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![(for Band 1) and Fig. 7 (for Band 2) show the spectra of the estimated outputs considering a 3D-DML behavioral model after applying OMP-LUT selection (i.e., 62 coeff. Band 1 and 73 coeff. Band 2) and reduced PLS coefficient estimation (i.e., 40 coeff. Band 1 and 48 coeff. Band 2). Finally, applying the aforementioned combination (i.e., OMP-LUT selection in the forward path and PLS reduction estimation in the feedback identification path) we can significantly reduce the complexity of the 3D-DML DPD while still meeting the specific linearity requirements as shown in Fig. 8. Further details on the linearization performance of the 3D-DML DPD can be found in [10].](profile/Pere-Gilabert/publication/326817781/figure/fig5/AS:676874808221700@1538390938777/for-Band-1-and-Fig-7-for-Band-2-show-the-spectra-of-the-estimated-outputs.png)
(for Band 1) and Fig. 7 (for Band 2) show the spectra of the estimated outputs considering a 3D-DML behavioral model after applying OMP-LUT selection (i.e., 62 coeff. Band 1 and 73 coeff. Band 2) and reduced PLS coefficient estimation (i.e., 40 coeff. Band 1 and 48 coeff. Band 2). Finally, applying the aforementioned combination (i.e., OMP-LUT selection in the forward path and PLS reduction estimation in the feedback identification path) we can significantly reduce the complexity of the 3D-DML DPD while still meeting the specific linearity requirements as shown in Fig. 8. Further details on the linearization performance of the 3D-DML DPD can be found in [10].
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This paper presents a technique to estimate the coefficients of a multiple-look-up table (LUT) digital predistortion (DPD) architecture based on the partial least-squares (PLS) regression method. The proposed 3-D distributed memory LUT architecture is suitable for efficient FPGA implementation and compensates for the distortion arising in concurren...
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... For this purpose, the WM or HMbased LTI filter is used as a composite to account for memory modeling [106], [178], as explained in Section IIIA. However, irrespective of the polynomial orders, LUT provides a degree of freedom in avoiding analytical ill-conditioning cumbersome of high order polynomials with power-efficient modeling, and no extra cost [133], [179]. The solitary dominance of oversizing in LUT is well-reimbursed by replacing the pruning subsets of VoS polynomials with cross-term interpolation and extrapolation to form the less-complex linearized output in a sole LUT-based DPD [180]. ...
... Usecases: A variety of LUT-based DPDs have been demonstrated in the recent literature to support challenging usecases such as providing well-conditioned parameter estimation in large-scale polynomial coefficients. One such lower complexity solution is an extension of the conventional direct learning adaption of LUT coefficients, is the concept of linearly interpolated LUT implementation [106], [179], [180]. With this approach, a subset of necessary basis functions is served and extracted from a wide distribution of many individually controllable multi-LUTs, providing an extra degree of freedom to the typical ill-conditioning problem. ...
... These circumstances are well-arduous for a decent DPD system. Hence, two kinds of precautionary measures can be taken to alleviate the ill-conditioning issues in ADPD, that is 1) pruning of PD polynomial model to update relevant coefficient sets of basis function [183]- [185]; 2) applying regularization matrix to steady the training samples of weight vector especially in iterative online linearization [60], [100], [179], [186]- [188]. ...
The next-generation (5G/6G) wireless communication aims to leapfrog the currently occupied sub-6 GHz spectrum to the wideband millimeter-wave (MMW) spectrum. However, MMW spectrums with high-order modulation schemes drive the power amplifier (PA) at significant back-off, causing severe nonlinear distortions, thus deteriorating the transceiver’s (TRXs) modulation process. Typically, the TRX efficacy is quantified with standardized linearization matrices, which take advantage of different predistortion (PD) schemes to handle deep compression of the PA. In this regard, TRX baseband signals are mostly linearized in the digital domain, where digitally controlled linearization needs higher sampling rates due to increasing MMW bandwidths to compensate for intermodulation (IMD) products, resulting in increased system cost and power consumption. Alternately, the digitally controlled analog-based linearization, i.e., the hybridization of digital predistortion (DPD) and analog predistortion (APD), is highly productive and cost-effective for fulfilling the linearized energy-efficient design vision of MMW networks. Therefore, this paper puts an extensive spotlight on the progress in PD-based linearization for 5G and beyond communications. It first provides background information on the advancements of PD schemes through recent surveys, then classifies the general roadmap of PD waveform processing across the TRX system models as preliminary. After this, we present three prominent PD architectures and their design approaches with intrinsic performance metrics. Finally, we explore four case studies encompassing PD operation under certain nonlinear constraints of different communication schemes. We examine the suitability of PD-based linearization solutions, both existing and proposed till the first quarter of 2022, and identify the potential prospects in this domain.
... At present, many digital filter methods-including denoising SVD algorithm accelerating [26] and partial least squares (PLS) algorithm implementation [27] based on FPGAhave already been applied in different areas such as electroencephalograph (EEG) signal processing [28] to achieve real-time data, while the power consumption of the system is greatly reduced compared to the GPU/CPU system. However, little research has been carried out to implement a digital filter based on FPGA for the absorption spectrum data, and to match the filtering algorithm with the spectrum data characteristic on the CMOS system. ...
Ultraviolet-visible absorption spectroscopy is widely used to monitor water quality, and rapid optical signal detection is a key technology in the process of spectrum measurement. In this paper, an ultrafast spectrophotometer system that can achieve spectrum data acquisition in a single flash of the xenon lamp (within 200 ns) is introduced, and a real-time denoising method for the spectrum is implemented on a field programmable gate array (FPGA) to work cooperatively with the nanosecond spectrum acquisition system, in order to guarantee the quality of the spectrum signals without losing running speed. The hardware of the data acquisition and processing system are constructed on a Xilinx Spartan 6 FPGA chip and its peripheral circuit, including an analog to digital converter and a complementary metal-oxide-semiconductor transistor (CMOS) sensor’s diver circuit. An oversampling method that is suitable for the CMOS sensor’s output is proposed, which works on the CMOS sensor’s dark current noise and readout noise. Another moving-average filter method is designed adaptively, which works on the low-frequency component to filter out the residual spectrum noise of the spectrum signal. The implementation of the filter on the FPGA has been optimized by using a pipelined structure and dual high-speed random-access memory (RAM). As a result, the CMOS linear image sensor successfully captured the spectrum of xenon flash light at the readout clock frequency of 500 kHz and the processing manipulation to the full UV-Vis spectrum data was accomplished at a sub-microsecond speed performance. After the digital filter and oversampling technology were implemented, the coefficient of variation of the measurements reduced from 9.57% to 1.74%, while the signal noise ratio (SNR) of the absorption spectrum increased nine times, compared to the raw data of the CMOS sensor’s output. The tests towards different analyte samples were conducted, and the system shows good performance on distinguishing different concentrations of different analyte solutions on both ultra-violet and visible spectrum bands. The present work showcases the potential of the CMOS sensor’s technique for the fast detection of contaminated water containing nitrate and organic compounds.
... For addressing the latter case, feature extraction techniques have been proposed in the field of DPD linearization with a double objective: to ensure a proper, well-conditioned parameter identification; and, as an alternative to LS solutions (e.g., QR-LS), to reduce the number of coefficients to be estimated in the observation path subsystem. Some examples of feature extraction techniques used in the field of PA behavioral modeling and DPD linearization are the following: principal component analysis (PCA) [7,8], partial least squares (PLS) [9], independent component analysis (ICA) [10] and canonical correlation analysis (CCA) [11]. These techniques are not aimed at reducing the number of coefficients of the DPD function in the forward path. ...
The power amplifier (PA) is the most critical subsystem in terms of linearity and power efficiency. Digital predistortion (DPD) is commonly used to mitigate nonlinearities while the PA operates at levels close to saturation, where the device presents its highest power efficiency. Since the DPD is generally based on Volterra series models, its number of coefficients is high, producing ill-conditioned and over-fitted estimations. Recently, a plethora of techniques have been independently proposed for reducing their dimensionality. This paper is devoted to presenting a fair benchmark of the most relevant order reduction techniques present in the literature categorized by the following: (i) greedy pursuits, including Orthogonal Matching Pursuit (OMP), Doubly Orthogonal Matching Pursuit (DOMP), Subspace Pursuit (SP) and Random Forest (RF); (ii) regularization techniques, including ridge regression and least absolute shrinkage and selection operator (LASSO); (iii) heuristic local search methods, including hill climbing (HC) and dynamic model sizing (DMS); and (iv) global probabilistic optimization algorithms, including simulated annealing (SA), genetic algorithms (GA) and adaptive Lipschitz optimization (adaLIPO). The comparison is carried out with modeling and linearization performance and in terms of runtime. The results show that greedy pursuits, particularly the DOMP, provide the best trade-off between execution time and linearization robustness against dimensionality reduction.
... The main path and training complexities are thus high when compared to the methods presented in this article. It is finally also noted that multi-dimensional LUT based solutions exist [28]- [30]. However, the LUT size in the nested LUT scheme in [28] grows exponentially with the memory depth, thus requiring unfeasible total LUT size when the linearized system exhibits substantial memory. ...
... The 2-dimensional LUT technique in [29] is, in turn, limited in its memory modeling capability, since it uses a weighted average of past amplitude samples to index the second LUT dimension. Finally, [30] combines an orthogonal matching pursuit algorithm to select the best LUTs in the forward path, and a partial least-squares algorithm to estimate the DPD coefficients, which usually involves high complexity mainly due to the matrix inversion in the LS problem. ...
... ch. , (30) measuring thus the out-of-band performance. While ACLR is, by definition, a relative measure, an explicit out-of-band spectral density limit, in terms of dBm/MHz measured with a sliding 1 MHz window in the adjacent channel region, is also defined for certain base-station types [23], referred to as the absolute basic limit in 3GPP terminology. ...
In this paper, new digital predistortion (DPD) solutions for power amplifier (PA) linearization are proposed, with particular emphasis on reduced processing complexity in future 5G and beyond wideband radio systems. The first proposed method, referred to as the spline-based Hammerstein (SPH) approach, builds on complex spline-interpolated lookup table (LUT) followed by a linear finite impulse response (FIR) filter. The second proposed method, the spline-based memory polynomial (SMP) approach, contains multiple parallel complex spline-interpolated LUTs together with an input delay line such that more versatile memory modeling can be achieved. For both structures, gradient-based learning algorithms are derived to efficiently estimate the LUT control points and other related DPD parameters. Large set of experimental results are provided, with specific focus on 5G New Radio (NR) systems, showing successful linearization of multiple PA samples as well as a 28 GHz active antenna array, incorporating channel bandwidths up to 200 MHz. Explicit performance-complexity comparisons are also reported between the SPH and SMP DPD systems and the widely-applied ordinary memory-polynomial (MP) DPD solution. The results show that the linearization capabilities of the proposed methods are very close to that of the ordinary MP DPD, particularly with the proposed SMP approach, while having substantially lower processing complexity.
... To reduce the calculation time, many methods have been developed, such as look-up-table (LUT) method [18], wavefront recording plane method [19] and other derivative methods [20][21][22]. The LUT method is widely used to accelerate the calculations by utilizing the pre-calculated data to replace the complicated calculations [23]. Each complex amplitude distribution of the PLS is pre-calculated and stored. ...
In this paper, a fast hologram generation method is proposed based on the optimal segmentation of a sub-computer-generated-hologram (sub-CGH). The relationship between the pixels on the hologram and the corresponding reconstructed image is calculated firstly. Secondly, the sub-CGH corresponding to the object point from the recorded object is optimized and divided into the optimized diffraction area and the invalid diffraction area. Then, the optimized diffraction area of the sub-CGH for each object point is pre-calculated and saved. Finally, the final hologram can be generated by superimposing all the sub-CGHs. With the proposed method, the calculation time for the final hologram can be significantly reduced and the quality of the reconstructed image is not affected. Moreover, the proposed method has the advantages of perspective enlargement compared with the traditional method, and the experiment results verify its feasibility.
... Some of the aforementioned feature extraction techniques have been proposed by the authors in [20]- [22] as an alternative to one of the most commonly used solutions based on QR factorization combined with recursive least squares (QR-RLS) [23]. The objective of using these techniques is not only to ensure a proper well-conditioned estimation, but also a reduction in the number of parameters required in the identification or adaptation process. ...
... However, unlike with feature selection techniques, with feature extraction techniques, the number of coefficients of the DPD function in the forward path is not reduced. For that reason, in [22] the authors proposed the combination of an off-line OMP search for reducing the DPD basis in the forward path with PLS extraction in the adaptation (or observation) path. In comparison to PCA [20], where the new basis of components with maximal variance are obtained taking into account only the input data, with PLS the new basis of components show maximal covariance in relation to the signal to be estimated and thus, the reduction capabilities using PLS are significantly better than using PCA, as discussed in [22]. ...
... For that reason, in [22] the authors proposed the combination of an off-line OMP search for reducing the DPD basis in the forward path with PLS extraction in the adaptation (or observation) path. In comparison to PCA [20], where the new basis of components with maximal variance are obtained taking into account only the input data, with PLS the new basis of components show maximal covariance in relation to the signal to be estimated and thus, the reduction capabilities using PLS are significantly better than using PCA, as discussed in [22]. In [24], the authors extended the reduction capabilities by presenting a dynamic adaptation approach based on PLS where the basis of new components used in the DPD estimation is dynamically adjusted and thus, at every iteration of the adaptation process, only the minimum number of required components are used to minimize the linearization error. ...
This paper presents a new technique that dynamically estimates and updates the coefficients of a digital predistorter (DPD) for power amplifier (PA) linearization. The proposed technique is dynamic in the sense of estimating, at every iteration of the coefficient's update, only the minimum necessary parameters according to a criterion based on the residual estimation error. At the first step, the original basis functions defining the DPD in the forward path are orthonormalized for DPD adaptation in the feedback path by means of a precalculated principal component analysis (PCA) transformation. The robustness and reliability of the precalculated PCA transformation (i.e., PCA transformation matrix obtained off line and only once) is tested and verified. Then, at the second step, a properly modified partial least squares (PLS) method, named dynamic partial least squares (DPLS), is applied to obtain the minimum and most relevant transformed components required for updating the coefficients of the DPD linearizer. The combination of the PCA transformation with the DPLS extraction of components is equivalent to a canonical correlation analysis (CCA) updating solution, which is optimum in the sense of generating components with maximum correlation (instead of maximum covariance as in the case of the DPLS extraction alone). The proposed dynamic extraction technique is evaluated and compared in terms of computational cost and performance with the commonly used QR decomposition approach for solving the least squares (LS) problem. Experimental results show that the proposed method (i.e., combining PCA with DPLS) drastically reduces the amount of DPD coefficients to be estimated while maintaining the same linearization performance.
... ET and outphasing PA are unlikely to be deployed for ultra wideband applications in 5G mm-wave bands due to the bandwidth and power/cost budget limitations of these high efficient amplification architectures that require DPD linearization. However, in 5G sub-6 GHz macro basestations, by considering envelope bandwidth or slew-rate reduction techniques [25] properly combined with dimensionality reduction techniques [30] to meet the low complexity requirements of the DPD implementation, the use of dynamic supply (e.g., ET or class-G PAs) or dynamic load modulation techniques (e.g., outphasing or load modulated balanced PAs) can still be considered as interesting solutions for high efficient amplification. ...
... This particular 3-D DPD model was used in a concurrent dual-band transmission in [26], [30], to compensate for the unwanted nonlinear distortion of an envelope tracking PA. For example, Fig. 8-left shows the output spectra of an ET PA used in [30] before and after 3-D DPD. ...
... This particular 3-D DPD model was used in a concurrent dual-band transmission in [26], [30], to compensate for the unwanted nonlinear distortion of an envelope tracking PA. For example, Fig. 8-left shows the output spectra of an ET PA used in [30] before and after 3-D DPD. Using the slow envelope to dynamically supply the PA is a suboptimal solution from the power efficiency point of view in comparison to using the original RF signal's envelope. ...
Over at least the last two decades, digital predistortion (DPD) has become the most common and widespread solution to cope with the power amplifier's (PA's) inherent linearity-versus-efficiency tradeoff. When compared with other linearization techniques, such as Cartesian feedback or feedforward, DPD has proven able to adapt to the always-growing demands of technology: wider bandwidths, stringent spectrum masks, and reconfigurability. The principles of predistortion linearization (in its analog or digital forms) are straightforward, and the linearization subsystem precedes the PA (a nonlinear function in a digital signal processor in the case of DPD or nonlinear device in the case of analog predistortion and counteracts the nonlinear characteristic of the PA. Some excellent overviews on DPD can be found in [1]-[4]. Let us now look at the challenges that DPD linearization has faced and will continue to face in the near future with 5G new radio (5G-NR).
... The DPD order reduction can be done by properly selecting the most relevant basis functions (e.g., using a greedy algorithm such as the orthogonal matching pursuit -OMP- [1]) or by creating a new set of components that are the linear combinations of the original basis (e.g. using principal component analysis -PCA- [2] or partial least squares -PLS- [3]). Alternatively, both approaches (i.e., OMP combined with PLS/PCA) can be properly combined as in [4]. Besides, as discussed in [4], the order reduction obtained without loss of performance when using PLS is higher than with PCA, since the PLS obtains the new transformed basis of components taking into account the information of the PA output [3]. ...
... Alternatively, both approaches (i.e., OMP combined with PLS/PCA) can be properly combined as in [4]. Besides, as discussed in [4], the order reduction obtained without loss of performance when using PLS is higher than with PCA, since the PLS obtains the new transformed basis of components taking into account the information of the PA output [3]. ...
... Unlike in [4], where a new basis with a reduced but fixed number of properly selected components was obtained to guarantee a well-conditioned estimation, in this paper, PLS is employed inside the DPD adaptation loop to actively adjust the basis matrix in the DPD identification subsystem. The dynamic basis reduction is carried out at every iteration according to the residual linearization error, defined as the difference between the actual and the desired linear PA output signals. ...
To accomplish rapid adaptation of the digital predistortion (DPD) model, a low-complexity parameter extraction architecture is proposed in this article. The extracted DPD model coefficients are represented by a linear combination of the previous parameters (or pretrained parameters) in a novel basis parameter combination (BPC) method, thereby avoiding the extraction of high-dimensionality coefficients and significantly lowering the computational cost. Then, we developed a feature mapping technique (FMT) to coordinate the feature spaces corresponding to different DPD model structures, which facilitates the transfer learning of heterogeneous DPD model coefficients as the DPD model structure should be modified with the transmission configuration changes. Due to the good scalability of the proposed method, a dynamic transfer strategy (DTS) is presented to enhance the method’s flexibility and avoid incremental complications by combining it with dimensionality reduction techniques. The experimental results demonstrate that the proposed method outperforms the state-of-the-art in terms of computational complexity, adaptability, and modeling precision.
