A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA

A comparative analysis of behavioral models for RF power amplifiers

This paper proposes a system-level behavioral model for RF power amplifiers (PAs), which exhibit memory effects, that is based on the parallel Wiener system. The model extraction is performed using two-tone intermodulation distortion (IMD) measurements with different tone frequency spacings and power levels. It is found that by using such a model, more accurate adjacent-channel power-ratio levels may be predicted for high PAS close to the carrier frequency. This is validated using IS-95B CDMA signals on a low-power (0.5 W) class-AB PA, and on a high-power (45 W) class-B PA. The model also provides a means to quantify memory effects in terms of a figure-of-merit that calculates the relative contribution to the IMD of the memoryless and memory portion of the PA nonlinearity. This figure-of-merit is useful in providing an estimate of the amount of correction that a memoryless predistortion system may have on PAS that exhibit memory effects.

Quantifying memory effects in RF power amplifiers

This paper proposes a system-level behavioral model for RF power amplifiers (PAs) that exhibit memory effects. PAs with memory effects are shown to have two-tone intermodulation distortion (IMD) levels that vary depending on tone-spacing. Thus, typical single tone extracted AM/AM and AM/PM characteristics cannot accurately model PA memory effects. By varying the frequency spacing of two-tone signals, envelope frequency dependent transfer functions can be derived. Using these transfer functions, a behavioral model is developed which is based on the parallel-cascade linear and nonlinear (LN) system. This model gives more accurate results in predicting the behavior of PAs with memory effects close to the carrier frequency. The model is validated by comparing the predicted and measured adjacent channel power ratio (ACPR) of a CDMA signal amplified by a high power class-AB PA. It is found that the parallel cascade model improves ACPR prediction accuracy by as much as 4 dB compared to the single tone derived memoryless model.

Extraction of accurate behavioral models for power amplifiers with memory effects using two-tone measurements

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Modelling of Nonlinear Power Amplifiers for Wireless Communications

This paper is focused on digital predistortion using neural networks (NNETs) for linearization of power amplifiers. We propose a new architecture of NNET. It is based on a feedforward tapped delay line neural network for complex signals with one hidden layer but it includes both delayed and advanced samples at its input. We name this architecture TADNN (tapped advance and delay line neural net). We show that the introduction of advance taps improves the digital predistortion (DPD) performance. We also compare the TADNN predistorter with predistorters derived from Volterra series such as memory polynomial or dynamic deviation reduction models. This comparison is based on three elements: performance in linearization, complexity, increase of the peak to average power ratio (PAPR) by the predistorter. Indeed, one drawback of Volterra based predistorters is that they can generate predistorted signals with very high PAPR that cannot be applied directly at the input of the power amplifier. Conversely, the PAPR of the predistorted signals at the output of the TADNN remains moderate. The presented approach is evaluated on a real LDMOS (laterally diffused metal oxide semiconductor) push-pull power amplifier with 16 MHz bandwidth OFDM (orthogonal frequency-division multiplex) signal at a carrier frequency of 200 MHz.

Digital predistortion with advance/delay neural network and comparison with Volterra derived models

In recent years there have been some significant technological advancements in the design of solid power amplifiers (SSPAs). These have made the replacement of travelling wave tube amplifiers (TWTAs) by SSPAs possible and economical, and have stimulated the interest in modelling and analysis of nonlinear elements with memory such as SSPAs. This paper proposes two simple models for a class of nonlinear elements which can be represented by frequency-dependent AM/AM and AM/PM characteristics. The simplicity of these models makes them appealing for analysis and simulation considerations. With these models, the analysis techniques that have been developed to study the behavior of signals through effectively memoryless nonlinear elements such as helix-type TWTAs can directly be applied. Straightforward identification schemes associated with these models are also given.

X. T. Vuong

Papers

Modelling of nonlinear elements exhibiting frequency-dependent AM/AM and AM/PM transfer characteristics