Modelling Theory of Predistortion - An Important Method of PA-Linearization

Transcription

1 MS2006 Proceedings of the International Conference on Modeling and Simulation August 2006, Konya, TURKEY Paper No_A046 Modelling Theory of Predistortion - An Important Method of PA-Linearization erd F. Nowack, Heinz. öckler, Abdel-Messiah Khilla* Digital Signal Processing roup Ruhr-Universtiät Bochum, Universitätsstraße 150 D Bochum, ermany erd.nowack@rub.de, oeckler@nt.rub.de * Tesat-Spacecom mbh & CO.K, D Backnang, ermnany abdel-messiah.khilla@tesat.de ABSTRACT In this contribution the predistortion approach is applied to the linearization of highly non-linear travelling-wave-tube high-power amplifiers -HPA) used in satellite communications. Predistortion applies non-linear pre-processing of the HPA input signal to compensate for its non-linearity. Partly digital implementation of predistortion is investigated by simulation taking into account additional non-linear properties introduced in the measurement and control paths. A reduction of third order intermodulation by about 30 db is reported by processing the control signal at a rate of 1 Hz with an accuracy of 8 bit. Keywords: Satellite communication, power-amplifier in the frequency-range of 1 to 10 Hz, -HPA Travelling-Wave Tube High-Power Amplifier), high efficiency, non-linearity, modelling, simulation, predistortion, intermodulation 1. INTRODUCTION In satellite communications travelling-wave-tube highpower amplifiers -HPA) are widely used because of their potential high efficiency. In order to elucidate the importance of efficiency, we quote. E. Bosch and. Fleury [1]. The impact of efficiency is illustrated by the following budgets: 5.5 k /W and 55 k /kg, respectively, are required. A typical satellite, for instance, with 40 s of 100 W RF output power each, a 1% improvement of efficiency reduces the costs for power consumption: 40*2.0 W*5.5 k /W = 440 k and the launch costs by reducing the weight by 100 g/: 40*100 g*55 k /kg = 220 k. In the last thirty years mass reduction has been achieved of about 10%, and efficiency has increased from 35% to 70%. It is generally known that -HPAs are highly nonlinear. To get some insight we present a short overview of the physics within a depicted in Fig. 1. In a an electron beam is modulated by an electro/magnetic field. The electrical field component Fig. 1: Principle design of a travelling wave tube ) [2] accelerates or decelerates the electrons. The electron density varies more and more along the axis of the tube. In case of low modulation, only a small part of the AC-power is coupled to the electron beam. Contrary, high modulation means that the DC electron beam is formed in packets of electrons, where the electric component of the field is zero. In this case the ratio of AC to DC power is a maximum and the efficiency attains 100%. Of course it is a disadvantage that the current becomes pulse-like: state of saturation. The output power has reached its maximum nonlinearity, as to been seen from Fig. 2. Saleh described the non-linearity by a mathematical model [3]. As it is obvious from Fig. 2, a -HPA is the less non-linear the lower the input power, i.e. with a high input output) back-off. However, a low-level operational point leads to prohibitively low efficiency. Hence, for the desired high efficiency the must be operated close to saturation. The resulting non-

2 Fig. 4: Principle of predistortion [4] Fig. 2: Non-linear characteristic of amplitude and phase -PA) [4] linearity gives rise to severe distortions: i) Harmonics are generated that disturb adjacent channels. However, by the band-pass characteristic of the this effect is mitigated to some extend, and ii) the usable spectrum suffers from high degradation as a result of intermodulation. Both impacts of non-linearity are illustrated in Fig. 3. The goal of this contribution is the investigation and simulation of the 3 rd approach predistortion). Up to date this approach has exclusively been implemented by analogue means. In contrast, we consider digital realizations reading the respective corrections from look-up-tables LUT) [9, 10, 11]. Comparing digital and analogue predistortion, the advantages of digital predistortion are: high accuracy, simple modification and suitability for adaptive solutions. On the other hand, its disadvantages are: high sampling rate because the predistorted signal has a higher bandwidth than the base band signal, high power consumption of the needed high speed A/D-and D/A-converter. The evaluation of simulated systems often uses performance parameters, which cannot be measured. But last not least the quality of a simulation depends on the deviations of computed results from future) measured data. Particularly, it is desirable to simulate only with those data which can be measured. The comparison of simulation results with measured data is suitable to approximate theoretical simulations and practical implementations. Present-day satellite communication predominantly applies QAM in particular QPSK) modulation. In this paper we assume a base band signal bandwidth of 30MHz. In the following, digital predistortion is modelled and simulated. In section 2 the basic approach is described. Next, the hardware components are modelled using measured data. In the last section the simulation of the system and the computation of the LUT values are reported. Fig. 3: Widening regrowth) of a rectangular signal spectrum by non-linearity in the presence of noise [4] The outlined situation calls for linearization of a - HPA. Here, three basic approaches exist: a) Feedback approach, where part of the output power is fed back to control the input power. This method demands a high loop gain and a sufficient phase margin for stability. However, the impact of loop delay is considered too high in the regarded frequency range beyond 1Hz and, hence, prohibits this approach [6, 7, 8]. b) Feedforward compensation, where a suitable signal is added to the output signal for linearization. In the HPA case a high power summing point can hardly be implemented. c) Predistortion, where the input signal is predistorted in such a manner that the overall system becomes approximately linear, as depicted in Fig SYSTEM APPROACH TO PREDISTORTION Predistortion means that the HPA input signal is changed by a well-defined non-linearity to compensate for the non-linearity of the power amplifier as well as possible. The basic approach, as shown in the Fig. 5, has to compensate the amplitude error by a controllable attenuator and the phase error by a controllable phase shifter. These given units are controlled by analogue signals which are determined by the LUT data. Two D/A- converters DACs) are needed as interfaces. The digital words for the DAC inputs are taken from a fast ROM-memory the implemented look-up-table: LUT) whose data compensate the overall effects of all non-linear functions. The LUT output words are selected by suitably addressing the LUT. This address is deduced from the analogue output voltage of an envelope detector measuring the actual input-power of the, where an ADC Interface is needed. A variable delay line DL) is used for time adjustment of both branches.

3 MS2006 Proceedings of the International Conference on Modeling and Simulation August 2006, Konya, TURKEY Paper No_A046 Some linear) amplifiers are necessary for amplification, level shifts or matching of different dynamic ranges. Note that the bandwidth of the compensating signals is much higher than the bandwidth of the original base band signal. Fig. 6: Non-linearity of the base band detector [4] Fig. 5: Block diagram of the linearization method by predistortion [4] 3. SPECIFICATIONS OF COMPONENTS In addition to the power amplifier, other components that are necessary to implement the compensation of the non-linearity by predistortion, also exhibit nonlinear behaviour. The following conditions and properties are assumed: 1. The is given by two non-linear functions Fig. 2): Output power: P out = funcp in ) and phase shift: φ = funcp in ). 2. The diode detector generates a voltage signal proportional the base band input power. Fig. 6) 3. Level matching is assumed ideal. 4. The 8-bit-ADC is selected for 1 Hz sampling rate and low power consumption. 5. The ADC-output data word is concurrently used as an address of the fast two-folded memory of 2*256 Byte. 6. The contents of the twin-lut take into account all non-linearities of the signal and the measurement paths cf. Figs. 6-8). 7. The control signals are matched to the dynamics of the control ports of attenuator and phase shifter. 4. MODELLIN, SIMULATION AND LOOK-UP- TABLE LUT) The simulation of linearization technique realized with MATLAB and SIMULINK: Fig. 9) considers the properties of other technical components. They are given by measured data and transformed in adequate models: Fig. 10, 11 and 12. Fig. 7: Non-linearity of the attenuator [4] Fig. 8: Non-linearity of the phase shifter [4]

4 Hence two conditions must be satisfied: Fig. 9: Simulink model of the block diagram of the predistortion unit [4] Fig. 10: Simulink model of the ADC [4] At) ) Const At) 4) + At) ) 0 5) The necessary non-linearity of amplitude and phase of the predistorer can be determined: 1 At) Const At)) 6) - At) A t))) 7) Fig. 11: Simulink model of the attenuator of the predistortion unit [4] Fig. 12: Simulink model of the phase shifter of the predistortion unit [4] Subsequently, we start with deriving a procedure to calculate the LUT contents provided that the nonlinearity is modelled according to the measured data, whereas all other devices are assumed linear. Later on we include the non-linearity properties of all other devices. Mathematical Solution: A QAM signal can be written as: xt) = At) cos ω C t + ϕt)) 1) where At) represents the amplitude modulation and φt) the phase modulation. φt) can be disregarded subsequently. The output signal of the -HPA with predistortion is calculated by: yt) = At) ) x cos C t + + At) )) ω 2) where.) and.) represents amplitude and phase non-linearity, respectively. The suffix denotes the -HPA and the predistorer. The ratio of output to input signal shall be a constant: The necessary non-linearity of the -phase depends on predistorted non-linearity of the -amplitude. Next, the non-linearity of the envelope-detector *) is considered. The base band amplitude is: A t) = with the gain of the matching amplifier:. As a result, we get modified conditions for the necessary non-linearity of the predistorer: 1 Const - Const x ) )) 8) 9) 10) Finally we have to consider the amplitude non-linearity of the attenuator **) to get the LUT entries: ATT ) 1 ATT Const )) 11) yt) Const xt) 3)

5 MS2006 Proceedings of the International Conference on Modeling and Simulation August 2006, Konya, TURKEY Paper No_A046 and the phase non-linearity of the phase shifter, too: PS - Const PS ))) 12) Now we can calculate the data of the twin LUT to compensate for the amplitude 13) and phase nonlinearity 14): 2 LUTA = Max{ 2 LUTP = Max{ RES RES } } x x Fig. 13: LUT data to compensate for amplitude nonlinearity by digital predistortion [4] RES where 2 represents the resolution of the converters ADC or DAC). In Figs. 13 and 14 is presented an example of linearization by digital predistortion. Because of the fact that an analogue error is digitally compensated, an interpolation error remains. In addition, there is a quantisation error caused by finite resolution of the LUT data. More over, the bandwidth of the compensating signal has an important influence. In the best case, e.g. infinite sampling rate resolution remains 8 bit) improvements increase up to 50 db C/I3) for signals with a maximum dynamic range up to the saturation point of the. In the case of a more realistic oversampling factor of 14 the improvement reduces to 28 db. These figures can still be optimized to obtain better results starting from the calculated values. 5. RESULTS The linearization of the amplitude Fig. 15) and phase Fig. 16) responses results in a high improvement of the linearity of the overall system. The LUT is an 8Bitaddressed ROM with 8Bit resolution. A most commonly used measurement technique is the determination of the so called carrier to third order intermodulation ratio: C/I3. A pair of two harmonic signals with identical amplitudes and a very small frequency offset is applied to the input of a non-linear unit. The distorted output signal contains, in addition to the original spectrum, intermodulation products of odd order. The amplitude of the third order intermodulation is used to determine the C/I3-ratio. Fig. 14: LUT data to compensate for phase nonlinearity by digital predistortion [4] Fig. 15: Amplitude linearity of the overall system: predistorer and -HPA [4]

6 The challenge of the partly digital implementation of the proposed predistortion approach lies in the choice of the sampling rate for LUT processing. For proper linearization, the sampling frequency must satisfy the sampling theorem for all relevant harmonics of the predistorted input signal. As simulation shows, this value ranges far beyond 1 Hz for a useful bandwidth of 30 MHz. However, roughly 30 db of improvement can be achieved with 1 HZ sampling. Future research will investigate the performance of predistortion in dependence of LUT accuracy and sampling rate. In particular, we will look for a trade-off for a balanced degradation due to both LUT accuracy and choice of sampling frequency. In the meantime the discussed system is being implemented by TESAT. Fig. 16: Phase linearity of the overall system: predistorer and -HPA [4] For input signals of lower power described as back-off from saturation of the : Fig. 17) the improvement is smaller i.e. 35 db for input signals with a power level reduced by 10dB and infinite sampling rate), because not all LUT-data are used. Fig. 17: Carrier to third order intermodulation ratio C/I3 versus input power back-off of the [4] A second method to measure non-linearity is the noise-to-power-ratio NPR). In a white noise signal a small gap is inserted by band stop filtering. Nonlinearity will produce undesirable intermodulation in the frequency gap. The amplitude ratio NPR carrier to gap-power ratio) is the higher the lower the nonlinearity effects are. 6. CONCLUSION In this contribution an approach to linearization of a -HPA has been presented that applies predistortion of the amplitude and the phase of the input signal. Since the control signals of the signal path attenuator and phase shifter are derived from a look-up-table LUT), the linearizer is easily adapted to varying non-linearities caused, for instance, by the choice of different types of, or by changing environmental temperature, respectively. 7. ACKNOWLEDEMENT This work was supported by the Deutsches Zentrum für Luft und Raumfahrt under the contract number 50 YB 0403 for TESAT. Furthermore, we appreciate the contributions of Karsten Kwasny [4] and Ulf Papenfuß [5]: Setting up the simulation tools and performing the reported investigations. 8. REFERENCES 1. Ernst Bosch, eorges Fleury, Space s Today and their Importance in the Future, Thales Electron Devices mbh, AIAA , 9 12 May 2004, Monterey, Cal., USA 2. Andreas Peters: Die Wanderfeldröhre als Verstärker mit flexibler Ausgangsleistung Perspektiven und renzen, Thales Electron Devices mbh, Ulm, peters-flexible_twt.pdf 3. Adel Saleh: Frequency-Independent and Frequency-Dependent Nonlinear Models of Amplifiers, IEEE Transactions on Communications, Vol. 29, No 11, Nov Karsten Kwasny: Technische, µc-gesteuerte Linearisierungskonzepte für Verstärker der Satellitenkommunikation, Diplomarbeit, Ruhr- Universität Bochum Ulf Papenfuß: Erstellung und vergleichende Untersuchungen neuer Konzepte zur Linearisierung von Wanderfeldröhren-Leistungsverstärkern, Diplomarbeit, Ruhr-Universität Bochum Thomas Schubert, Ernest Kim: Active and nonlinear Electronics, John Wiley, N.Y., Alberto Isidori: Trends in Control, Springer-Verlag, London, raham oodwin, Kwai Sang Sin: Adaptive Filtering Prediction and Control, Prentice-Hall, New Jersey Shawn Stapleton: RF Predistortion of Power Amplifiers, Seminar, Agilent, Santa Rosa, CA, Jeonghyeon Cha etal: Optimum design of a Predistortion RF Power Amplifier for Multicarrier WCDMA Applications 11. Allen Katz: A Linearization, Apr Linearizer Technology Inc.,