Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels
Volterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of non...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Electronics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-9292/11/19/3067 |
| _version_ | 1797479895658397696 |
|---|---|
| author | Francesco Centurelli Pietro Monsurrò Giuseppe Scotti Pasquale Tommasino Alessandro Trifiletti |
| author_facet | Francesco Centurelli Pietro Monsurrò Giuseppe Scotti Pasquale Tommasino Alessandro Trifiletti |
| author_sort | Francesco Centurelli |
| collection | DOAJ |
| description | Volterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of nonlinear calibration, and improve stability and speed, while preserving accuracy. Several techniques (LASSO, DOMP and OBS) and their variants (WLASSO and OBD) are compared in this paper for the experimental calibration of an IF amplifier. The results show that Volterra models can be simplified, yielding models that are 4–5 times sparser, with a limited impact on accuracy. About 6 dB of improved Error Vector Magnitude (EVM) is obtained, improving the dynamic range of the amplifiers. The Symbol Error Rate (SER) is greatly reduced by calibration at a large input power, and pruning reduces the model complexity without hindering SER. Hence, pruning allows improving the dynamic range of the amplifier, with almost an order of magnitude reduction in model complexity. We propose the OBS technique, used in the neural network field, in conjunction with the better known DOMP technique, to prune the model with the best accuracy. The simulations show, in fact, that the OBS and DOMP techniques outperform the others, and OBD, LASSO and WLASSO are, in turn, less efficient. A methodology for pruning in the complex domain is described, based on the Frisch–Waugh–Lovell (FWL) theorem, to separate the linear and nonlinear sections of the model. This is essential because linear models are used for equalization and cannot be pruned to preserve model generality vis-a-vis channel variations, whereas nonlinear models must be pruned as much as possible to minimize the computational overhead. This methodology can be extended to models other than the Volterra one, as the only conditions we impose on the nonlinear model are that it is feedforward and linear in the parameters. |
| first_indexed | 2024-03-09T21:52:22Z |
| format | Article |
| id | doaj.art-f24dab6f49b041de99dc236e143d398e |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-09T21:52:22Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-f24dab6f49b041de99dc236e143d398e2023-11-23T20:05:44ZengMDPI AGElectronics2079-92922022-09-011119306710.3390/electronics11193067Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra KernelsFrancesco Centurelli0Pietro Monsurrò1Giuseppe Scotti2Pasquale Tommasino3Alessandro Trifiletti4Department of Information, Electronics and Telecommunications Engineering, Sapienza University, 00184 Roma, ItalyDepartment of Information, Electronics and Telecommunications Engineering, Sapienza University, 00184 Roma, ItalyDepartment of Information, Electronics and Telecommunications Engineering, Sapienza University, 00184 Roma, ItalyDepartment of Information, Electronics and Telecommunications Engineering, Sapienza University, 00184 Roma, ItalyDepartment of Information, Electronics and Telecommunications Engineering, Sapienza University, 00184 Roma, ItalyVolterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of nonlinear calibration, and improve stability and speed, while preserving accuracy. Several techniques (LASSO, DOMP and OBS) and their variants (WLASSO and OBD) are compared in this paper for the experimental calibration of an IF amplifier. The results show that Volterra models can be simplified, yielding models that are 4–5 times sparser, with a limited impact on accuracy. About 6 dB of improved Error Vector Magnitude (EVM) is obtained, improving the dynamic range of the amplifiers. The Symbol Error Rate (SER) is greatly reduced by calibration at a large input power, and pruning reduces the model complexity without hindering SER. Hence, pruning allows improving the dynamic range of the amplifier, with almost an order of magnitude reduction in model complexity. We propose the OBS technique, used in the neural network field, in conjunction with the better known DOMP technique, to prune the model with the best accuracy. The simulations show, in fact, that the OBS and DOMP techniques outperform the others, and OBD, LASSO and WLASSO are, in turn, less efficient. A methodology for pruning in the complex domain is described, based on the Frisch–Waugh–Lovell (FWL) theorem, to separate the linear and nonlinear sections of the model. This is essential because linear models are used for equalization and cannot be pruned to preserve model generality vis-a-vis channel variations, whereas nonlinear models must be pruned as much as possible to minimize the computational overhead. This methodology can be extended to models other than the Volterra one, as the only conditions we impose on the nonlinear model are that it is feedforward and linear in the parameters.https://www.mdpi.com/2079-9292/11/19/3067digital calibrationnonlinear modelscomplexity reductionamplifiersanalog circuitsoptimal brain surgeon |
| spellingShingle | Francesco Centurelli Pietro Monsurrò Giuseppe Scotti Pasquale Tommasino Alessandro Trifiletti Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels Electronics digital calibration nonlinear models complexity reduction amplifiers analog circuits optimal brain surgeon |
| title | Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels |
| title_full | Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels |
| title_fullStr | Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels |
| title_full_unstemmed | Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels |
| title_short | Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels |
| title_sort | methods for model complexity reduction for the nonlinear calibration of amplifiers using volterra kernels |
| topic | digital calibration nonlinear models complexity reduction amplifiers analog circuits optimal brain surgeon |
| url | https://www.mdpi.com/2079-9292/11/19/3067 |
| work_keys_str_mv | AT francescocenturelli methodsformodelcomplexityreductionforthenonlinearcalibrationofamplifiersusingvolterrakernels AT pietromonsurro methodsformodelcomplexityreductionforthenonlinearcalibrationofamplifiersusingvolterrakernels AT giuseppescotti methodsformodelcomplexityreductionforthenonlinearcalibrationofamplifiersusingvolterrakernels AT pasqualetommasino methodsformodelcomplexityreductionforthenonlinearcalibrationofamplifiersusingvolterrakernels AT alessandrotrifiletti methodsformodelcomplexityreductionforthenonlinearcalibrationofamplifiersusingvolterrakernels |