

The crosstalk and transceiver noise is an intrinsic part of the multiple-input and multiple-output (MIMO) System, becoming more prominent in low-cost systems. Moreover, the power amplifiers (PAs) cause nonlinearity, propagating to the complete chain. The conventional techniques do not provide the joint method for crosstalk, transceiver noise, and PA nonlinearity. This results in the performance limitation of the digital predistortion (DPD). Hence we propose a wavelet multiscale principal component analysis (PCA) based technique to deal with such problems (crosstalk, transceiver noise, and system nonlinearities). It is reported using measurement and simulation that numerical stability issue is no longer an issue when wavelet multiscale PCA-based DPD is applied. The effect of wavelet multiscale PCA on bit-resolution of DPD is shown to be better than established DPD Models. On a field-programmable gate array and direct conversion transceiver-based platform, the performance of the proposed model is analyzed using PA. Parameters like normalized mean square error have shown an improvement of around 23 dB and adjacent channel error power ratio has shown an improvement of around 22 dBc for a ZX60-V63+ power amplifier using LTE-OFDM signals.

A Residual-Fitting Modeling Method for Digital Predistortion of Broadband Power Amplifiers

This letter proposes a residual-fitting modeling method for digital predistortion (DPD) of broadband power amplifiers (PAs), and then constructs a residual-fitting model. To avoid directly modeling strong nonlinearity and memory effect, the model is split into a conversion, fitting, and recovery module. In this way, the nonlinearity and memory effect of the output signal of PAs are reduced after the conversion module, and then the fitting module models the converted signal, finally the behavioral characteristics of PAs are recovered by the recovery module. In the experimental test, a 100 MHz orthogonal frequency division multiplexing (OFDM) signal is used as input signal of a Doherty PA. The experimental results show that compared with the existing augmented real-valued time-delay neural network (ARVTDNN), the proposed residual-fitting memory polynomial-ARVTDNN (MP-ARVTDNN) model with much fewer coefficients lowers normalized mean square error (NMSE) and adjacent channel power ratio (ACPR).

GaN Power Amplifier Digital Predistortion by Multi-Objective Optimization for Maximum RF Output Power

While digital predistortion (DPD) usually targets only the linearity performance of the radio–frequency (RF) power amplifier (PA), this work addresses more than a single PA performance metric exploiting a multi-objective optimization approach. We present a predistorer learning procedure based on a constrained optimization algorithm that maximizes the RF output power, while guaranteeing a prescribed linearity level, i.e., a maximum normalized mean square error (NMSE) or adjacent-channel power ratio (ACPR). Experimental results on a Gallium Nitride (GaN) PA show that the proposed approach outperforms the classical indirect learning architecture (ILA), yet using the same predistorter structure with predetermined nonlinearity and memory orders.

Design of an arbitrary ratio optical power splitter based on a discrete differential multiobjective evolutionary algorithm.

Traditional photonic integrated devices are designed to predict their optical response by transforming the structure and parameters, and it is often difficult to obtain devices with excellent performance in all aspects. The nanophotonic computing design method based on the optimization algorithm has revolutionized the traditional photonic integrated device design technology. Here, we report a discrete differential evolution algorithm that simulates a natural selection process to achieve an ultracompact arbitrary power ratio splitter. The footprint of the designed splitter is only ${2.5}\;\unicode{x00B5} {\rm m} \times {2}.{5}\;\unicode{x00B5} {\rm m}$2.5µm×2.5µm, the simulated total transmission efficiency is above 90%, the power ratio error is less than 3%, and it can work normally over the C-band. Our algorithm can provide new ideas for the application of genetic algorithms to the automatic optimization of photonic integrated devices.

Digital Predistortion for Linearity Improvement of VCSEL-SSMF-Based Radio-Over-Fiber Links

This letter unfolds a digital predistortion (DPD) technique that improves the linearity of limited range mobile front haul links for the contemporary long-term evolution (LTE) and future (5G) networks. In particular, the proposed technique is applied to radio-over-fiber links based on single-mode (SM) vertical cavity surface emitting lasers emitting at 850 nm and standard SM fibers. Both the memory and generalized memory polynomial models are exploited for the predistorter and identified by utilizing indirect learning architecture. The impact of the DPD technique is observed by the link performance improvement in terms of normalized mean square error and adjacent channel power ratio, referring to complete LTE frames of 10 ms occupying 5-MHz bandwidth and having 64-quadrature amplitude modulation format. Furthermore, the effectiveness of the DPD approach, when varying input power levels, is investigated. The experimental results demonstrate the capability of the proposed DPD technique to achieve promising linearization performance.

Temperature characteristics of single mode fiber-optic 3 × 3 couplers

Abstract This paper focuses on the temperature characteristics of single mode fiber-optic 3 × 3 couplers. Temperature change will result in the optical fiber parameters change, such as the core or cladding refractive index change and the length quantity expansion. This will affect the transmission property of the fiber-optic coupler, which can be characterized by power ratio error and phase difference error. It is found that the optical fiber geometrical expansion caused by temperature variation has little influence on the transmission characteristics of the coupler. The change of the refractive indexes, especially the core refractive index, which is caused by the thermal stress in the fiber due to temperature variation, has great influence on the transmission characteristics of the fiber-optic coupler.

Optimal Parameter Identification for Look-up Table based Band-limited Memory Polynomial Model using Direct and Indirect Learnings

The linearization of radio frequency power amplifiers (PAs) for wireless communication systems can be performed by a digital baseband predistorter (DPD). The DPD design includes the parameter identification of a post-inverse or a pre-inverse model. Such process depends on measurements of discrete-time complex-valued envelopes. With the adoption of larger envelope bandwidths and the PA operation at stronger nonlinear regimes, the requirements on the sampling frequency are very stringent. To relax the specifications on the analog-to-digital and digital-to-analog converters, a band-limited memory polynomial can be employed. To reduce the amount of calculations, polynomials can be replaced by linearly interpolated look-up tables (LUTs). Traditionally, a non optimal two step procedure is performed to identify the values to be stored in the LUTs. This work contribution is to propose an optimal identification technique that computes directly the values to be stored in the LUTs. The reported case study uses an LTE OFDMA envelope and Matlab simulation results show that the modeling accuracy can be significantly improved by the adoption of the proposed technique instead of the traditional one, quantified by reductions in normalized mean square error and adjacent channel power ratio of up to 10.8 dB and 12.4 dB, respectively.

Detection of Underwater Targets Using a Subspace-Based Method With Learning

This paper introduces a new subspace-based detection method for multichannel (high frequency and broadband) synthetic aperture sonar (SAS) imagery. An image-dependent dictionary learning method is applied to form the appropriate dictionary matrices for representing target and nontarget image snippets. The hypothesis testing is done by forming a test statistic that relies on the residual error power ratio in representing an unknown image snippet using the target and nontarget dictionary matrices. To avoid the computational bottleneck in most dictionary learning methods, a new recursive method is introduced which does not require any matrix inversion or singular value decomposition (SVD). The proposed detection method was then implemented and benchmarked against a matched subspace detection method for detecting mine-like objects. Results are then presented on two sonar imagery data sets collected in two geographically disparate locations.

2D Extended envelope memory polynomial model for concurrent dual-band RF transmitters

The paper presents a two-dimensional (2D) extended envelope memory polynomial model for concurrent dual-band radio frequency (RF) power amplifiers (PAs). The model is derived based on the physical knowledge of a dual-band RF PA. The derived model contains cross-modulation terms not included in previously published models; these terms are found to be of importance for both behavioral modeling and digital predistortion (DPD). The performance of the derived model is evaluated both as the behavioral model and DPD, and the performance is compared with state-of-the-art 2D-DPD and dual-band generalized memory polynomial (DB-GMP) models. Experimental result shows that the proposed model resulted in normalized mean square error of −51.7/−51.6 dB and adjacent channel error power ratio of −63.1/−63.4 dB, for channel 1/2, whereas the 2D-DPD resulted in the largest model error and DB-GMP resulted in model parameters that are three times more than those resulted with the proposed model with the same performance. As pre-distorter, the proposed model resulted in adjacent channel power ratio of −55.8/−54.6 dB for channel 1/2 and is 7–10 dB lower than those resulted with the 2D-DPD model and 2–4 dB lower compared with the DB-GMP model.

Application of principal component analysis based effective digital predistortion technique for low-cost FPGA implementation

This article investigates the issue of low-cost digital predistortion (DPD) implementation in fixed-point field programmable gate array (FPGA) by considering the bit-resolution along with lower number of coefficients. The impact of principle component analysis (PCA) on bit-resolution of DPD solution is proposed within the context of established DPD models. Unlike previously proposed PCA based solutions, it is established by simulation and measurement that the numerical stability problem associated with popular models such as memory polynomial (MP) can be alleviated when PCA is applied to the observation data matrix. It is reported with measurement results that PCA based model provides better linearization performance with the least memory size requirement and number of LUTs in 16-bit fixed-point FPGA operation than MP, orthogonal memory polynomial (OMP), and generalized memory polynomial (GMP) models. The performance of the proposed model, is evaluated in terms of normalized mean square error, adjacent channel error power ratio, matrix condition number, and dispersion coefficient for continuous Class-AB and ZX60-V63+ power amplifiers using wide code-division multiple access signal (WCDMA) and long term evolution (LTE) signal with peak-to-average-power ratio (PAPR) around 9.895 and 11.92 dB, respectively.

3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth

In this paper, the design, implementation, and measurement results of a new digital predistortion (DPD) method for a concurrent dual-band envelope tracking (ET) power amplifier (PA) system is presented. The PA gain is represented using a set of 3-D orthogonal Fourier series basis functions, which accounts for the distortions introduced by the two signal bands, as well as the supply modulation voltage. Here, the new Fourier series basis is shown to substantially outperform the traditional memory polynomial approach in terms of its linearization capability for subsequent data for which it was not trained for (prediction) due to its well-defined numerical rank and stability. The new DPD system was implemented using a 10-W peak gallium–nitride (GaN) ET PA operating with a dual-band input based on long-term evolution and WCDMA signals center frequency (1.89 and 2.2 GHz) spaced by 310 MHz. The linearization results are compared to the 3-D memory polynomial in two steps: extraction and prediction. In the DPD coefficient extraction phase, tested under the same signal, the traditional memory polynomial and the Fouries series reach close results in both normalized mean square error (NMSE) and adjacent channel power ratio (ACPR). In the prediction phase, however, the proposed method provides a significant performance improvement. A performance improvement as high as 17 dB in terms of NMSE and 4.6 dB in terms of ACPR in comparison to the conventional dual-band 3-D memory polynomial method implementing ET. Furthermore, the well-defined numerical rank of the Fourier series approach allows for a substantial reduction in coefficients using principal component analysis without detrimenting performance.

RF Power Amplifier Behavioral Modeling Based on Takenaka–Malmquist–Volterra Series

In this paper, a Takenaka---Malmquist---Volterra (TMV) model structure is employed to improve the approximations in the low-pass equivalent behavioral modeling of radio frequency (RF) power amplifiers (PAs). The Takenaka---Malmquist basis generalizes the orthonormal basis functions previously used in this context. In addition, it allows each nonlinearity order in the expanded Volterra model to be parameterized by multiple complex poles (dynamics). The state-space realizations for the TMV models are introduced. The pole sets for the TMV model and also for the previous Laguerre---Volterra (LV) and Kautz---Volterra (KV) models are obtained using a constrained nonlinear optimization approach. Based on experimental data measured on a GaN HEMT class AB RF PA excited by a WCDMA signal, it is observed that the TMV model reduces the normalized mean-square error and the adjacent channel error power ratio for the upper adjacent channel (upper ACEPR) by 1.6 dB when it is compared to the previous LV and KV models under the same computational complexity.

Two novel memory polynomial models for modeling of RF power amplifiers

Two novel memory polynomial models are derived based on physical knowledge of a general power amplifier (PA). The derivations are given in detail to facilitate derivations of other model structures. The model error in terms of normalized mean square error (NMSE) and adjacent channel error power ratio (ACEPR) of the novel model structures are compared to that of established models based on the number of parameters using data measured on two different amplifiers, one high-power base-station PA and one low-power general purpose amplifier. The novel models show both lower NMSE and ACEPR for any chosen number of parameters compared to the established models. The low model errors make the novel models suitable candidates for both modeling and digital predistortion.

Behavioral Modeling and Linearization of Crosstalk and Memory Effects in RF MIMO Transmitters

This paper proposes three novel models for behavioral modeling and digital pre-distortion (DPD) of nonlinear 2 × 2 multiple-input multiple-output (MIMO) transmitters in the presence of crosstalk. The proposed models are extensions of the single-input single-output generalized memory polynomial model. Three types of crosstalk effects were studied and characterized as linear, nonlinear, and nonlinear & linear crosstalk. A comparative study was performed with previously published models for the linearization of crosstalk in a nonlinear 2 × 2 MIMO transmitter. The experiments indicate that, depending on the type of crosstalk, the selection of the correct model in the transmitter is necessary for behavioral modeling and sufficient DPD performance. The effects of coherent and partially noncoherent signal generation on the performance of DPD were also studied. For crosstalk levels of -30 dB, the difference in the normalized mean square error and adjacent channel power ratio was found to be 3-4 dB between coherent and partially noncoherent signal generation.

Rational Function Based Model for the Joint Mitigation of I/Q Imbalance and PA Nonlinearity

Nonlinearity in power amplifiers and In-phase and Quadrature phase (I/Q) imperfections degrade the performance of direct conversion transmitters. In this letter, a novel rational function based model is proposed to jointly alleviate both these impairments. The performance of the model is evaluated in terms of Normalized mean square error (NMSE) and Adjacent channel error power ratio (ACEPR). Simulation results and measurements show that the model has an improvement of around 2 dB NMSE and around 3 dB in ACEPR than the state of the art parallel Hammerstein based model . Also the model attains a lower complexity while maintaining almost same performance.

Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters

The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions.

Enhanced Hammerstein Behavioral Model for Broadband Wireless Transmitters

A novel enhanced Hammerstein behavior model consisting of a weighted memoryless polynomial followed by a Volterra filter is proposed. The weighted polynomial is used for predicting the strong static nonlinear behaviors of the power amplifiers (PAs). Since the Volterra filter is employed only for the mild dynamic nonlinearities, the filter can be implemented with low nonlinear order. Thus, this proposed model is capable of predicting both the static and dynamic nonlinearities of RF PAs with the acceptable complexity. The modeling performance of the proposed model is assessed in terms of in-band and out-of-band errors, such as normalized mean square error and adjacent channel error power ratio, and it is compared with a conventional Hammerstein, an augmented Hammerstein, and a Volterra series with respect to computation complexities such as the number of floating point operations and coefficients. The excellent estimation capability of the enhanced Hammerstein model is validated by two kinds of PAs: Si lateral diffusion metal-oxide-semiconductor and GaN high electron-mobility transistor amplifiers. Furthermore, the proposed scheme is applied to the digital predistortion (DPD) to cancel the nonlinearities of the PAs. The modeling performances and DPD experimental results clearly demonstrate the superiority of the enhanced Hammerstein scheme: the computational complexity is comparable with the augmented Hammerstein behavioral model, but the modeling performance is similar to the Volterra filter, which is the most accurate model.