This book provides a comprehensive treatment of radio-frequency (RF) nonlinear power amplifier behavioural modelling, from the fundamental concepts and principles through to the range of classical and, especially, current modelling techniques.

The continuing rapid growth of wireless communications and radio transmission systems, with their ever increasing sophistication, complexity and range of application, has been paralleled by a similar growth in research into all aspects of electronic components, systems and subsystems. This has given rise to a great variety of new and advanced technologies catering for the breadth of frequencies, bandwidths and powers expected in new and existing air interfaces and in the mobile wireless world, for the ever increasing integration of widely differing interfaces into single devices, with the future likelihood that these devices will be active on two or more interfaces simultaneously. For radio communications, or simply radio transmission systems, from the high-frequency (HF) band to the microwave and millimetrewave bands, the transmitter power amplifier (PA) is a pivotal enabling component. This is especially apparent when setting and satisfying air-interface specifications, the correct transmitted signal power levels and tolerable levels of inband and out-of-band signal impairment. The reason for this high-profile role of the PA is that it is the major source of signal distortion and spurious signal generation, harmonics and intermodulation products. Further, it is by far the greatest energy-consuming component in the radio transmission path. Depending on the class of amplifier and the operating conditions dictated by the complexity of the signals to be amplified, its DC to RF power-conversion efficiency is generally poor, resulting in power wastage.

Introduction

Since the early 1980s, the range and variety of wireless communication air interfaces has seen immense growth. This has been driven, and is being driven further, by the need for ever greater information throughput. This requires greater bandwidths, higher output transmitter powers and the more efficient use of handheld battery energy resources and all at ever higher frequencies, although some lower frequencies have been freed up from the traditional broadcast communication services and are becoming available.

One complex modulation scheme that has grown in importance over the last decade is orthogonal frequency-division multiplexing (OFDM). It is a scheme which increases bandwidth efficiency and data capacity by splitting broadband channels into multiple narrowband channels, each using a different frequency, which can then carry different parts of a message simultaneously at bit per hertz capacities that are dynamically adaptable to the wireless channel quality.

This trend is set to continue for the foreseeable future and will result in a wide range of complex wireless communications systems sharing a common physical space. This has major implications for the development of communicationsimulation tools.

In this appendix some advanced wireless interface standards are summarised with a view to highlighting the broad range of signal formats and figures of merit that have to be considered when developing system simulators. These are especially relevant when simulators with embedded nonlinear elements such as nonlinear PA behavioural models are being developed.

The three interfaces selected provide wireless coverage from long range to very short range and have been developed by the Institute of Electrical and Electronics Engineers Inc. through the IEEE 802.11, 802.15 and 802.16 Work Groups.

Introduction

This chapter contains a comprehensive overview of the approaches for modelling nonlinear PAs with nonlinear memory. The difference between linear and nonlinear memory effects was presented in subsection 1.2.2 on the basis of the model presented in Figure 1.6.

The simplest modelling approach is the memory polynomial model. It will be explained that introducing non-uniform time-delay taps yields better results. Two more elaborate approaches that are closely related to the memory polynomial model are the time-delay neural network (TDNN) model and the nonlinear autoregressive moving-average (NARMA) model.

In the case of the TDNN model, the memoryless nonlinear network is described by an artificial neural network (ANN). Since ANNs have gained importance in microwave PA behavioural modelling, the concept will be explained in a separate section. In the case of the NARMA model the output depends not only on past values of the input but also on past values of the output. Stability may be a problem with this modelling approach, but criteria are derived to check for this.

Another way to model nonlinear PAs with nonlinear memory effects is by an extension of the well-known Wiener modelling approach. By introducing parallel branches consisting of a linear time-invariant (LTI) system followed by a memoryless nonlinear system, nonlinear memory effects can be modelled adequately.

A further category of models comprises the Volterra-series-based models. It is often said that the computation of Volterra kernels is difficult when the system has complex nonlinearity. A number of extended approaches have been developed to overcome the intrinsic disadvantages of Volterra models.

Introduction

Simulation is widely used in the design and analysis of complex communications systems. The aim is to describe the operating characteristics and performance of all or part of a communication link, whether simple or complex, and to mimic through mathematical models all the analogue and digital signal processing activities, whether at baseband, IF or RF frequencies. System-level simulations can be based on time-domain or frequency-domain techniques or on a combination of both. Time-domain models are the norm in system-level digital signal processing (DSP) simulations while the frequency-domain approach is a popular choice for RF circuitlevel simulation, even though time-domain simulation is also much used, especially in connection with equivalent baseband envelope techniques such as the circuit envelope. When nonlinearities exist in the system it is difficult to simulate other than in the time domain, although harmonic-balance, mixed frequency-domain and time-domain approaches on statistical techniques may be used.

Well-known commercial dedicated simulation and electronic design automation software systems, such as Applied Wave Research's Microwave Office (AWR-MO) and Virtual System Simulator (AWR-VSS) and Agilent's Advanced Design System (ADS), provide both circuit-level and system-level simulation capability, with the possibility of including nonlinear microwave PA models also. Other robust commercial simulation tools for circuit-level mixed (analogue and digital signal) communication systems are the ‘Virtuoso’ platform from Cadence and the HSPICE simulator from Synopsis. There is ongoing widespread research in this area especially to increase the capacity to handle more complex systems, to develop library modules for new technologies and to improve simulation efficiency.

Introduction

This chapter presents an overview and comparative assessment of the various approaches to RF power amplifier (PA) modelling that have received widespread attention by the scientific community. The chapter is organised into three sections: power amplifier modelling basics, system-level power amplifier models and circuitlevel power amplifier models.

Section 1.2 on power amplifier modelling basics provides the basic knowledge to support the subsequent PA model classification and analysis. First, physical and behavioural modelling strategies are addressed and then behavioural models are classified as either static or dynamic with varying levels of complexity. Then, a distinction is made between the heuristic and systematic approaches, hence creating a theoretical framework for comparing different behavioural model formats with respect to their formulation, extraction and, in most cases, predictive capabilities.

In Section 1.3, dedicated to system-level power amplifier models, PA representations intended to be used in system-level simulators are considered. These are analytic signal- or complex-envelope-based techniques; they do not represent the RF carrier directly and RF effects are not specifically included. They are single-input–single-output (SISO) low-pass equivalent models, whose input and output constitute the complex functions needed to represent the bidimensional nature of amplitude and phase modulation.

The final section, on circuit-level power amplifier models, provides an overview of behavioural models intended for use in conventional PA circuit simulators. These models handle the complete input and output RF modulated signals, which are real entities, at two different time scales, one, very fast, for the RF carrier and another, much slower, for the modulating envelope.

Chapter 1

J. C. Pedro (Universidade de Aveiro, Portugal)

Chapter 2

M. Gadringer, D. Silveira (Technische Universität Wien, Austria)

D. Schreurs, M. Myslinski (Katholieke Universiteit Leuven, Belgium)

M. O'Droma (University of Limerick, Ireland)

J. A. García, A. Mediavilla (Universidad de Cantabria, Spain)

Chapter 3

M. O'Droma, Y. Lei, S. Meza (University of Limerick, Ireland)

V. Camarchia, M. Pirola (Politecnico di Torino, Italy)

Chapter 4

M. Gadringer, D. Silveira (Technische Universtität Wien, Austria)

A. Zhu, C. Devlin (University College Dublin, Ireland)

Chapter 5

E. R. Srinidhi, G. Kompa (Universität Kassel, Germany)

D. Schreurs, M. Myslinski (Katholieke Universiteit Leuven, Belgium)

P. Gilabert, G. Montoro Lopez, E. Bertran (Universitat Politecnica de Catalunya, Spain)

A. Zhu, C. Devlin (University College Dublin, Ireland)

J. A. Lonac, C. Florian, I. Melczarsky (Università di Bologna, Italy)

Y. Gurbuz, I. Tekin (Sabanci Üniversitesi, Turkey)

S. Donati Guerrieri, M. Pirola (Politecnico di Torino, Italy)

Chapter 6

I. Melczarsky, A. Santarelli, F. Filicori (Università di Bologna, Italy)

M. Gadringer, D. Silveira (Technische Universtität Wien, Austria)

D. Schreurs (Katholieke Universiteit Leuven, Belgium)

Chapter 7

M. O'Droma, A. A. Goacher (University of Limerick, Ireland)

M. Olavsbråten (NTNU Trondheim, Norway)

Appendix A

Y. Gurbuz, C. Kavlak, I. Tekin (Sabanci Üniversitesi, Turkey)

A. A. Goacher (University of Limerick, Ireland)

Introduction

In Chapter 1 we introduced and classified models according to the mathematical structure of the model. However, several other properties and classifications of PA behavioural models are possible that are not directly related to the model itself. They are a result of the observed PA characteristics, which are reflected by the model.

Here we will highlight aspects and properties of behavioural models and will also discuss important issues concerning the characterisation of microwave amplifiers. The model properties and classifications used in this context can be divided into the following major groups:

• properties derived from the model structure;

• properties introduced by the PA modelling application;

• properties reflecting the behaviour of the observed amplifier under a specific excitation.

The most important of these properties are summarised in Figure 2.1.

Obviously, a model can represent several of these characteristics simultaneously. Some properties listed in the figure describe the same model characteristic from different points of view. For example, one may classify models according to the presence of linear or nonlinear memory effects using the structure presented in Figure 1.6, whereas another possibility is to assume a specific structure for the observed amplifier and then divide the dynamic nonlinear behaviour into shortand long-term memory effects.

In Section 2.2, model- and model-structure-based properties of behavioural models are summarised for completeness. Most of these properties and classifications were introduced in Chapter 1.

In Section 2.3 we briefly present the differences between models classified as circuit-level and system-level.

Introduction

This chapter deals with PA model validation and comparison. In general PAs are complex dynamic systems that combine both short- and long-term memory effects with nonlinear phenomena. In contrast with linear systems with memory, where superposition holds and so any test signal can be used, or nonlinear systems with linear memory, where memory effects can be separately characterised and de-embedded to obtain a simple algebraic descriptive function, nonlinear dynamical systems must be ‘locally’ modelled and validated. Therefore, test signals and model comparison criteria must be carefully chosen to suit a particular set of typical operating conditions.

This chapter proposes suitable figures and characteristics of merit (i.e. metrics) that enable the performance of different PA models for telecommunication applications to be compared. It is divided into two parts.

In the first part, general figures of merit (FOMs) are presented and the main concepts regarding their applicability are explained. Although most of the proposed metrics can be generalised for sampled and/or stochastic signals, only deterministic continuous-time signals are considered here. Starting from a general time-domain metric, several variants are proposed, each specially suitable for a certain measurement setup.

The second part of the chapter deals with more realistic applications, in that most of the proposed FOMs are formulated for sampled (i.e. discrete-time) signals and are in terms of statistical measures such as the covariance and the power spectral density (PSD). The stochastic-process point of view may be useful for modern measurement instruments and system simulators, where complex telecommunication standards test signals are usually characterised statistically.

Introduction

In this chapter we focus on memoryless nonlinear power amplifier behavioural models for use in transmitter or full communications-channel system simulations. Static envelope characteristics, i.e. static AM–AM and AM–PM characteristics, are the basis for defining a behavioural model as memoryless.

Memoryless behavioural modelling has been used for many years because of its generally easier computational implementation, its relative efficiency in system simulations and its acceptable level of accuracy in many situations. Historically, this approach has found particular favour in predicting intermodulation distortion problems in the robust multicarrier travelling-wave tube amplifiers (TWTAs) used in communication satellite transponders. Travelling-wave tube amplifiers are inherently wideband devices, with a bandwidth of e.g. 500 MHz, and have a near-constant group delay. Any memory-like effects will be those introduced by the channelising demultiplexers on the input, which mainly result in multipath and crosstalk effects, and by the zonal filters that are used on the output to remove especially harmonics but also out-of-band intermodulation products (IMPs). Generally these amplifiers operate under stable temperature conditions, even if the satellites themselves are subject to large temperature variations. The simultaneous multiple air-interface multicarrier configuration of many of these transponder amplifiers is complex by comparison with the single-carrier solid-state power amplifiers (SSPAs) encountered in mobile handsets and the like. In recent years, however, the use of air interfaces based on multicarrier modulation schemes (e.g. orthogonal frequency-division multiplex, OFDM) has grown because of their excellent spectral efficiency and reduced susceptibility to multipath fading. But the simultaneous common nonlinear power amplification of multiple air-interfaces, the parallel of the multicarrier satellite transponder, is not yet normal in SSPA applications.

Introduction

Conventional nonlinear static models, such as AM–AM and AM–PM representations, are frequency independent and can represent with reasonable accuracy the characteristics of various amplifiers driven by narrowband input signals. However, if an attempt is made to amplify ‘wideband’ signals, where the bandwidth of the signal is comparable with the inherent bandwidth of the amplifier, frequency-dependent behaviour will be encountered in the system. This kind of phenomenon is described as a memory effect and can be classified as linear or nonlinear (subsection 1.2.2) or as short- or long-term (subsection 2.4.1). Taking account of both nonlinearities and memory effects when modelling a PA becomes very important in wideband system designs.

In this chapter we focus on investigating nonlinear models that include memory effects (i.e. frequency-dependent behaviour) by using linear filters. The models considered are categorised, according to the selected structure, as two-box, three-box or parallel-cascade models. In the two-box-model section the Wiener and Hammerstein models are discussed, while the three-box-model section includes the Poza–Sarkozy–Berger (PSB) model and the frequency-dependent Saleh model. These models represent some first attempts at extending the nonlinear static AM–AM and AM–PM models to cover frequency-dependent effects. The Abuelma'atti and polyspectral models are major representatives of models organised in parallel branches describing linear memory and will be introduced in the parallel-cascade-model section.

Two-box models

The two-box modelling technique is also known as the modular or feed-forward block-oriented approach.