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We propose a two-step identification approach for twin-box model (Wiener or Hammerstein) of RF power amplifier. The linear filter block and the static nonlinearity block are extracted, respectively, based on least-squares method, by iterative calculation. Simulations show that the method can get quite accurate parameters to model different nonlinear models with memory such as Wiener, Hammerstein, Wiener-Hammerstein (W-H), and memory polynomial models, hence, demonstrating its robustness. Furthermore, experimental results show excellent agreement between measured output and modeled output, where one carrier WCDMA signal is used as the excitation for a wideband RF amplifier.

New signal modulation formats in modern communication systems are with high peak to average ratio (PAR) and wide bandwidth. Power amplifiers (PAs) excited by such signals exhibit different nonlinearity and memory effects compared with the case of single-tone excitation. Consequently, the development of behavioral models is indispensable for performance analysis of PAs and system simulation with PAs. The Volterra model [

In this paper, we consider the twin-box models identification process and propose a novel identification method with simplicity. The model output is with a high degree of accuracy compared with the measured output. Different models such as Wiener, Hammerstein, Wiener-Hammerstein (W-H), and memory polynomial models can be modeled by either twin-box models (Wiener, or Hammerstein) with this identification method. As a further evaluation, measurement setup and experimental results for a wideband amplifier operating at 2.14 GHz of one carrier WCDMA signal are presented. The results show high accuracy of the models.

The relationship between input and output complex envelopes of PAs can be described as Wiener model or Hammerstein model, as shown in Figures

Block diagram of the twin-box models: (a) Wiener model and (b) Hammerstein model.

In our identification approach, the linear filter block and the static nonlinearity block are extracted, respectively, according to the collection of baseband input

(1) Collecting input and output samples:

(2) Initialization:

(3) Step 1: identifying static nonlinear block. Let

(4) Step 2: identifying linear filter block. Let

After that, we use

(5) Going back to (3) and (4) to iteratively extract the coefficients of

This identification method is with high accuracy and fast convergence speed. In most cases, it can converge within two iterations. A similar approach to identify Hammerstein model can be deduced. Noticeably, for Hammerstein model identification, the static nonlinear block should be identified firstly and then followed by the linear filter identification process during the iterations.

In order to evaluate the performance of the proposed two-step identification approach, we apply the method to different nonlinear models with memory through computer simulations. The Wiener, Hammerstein, Wiener-Hammerstein (W-H), and memory polynomial models PAs are considered as the PAs we want to identify. The coefficients of these PAs are set as practical-like ones. The coefficients of them are listed in Table

PAs coefficients used for simulation.

Wiener PA | |
---|---|

Hammerstein PA | |

W-H PA | |

Mem. poly. PA | |

We extract the modeling parameters of twin-box models through 64QAM with 8× sampling rate firstly. Then the models are validated by using a different type signal of one carrier WCDMA with 10× sampling rate. Normalized mean square error (NMSE) is used to evaluate the modeling accuracy, which is defined as

The results of one carrier WCDMA validation for different PAs identified as either Wiener model or Hammerstein model are summarized in Table

Modeling performances of twin-box models for different PAs with one carrier WCDMA excitation.

NMSE [dB] of Wiener modeling | NMSE [dB] of Hammerstein modeling | NMSE [dB] of Wiener modeling with the method in [ | |
---|---|---|---|

Wiener PA | −289.2 | −49.1 | −40.9 |

Hammerstein PA | −48.0 | −92.1 | −39.8 |

W-H PA | −49.1 | −39.6 | −39.1 |

Mem. poly. PA | −40.4 | −40.0 | −34.7 |

During the experimental validation process, an extensively used test bed is employed for measurement purpose, which is based on an arbitrary waveform generator and a vector signal analyzer. The baseband 10× sampled WCDMA signal with 5 MHz bandwidth is uploaded into the arbitrary waveform generator and upconverted to 2.14 GHz to construct the real world RF signal. Then, the signal is transferred to a wideband RF amplifier, which operates from 100 kHz to 3 GHz with

Figure

Measured and modeled characteristics of the RF amplifier: (a) AM/AM and (b) AM/PM.

The normalized measured and modeled spectra for the amplifier are depicted in Figure

Measured and modeled spectra of the RF power amplifier.

The twin-box models have been extensively used in power amplifier modeling with memory effects and in digital predistortion linearization technique. The novel two-step identification approach has been validated through 5 MHz WCDMA signal excitation. Simulations show very small modeling error in the order of