Power-amplifier (PA) distortion must be minimized in any broadcast application to prevent interference with adjacent channels. Distortion can be present in the form of amplifier clipping, intermodulation distortion (IMD), and memory effects. For some communications standards, such as Brazil's ISDB-T standard, which is based on orthogonal frequency- division-multiplex (OFDM) modulation, excessive phase distortion in the transmit amplifiers can disrupt proper system operation. But by the use of proper models and linearization techniques, it is possible to minimize PA distortion even in demanding OFDM-based communications systems.

All PAs suffer from some distortion, independent of input signal level and device technology, since transistors are not ideal linear components.^{1} The three basic types of distortion are amplitude, frequency, and phase distortion. Amplitude distortion is caused by amplifier gain compression (P1dB), which is device dependent. During amplifier clipping, unwanted harmonics are generated, a form of frequency distortion. The magnitude of these harmonics is increased with the amount of signal clipping, consequently increasing the amplifier's overall distortion.

PA phase distortion in power amplifiers is caused mainly by memory effects from a variety of factors, including device bias conditions, transistor transit-time, and thermal effects. Operating an amplifier with significant backoff can minimize phase distortion but with degradation of amplifier efficiency. One method for minimizing amplifier phase distortion while maintaining efficiency is the use of linearization techniques.

Linear Equipamentos Eletronicos S/A began research on power amplifier (PA) linearization some years ago. Initial results for AM/AM analysis were obtained by inferring that the transfer function of a PA's output voltage had third-order nonlinear dependence with respect to the input signal. Although the numerical approach adopted for this analysis was efficient in this particular case, it did not compensate for the nonlinear effects of amplitude-modulation/ phase-modulation (AM/PM) distortion.^{2, 3} References 4 and 5 provide examples of models that can compensate for these and other distortions; in ref. 5, for example, a study was performed involving several practical models. An accurate model represents the first step for implementing an efficient predistortion system. Using the parallel model described in ref. 5, Linear Equipamentos Eletronicos obtained good results, compensating for both AM/ AM distortion, AM/PM distortion, and memory effects.

Communications systems based on OFDM techniques can employ signals with thousands of carriers, as in standard ISDB-T systems. The carrier combination can generate a reasonable number of voltage spikes in the time domain, depending on its phase. The magnitude of these peaks can be measured through a figure of merit, the peak to average ratio (PAR), which is defined by:

PAR = 20log(|X_{peak}|/X_{av})

where X_{peak} and X_{av} are the maximum and average values (in V), respectively, of a signal under test.

The X_{peak} value can be measured in the time domain using an oscilloscope with sufficient bandwidth. The X_{av} value can be measured using a wattmeter and then converting the value to voltage, assuming a 50-Ohm load. The PAR from some commonly used signals are: 3 (dB) for a continuous wave (CW) signal, 3.5 to 4 dB for a QPSK signal, and approximately 12 dB for the ISDB-T standard OFDM signal. This implies that, if a Class AB PA has a 1-dB compression point at +10 dBm (* Fig. 1*), an OFDM signal per the ISDB-T standard can be boosted without compression using this amplifier with input levels to -2 dBm. This indicates that all amplifiers used in the ISDB-T transmitter chain require a large backoff compared to amplifiers used in analog broadcast transmitters.

Amplifier gain compression results from the IMD characteristics of the amplifier's transistors, with major influence of the third-harmonic component.6 Intermodulation can be easily measured when more than one carrier is used as a PA input signal, such as using a test signal consisting of two-tones with equal amplitude. When a two-tone test signal is applied to an amplifier, it is possible to observe several IMD components in the output spectrum generated due to the nonlinear behavior of the transistors (* Fig. 2*).

In an ISDB-T standard OFDM signal with thousands of carriers, distortion can appear as multiple distortion signals (* Fig. 3*). The bandwidth of the distortion is related to the signal bandwidth. Thus, if a signal has a bandwidth of 5.6 MHz at the fundamental frequency, the bandwidth of the second-order distortion will be 2 x 5.6 = 11.2 MHz, the third-order distortion will have a bandwidth of 3 x 5.6 MHz, and so on. Odd-order distortion lies within the fundamental zone, requiring a different treatment than for even-order ones. These lie outside the fundamental zone and at the DC zone, and can be removed by means of filters.

^{7}

One way to avoid PA IMD is through backoff techniques, although this increases transmission costs by the need for an increased number of PAs for a required transmit power. The approach does guarantee high quality of the transmitted ISDB-T signal, measured by the modulation error ratio (MER, in dB),^{8} by which excellent levels are over 40 dB. Unfortunately, if high backoff values are used, the PA efficiency is degraded. As a result, a tradeoff between backoff (or high MER values) and PA efficiency must be established.

In a system with memory effects, the condition of the output signal is dependent upon the past states of the input signal. The extent of the memory effects can be estimated through observation of the first-order Volterra kernel. The amount of memory is defined as the time between the origin of the kernel until the point where it passes through zero, and is directly dependent on the bandwidth of the transmitted signal.^{9}

An RF PA has a complex structure with many different types of memory effects. These can be classified^{10} as low-frequency (kHz to MHz) effects (such as thermal effects, trapping effects, the influence of biasing circuits, and the influence of AGC loops) and high-frequency (GHz) effects (such as transistor transit time and reactance parasitic and group delay from matching networks).

Such memory effects are mixed together (nonlinearly coupled) in a PA and the problem of estimating behavioral models becomes very difficult.^{11} A general classification of memory effects, in linear and nonlinear form, can be found in ref. 12. A memoryless system is one in which the output signal envelope follows the variations of the input signal envelope. Matching networks are the origin of linear memory, and nonlinear memories are generated in the nonlinear dynamic interactions of the input signal. A practical RF PA output signal has both linear and nonlinear memory, and an ISDB-T OFDM signal that occupies a bandwidth of 5.7 (MHz) and as many as 8,000 carriers will cause more memory effects in a PA than an analog signal, which has only three carriers.

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The influence of memory effects on a system can be seen in the form of AM/AM effects in * Fig. 4* and AM/ PM effects in

*, where the central line shows the behavior of an amplifier without memory effects. The spreading of points around the curves for a particular instantaneous power level indicates a greater amount of memory effects, although close to the origin at the abscissas axis may include some errors of synchronization as well as measurement noise. The plots in*

**Fig. 5***and*

**Figs. 4***were obtained from time-domain measurements performed by a vector signal analyzer (VSA). Another definition for memory effects is given in ref. 13, as "a time interval between AM/AM and AM/PM curves." IMD mixed with an amplifier's memory effects can generate distortion that seriously degrades the quality of the PA's output signal, and makes the task of achieving the required spectral mask for ISDB-T even more difficult. Because every amplifier exhibits some amount of distortion, the only way to produce efficient, cost-effective amplifiers is by implementing methods to compensate for or correct the distortion.*

**5** Amplitude-related distortion can be corrected by means of amplifier backoff, although efficiency will suffer. If linearization is used, many methods are available. The most frequently used ones are feed-forward and predistortion. ^{14, 15} The amount of distortion compensation varies according to the RF PA, the occupied bandwidth, and the model structure and complexity used for the predistortion implementation whether a model with or without memory effects. If a memoryless model is chosen, like ordinary polynomials, a considerable part of the distortion can be compensated for, but only models that include memory in their structures can be effective against distortion generated by modern RF PAs. Examples of these models, the Wiener and Hammerstein models, are shown in * Fig. 6*. Additional models are listed in ref. 5. Choosing the right model is the key to compensate for the various forms of distortion generated by an RF PA.

Linear Equipamentos Eletronicos has built a basic evaluation platform that can simulate several models together with ISDB-T OFDM signal generation. The circuit-board architecture includes essential devices such as analog-to-digital converters (ADCs), digital-to-analog converters (DACs), memory, and a field-programmable gate array (FPGA), which was used to realize the multiplexer and demultiplexer for Trelis- Encoder and Reed-Solomon advanced digital communications formats.

In this platform, the FPGA and digital-signalprocessing (DSP) techniques were used to implement digital filters with excellent sideband rejection, without the need for analog filters, such as a surface-acousticwave (SAW) filter, which can present problems with passband ripple, high insertion loss, and high cost. In addition, it was also possible to compare two distinct theoretical and experimental approaches; Weaver and Frequency Complex Methods combined with DSP techniques, which permit it to generate amplitudemodulation- vestigial-sideband (AM-VSB) analog television and eight-state vestigial-sideband (8-VSB) digital television signals through a simplified architecture.^{16,17}

This FPGA structure was used to implement the nonlinear experimental approach discussed in this report, and to achieve the best results for the use of predistortion approaches. This architecture was designed, implemented, tested and was in industrial production as part of the first transmission high-definition-television (HDTV) equipment in Brazil for the ISDB-T standard. The same architecture can also serve other complex communications standards.

REFERENCES

1. K. Clarke, D. Hess, *Communication Circuits: Analysis and Design*, Krieger Publishing Company, 2nd ed., 1994.

2. A. A. Mello, H. D. Rodrigues, M. P. Silva, and M. Silveira, "Adaptive Digital Pre-Distortion to Reduce the Power Amplifier Non-Linearity," IEEE APS-URSI 2003, Columbus, OH.

3. A. A. Mello, H. D. Rodrigues, J. Souza Lima, M. P. Silva, and M. Silveira, "A New Numerical Approach in the Linear Analysis of RF Amplifiers," IEEE 33rd European Microwave Conference, 2003 Munich, Germany.

4. J. Kim and K. Konstantinou, "Digital predistortion of wideband signals based on power amplifier model with memory," *Electronics Letters*, Vol. 37, No. 23, 2001, pp. 1417-1418.

5. D. D. Silveira, P. L. Gilabert, P. M. Lavrador, J. C. Pedro, M. Gadringer, G. Montoro, E. Bertran, G. Magerl, "Improvements and analysis of nonlinear parallel behavioral models," International Journal of RF and Microwave Computer-Aided Engineering, DOI: 10.1002/ mmce.20385.

6. P. B. Kenington, *High Linearity RF Amplifier Design*, Artech House, Norwood, MA, 2000.

7. J. Vuolevi and T. Rahkonnen, *Distortion in RF Power Amplifiers*, Artech House, Norwood, MA, 2003.

8. W. Fischer, *Digital Video and Audio Broadcasting Technology A practical engineering guid*e, Springer, New York, 2008.

9. V. Z. Marmarelis, *Nonlinear Dynamic Modelling of Physiological Systems*, Wiley, New York, 2004.

10. E. Ngoya and A. Soury, "Modeling Memory Effects in Non-Linear Subsystems by Dynamic Volterra Series" IEEE Behavioral Modeling and Simulation Workshop, 2003.

11. N. Le Gallou, E. Ngoya, H. Buret, D. Barataud, and J. M. Nebus, "An improved behavioral modeling technique for high power amplifiers with memory" IEEE MTT-S International Microwave Symposium Digest, Vol. 1, 2001, pp. 983-986.

12. J. C. Pedro and S. Maas, "A comparative overview of microwave and wireless poweramplifier behavioral modeling approaches," *IEEE Transactions on Microwave Theory and Techniques*, Vol. 53, No. 4, 2005, pp. 1150-1163.

13. S. C. Cripps, *Advanced Techniques in RF Power Amplifier Design, Artech House*, Norwood, MA, 2002.

14. P. B. Kenington, "Analysis of instability in feed-forward loop," *Electronic Letters*, Vol. 33, 1997.

15. J. K. Cavers, "Amplifier Linearization Using a Digital Pre-Distorter with Fast Adaptation and Low Memory Requirements," *IEEE Transactions on Vehicular Technology*, Vol. 39, No. 4, November 1990, pp. 374382.

16. J. S. Lima and M. Silveira, "The Weaver theoretical approach to generate some important TV digital signals for the transmission systems", IEEE International Microwave and Optoelectronic Conference 2005, Belm, PA, Brazil.

17. H.D. Rodrigues, M. Silveira, J.A.J. Ribeiro, and D. G. da Silva, "Complex Filtering for Generation of SSB and VSB Signals", IEEE Asia Pacific Microwave Conference 2008, Hong Kong, China.