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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 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., This work was supported in part by the Spanish Government (Ministerio de Ciencia, Inno- vación y Universidades) and Fondo Europeo de Desarrollo Regional (FEDER) under Grants TEC2017- 83343-C4-2-R and PID2020-113832RB-C21 and in part by the Government of Catalonia and the European Social Fund under Grants 2017-SGR-813 and 2021-FI-B-137., Peer Reviewed, Postprint (published version)

Over the past half century, the improvements in spacecraft technology have been primarily in the areas of microelectronics for on-board processing, high frequency electronic devices, and integrated circuits for communications and navigation, solar cells and batteries for on-board power generation and storage among many others. Despite the fact that energy-storage technologies have advanced dramatically over the past years, the power consumption of on-board communications, sensors and digital signal processing systems is of paramount importance in battery or solar powered systems such as small satellites, HAPs or UAVs (drones). There is multiple applications that involves the use of these systems, e.g., Earth observation applications, surveillance, broadcast communications, scientific research, etc. In wireless communications, the power amplifier is a critical subsystem in the transmitter chain. Not only because it is one of the most power hungry devices that accounts for most of the direct current power consumption, but also because it is the main source of nonlinear distortion in the transmitter. Amplitude and phase modulated communications signals presenting high peak-to-average power ratio have a negative impact in the transmitter's power efficiency, because the PA has to be operated at high power back-off levels to avoid introducing nonlinear distortion. Digital predistortion (DPD) linearization is the most common and spread solution to cope with power amplifiers (PA) inherent linearity versus efficiency trade-off. When considering wide bandwidth signals, such as Doherty PAs, envelope tracking PAs or outphasing transmitters, the number of parameters required in the DPD model to compensate for both nonlinearities and memory effects can be very high. This has a negative impact in the DPD ceofficients extraction, because increases the computational complexity and drives to over-fitting and uncertainty. However, by applying dimensionality reduction techniques we can

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 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.

We present the second update to a data set of gridded land‐based temperature and precipitation extremes indices: HadEX3. This consists of 17 temperature and 12 precipitation indices derived from daily, in situ observations and recommended by the World Meteorological Organization (WMO) Expert Team on Climate Change Detection and Indices (ETCCDI). These indices have been calculated at around 7,000 locations for temperature and 17,000 for precipitation. The annual (and monthly) indices have been interpolated on a 1.875°×1.25° longitude‐latitude grid, covering 1901–2018. We show changes in these indices by examining ”global”‐average time series in comparison with previous observational data sets and also estimating the uncertainty resulting from the nonuniform distribution of meteorological stations. Both the short and long time scale behavior of HadEX3 agrees well with existing products. Changes in the temperature indices are widespread and consistent with global‐scale warming. The extremes related to daily minimum temperatures are changing faster than the maximum. Spatial changes in the linear trends of precipitation indices over 1950–2018 are less spatially coherent than those for temperature indices. Globally, there are more heavy precipitation events that are also more intense and contribute a greater fraction to the total. Some of the indices use a reference period for calculating exceedance thresholds. We present a comparison between using 1961–1990 and 1981–2010. The differences between the time series of the temperature indices observed over longer time scales are shown to be the result of the interaction of the reference period with a warming climate. The gridded netCDF files and, where possible, underlying station indices are available from www.metoffice.gov.uk/hadobs/hadex3 and www.climdex.org., Robert Dunn was supported by the Met Office Hadley Centre Climate Programme funded by BEIS and Defra (GA01101) and thanks Nick Rayner and Lizzie Good for helpful comments on the manuscript. Lisa Alexander is supported by the Australian Research Council (ARC) Grants DP160103439 and CE170100023. Markus Donat acknowledges funding by the Spanish Ministry for the Economy, Industry and Competitiveness Ramón y Cajal 2017 Grant Reference RYC‐2017‐22964. Mohd Noor'Arifin Bin Hj Yussof and Muhammad Khairul Izzat Bin Ibrahim thank the Brunei Darussalam Meteorological Department (BDMD). Ying Sun was supported by China funding agencies 2018YFA0605604 and 2018YFC1507702. Fatemeh Rahimzadeh and Mahbobeh Khoshkam thank I.R. of Iranian Meteorological Organization (IRIMO) and the Atmospheric Science and Meteorological Organization Research Center (ASMERC) for Data and also sharing their experiences, especially Abbas Rangbar. Jose Marengo was supported by the National Institute of Science and Technology for Climate Change Phase 2 under CNPq Grant 465501/2014‐1, FAPESP Grants 2014/50848‐9 and 2015/03804‐9, and the National Coordination for High Level Education and Training (CAPES) Grant 88887.136402‐00INCT. The team that worked on the data in West Africa received funding from the UK's National Environment Research Council (NERC)/Department for International Development DFID) Future Climate For Africa programme, under the AMMA‐2050 project (Grants NE/M020428/1 and NE/M019969/1). Data from Southeast Asia (excl. Indonesia) was supported by work on using ClimPACT2 during the Second Workshop on ASEAN Regional Climate Data, Analysis and Projections (ARCDAP‐2), 25–29 March 2019, Singapore, jointly funded by Meteorological Service Singapore and WMO through the Canada‐Climate Risk and Early Warning Systems (CREWS) initiative. This research was supported by Thai Meteorological Department (TMD) and Thailand Science Research and Innovation (TSRI) under Grant RDG6030003. Daily data for Mexico were, Peer Reviewed, Postprint (published version)

We present the second update to a data set of gridded land-based temperature and precipitation extremes indices: HadEX3. This consists of 17 temperature and 12 precipitation indices derived from daily, in situ observations and recommended by the World Meteorological Organization (WMO) Expert Team on Climate Change Detection and Indices (ETCCDI). These indices have been calculated at around 7,000 locations for temperature and 17,000 for precipitation. The annual (and monthly) indices have been interpolated on a1.875 degrees x1.25 degrees longitude-latitude grid, covering 1901-2018. We show changes in these indices by examining global-average time series in comparison with previous observational data sets and also estimating the uncertainty resulting from the nonuniform distribution of meteorological stations. Both the short and long time scale behavior of HadEX3 agrees well with existing products. Changes in the temperature indices are widespread and consistent with global-scale warming. The extremes related to daily minimum temperatures are changing faster than the maximum. Spatial changes in the linear trends of precipitation indices over 1950-2018 are less spatially coherent than those for temperature indices. Globally, there are more heavy precipitation events that are also more intense and contribute a greater fraction to the total. Some of the indices use a reference period for calculating exceedance thresholds. We present a comparison between using 1961-1990 and 1981-2010. The differences between the time series of the temperature indices observed over longer time scales are shown to be the result of the interaction of the reference period with a warming climate. The gridded netCDF files and, where possible, underlying station indices are available from and .