Institutionen för systemteknik Department of Electrical Engineering Examensarbete ADS and Matlab to Optimize Predistortion of Amplifiers Examensarbete utfört i Signalbehandling av Jessica Trinh LiTH-ISY-EX--15/4880--SE Linköping 2015 TEKNISKA HÖGSKOLAN LINKÖPINGS UNIVERSITET Department of Electrical Engineering Linköping University S-581 83 Linköping, Sweden Linköpings tekniska högskola Institutionen för systemteknik 581 83 Linköping ADS and Matlab to Optimize Predistortion of Amplifiers Examensarbete utfört i Signalbehandling vid Linköpings tekniska högskola av Jessica Trinh LiTH-ISY-EX--15/4880--SE Handledare: Daniel Axehill Examinator: Fredrik Gunnarsson Linköping 10 juni 2015 Presentationsdatum Institution och avdelning Institutionen för systemteknik 2015-06-10 Publiceringsdatum (elektronisk version) Department of Electrical Engineering 2015-06-11 Språk Typ av publikation ISBN (licentiatavhandling) Svenska X Annat (ange nedan) Licentiatavhandling X Examensarbete C-uppsats D-uppsats Rapport Annat (ange nedan) ISRN LiTH-ISY-EX--15/4880--SE English Antal sidor 76 Serietitel (licentiatavhandling) Serienummer/ISSN (licentiatavhandling) URL för elektronisk version http://www.ep.liu.se Publikationens titel ADS and Matlab to Optimize Predistortion of Amplifiers Författare Jessica Trinh Sammanfattning This master’s thesis deals with integrating simulations using Agilents Electronic Design Automation tool ADS with customized Matlab scripts, for solving complex analog and digital radio architectures. In particular, it addresses predistortion, realized in the digital domain, of power amplifiers, modeled in the analog domain. The former is implemented in Matlab while the latter is implemented in ADS. Two versions of integrating the two systems have been tested: 1) Iterative approach on sample basis and 2) Scheduled batch solution by matrix inversion. The concept has been tested on two different PA configurations: 1) a standard class-AB PA and 2) a Doherty PA architecture. Evaluation has also been done on ADS ability to correctly simulate memory effects in PAs and on the actual DPD-algorithms ability to compensate for these memory effects. An integrated simulation environment for ADS and Matlab was successfully established within the work of this thesis. Matlab scripts, used in predistortion algorithms in the digital domain, could interact directly with component-based PA models, in an enclosed simulation system. The simulation results show that sample basis method is the most accurate, fast and reliable method to linearize a PA. The PA1 proved to be easier than the DPA to linearize, except for when being close to saturation where better IMD-suppression was achieved with the DPA. ADS is clearly able to simulate memory effects in the analog domain. At low gain-levels the applied compensating memoryalgorithms showed a great improvement to the linearization of the output signal of the PA. At higher gain-levels though, the compensation for memory effects lost their efficiency because the non-linearity of the PA became too significant. Nyckelord Predistortion, Digital predistortion, DPD, ADS, ACLR, WCDMA, IMD, Memory effect Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Abstract This master’s thesis deals with integrating simulations using Agilents Electronic Design Automation tool ADS with customized Matlab scripts, for solving complex analog and digital radio architectures. In particular, it addresses predistortion, realized in the digital domain, of power amplifiers, modeled in the analog domain. The former is implemented in Matlab while the latter is implemented in ADS. Two versions of integrating the two systems have been tested: 1) Iterative approach on sample basis and 2) Scheduled batch solution by matrix inversion. The concept has been tested on two different PA configurations: 1) a standard class-AB PA and 2) a Doherty PA architecture. Evaluation has also been done on ADS ability to correctly simulate memory effects in PAs and on the actual DPD-algorithms ability to compensate for these memory effects. An integrated simulation environment for ADS and Matlab was successfully established within the work of this thesis. Matlab scripts, used in predistortion algorithms in the digital domain, could interact directly with component-based PA models, in an enclosed simulation system. The simulation results show that sample basis method is the most accurate, fast and reliable method to linearize a PA. The PA1 proved to be easier than the DPA to linearize, except for when being close to saturation where better IMD-suppression was achieved with the DPA. ADS is clearly able to simulate memory effects in the analog domain. At low gain-levels the applied compensating memory-algorithms showed a great improvement to the linearization of the output signal of the PA. At higher gain-levels though, the compensation for memory effects lost their efficiency because the non-linearity of the PA became too significant. 1 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Preface This thesis work is carried out at the Digital Radio group at Ericsson in Kista. I would like to thank my supervisor Leonard Rexberg at Ericsson, my advisor Daniel Axehill at LiTH and my examiner Fredrik Gunnarsson for making this work possible. Jessica Trinh Linköping, May 2015 2 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Table of contents Abstract ............................................................................................. 1 Preface .............................................................................................. 2 Table of contents ............................................................................... 3 Acronyms .......................................................................................... 5 1 Introduction ........................................................................... 6 1.1 1.2 1.3 2 Preliminaries ......................................................................... 9 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.5 3 Purpose..................................................................................... 7 Scope ........................................................................................ 7 Background .............................................................................. 7 The RF signal ........................................................................... 9 Modulation techniques ......................................................... 9 Multiplexing ....................................................................... 10 Complex baseband signal representation ........................... 11 Power Amplifiers ................................................................... 14 Nonlinear systems .............................................................. 15 PA memory effects ............................................................. 16 Polynomial modeling without memory effects .................. 16 Polynomial modeling with memory effects ....................... 17 Linearization techniques ........................................................ 17 Feedback ............................................................................ 18 Feedforward (FF) ............................................................... 18 Predistortion (PD) .............................................................. 19 Digital predistortion (DPD)................................................ 20 Behavioral modeling or Component-based modeling ........... 21 Advanced Design System (ADS)........................................... 21 Modelling of Power Amplifiers and Digital Predistortion 22 3.1 The Digital Predistortion algorithm ....................................... 22 3.1.1 Iterative solution on sample basis ...................................... 22 3.1.2 Iterative solution on matrix inversion basis ....................... 24 3.1.3 With memory effect ............................................................ 24 3.2 Component-based PA-modeling in ADS ............................... 25 3.2.1 The MRF5S21 PA (PA1) .................................................... 25 3.2.2 The Doherty PA (DPA) ....................................................... 26 3.3 System overview, Matlab-ADS integration ........................... 29 3 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 3.4 Matlab-ADS integration methods .......................................... 30 3.4.1 Approach 1: Iterative solution on sample basis ................. 30 3.4.2 Approach 2: Matrix inversion basis with post-distortion ... 33 3.5 Intermodulation distortion and the ACLR ............................. 36 3.6 ADS-simulators ..................................................................... 38 4 Simulation and evaluation ................................................. 39 4.1 4.2 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 5 ADS-Matlab integration in practice ....................................... 39 How the simulations were executed ...................................... 40 Simulation variables .............................................................. 43 PA gain ............................................................................... 43 Polynomial degree .............................................................. 43 Memory-depth .................................................................... 44 Simulation results .................................................................. 44 Non-linear and linearized signal ........................................ 45 ACLR1 and ACLR2 ........................................................... 46 Linearization relative to gain-levels ................................... 47 Polynomial degree (N-value) ............................................. 50 Memory effects .................................................................. 53 Sample and Matrix simulation ........................................... 62 Summary and conclusions ................................................ 64 Appendix 1. Appendix 2. Appendix 3. Appendix 4. Appendix 5. Schematics of the PA1 and DPA..................................... 67 Schematics of the input and output matching networks . 69 Top level schematics ....................................................... 72 Schematics of modulators............................................... 75 The WCDMA test signal ................................................ 76 4 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Acronyms 3GPP Third Generation Partnership Project ACLR ADS ASK BB BPSK CE dB dBc DPA DPD DSP DUT EDA FF FSK HB IM IMD LDMOS LMS PA PAR PSD PSK QPSK QAM RF RRC UMTS WCDMA Adjacent Channel Power Leakage Ratio Advanced Design System Amplitude Shift Keying Base Band Binary Phase-Shift Keying Circuit Envelope Decibel Decibel Below Carrier Doherty Power Amplifier Digital Predistortion/Predistorter Digital Signal Processor Device Under Test Electronic Design Automation Feedforward linearization Frequency Shift Keying Harmonic Balance Inter Modulation Inter Modulation Distortion Laterally Diffused Metal Oxide Silicon Least Mean Square Power Amplifier Peak-To-Average Ratio Power Spectral Density Phase Shift Keying Quadrature Phase-Shift Keying Quadrature Amplitude Modulation Radio Frequency Raised Root Cosine Universal Mobile Telecommunication System Wideband Code Division Multiple Access 5 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 1 Introduction The use of radio communication services is augmenting continuously and has created an increasing demand for channels with greater capacity and higher data transmission rates. Since the available radio spectrum is limited and the number of base stations is growing rapidly, two of the most essential factors when designing modern wireless communication systems are spectrum efficiency and power efficiency. Power efficiency: In a mobile communication system, the power amplifier (PA) is considered one of the most power consuming components. Linear PAs are not desirable since they offer poor power efficiency, which leads to heat dissipation in the base station and shorter battery stand-by time in the mobile unit. To obtain higher power efficiency, modern PAs are driven to operate in the non-linear region, as near saturation as possible. Spectrum efficiency: The Wideband Code Division Multiple Access (WCDMA), which is used as a standard in today’s Third Generation (3G) base stations, is a spectrum efficient modulation method using nonconstant envelope modulation schemes. This technique allows a large number of channels to be transmitted on the same frequency by using orthogonal spreading codes and by placing the channels very close to each other as to minimize unused spectrum. Combining these two competing factors is however a difficult task. The fact that the WCDMA signal has a high peak-to-average power ratio (PAR) implies a very high requirement on the linearity of the power amplifier used. The large fluctuations in the signal envelopes lead to intermodulation distortion (IMD) and hence spectral regrowth in nonlinear amplifiers. In another word, in a system with WCDMA signals, the nonlinearity of the PA degrades the system performance significantly by introducing new, unwanted frequency components at its output, causing expansion of the signal spectrum into the channels nearby. In order to maintain both efficiency and linearity, one solution is to linearize a power efficient PA by using an external circuitry. Thus, a lot of research has been done on different linearization techniques. This thesis focuses on digital predistortion (DPD), a cost-effective and reliable linearization method that has been the subject to intensive researches worldwide in recent years. Especially, the possibilities to integrate the DPD technique into a simulation environment during the development of PAs are investigated. 6 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 1.1 Purpose The purpose of this master’s thesis is to create an integrated simulation environment for ADS and Matlab, connecting the analog/RF and digital domain, in a digital predistortion-PA system to be able to optimize the parameters of the two subsystems as one entity. The purpose is also to evaluate the reliability and robustness of component-based modeling in ADS as an alternative to polynomial modeling. 1.2 Scope In this thesis a class AB PA model and a Doherty PA model will be linearized by using a digital predistortion technique that is based on LMSalgorithm. The goal is to create a simulation environment where we potentially can switch between different DPD-algorithms and PA-designs easily, in order to study the ability of model-based predistortion on component-based PA modeling. Two different approaches will be tested and evaluated; the sample and the matrix method. Some of the questions to be answered are: How much can IMD be suppressed after linearization? Are there any differences between the sample or matrix approach? Can we model memory effects in ADS? If so, can memory effects be counteracted? Do the Doherty PA and the class AB PA behave differently according to the linearization algorithms? 1.3 Background One way to attain both linearity and power efficiency when amplifying a signal is to linearize a nonlinear but power efficient PA by using digital predistortion technique. The idea is to insert a nonlinear element into the signal path prior to the PA such that the combined transfer characteristic of these two blocks is linear. A simplified block diagram of such a combined system is shown in Figure 1. 7 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 1. Placing a DPD block (implemented in Matlab) with the inverse characteristics of the amplifier response in front of the PA block (implemented in ADS) results in distortion cancellation and hence a linear output signal. However, with the cascade of different options in designing these two subsystems, that are normally developed separately in digital domain and RF domain respectively, we are faced with the issue of optimizing the integrated system for which the requirements are specified for, and not each subsystem. As a consequence, designers of each subsystem have to estimate a reasonable subsystem requirement to follow while designing in each domain. This is not optimal, especially not in RF design. It is therefore of great interest to create an environment that allows simulation of both analog and DSP subsystems. The purpose is to make them co-simulate throughout the design cycle, as to optimize subsystem parameters and also to minimize the system integration problems in hardware implementations later on. Power amplifiers (PA) are often designed in the RF-domain using computer aided design systems like ADS whereas linearization is best performed in Matlab. As a consequence, the challenge lies within making Matlab interact with ADS, either way as a stand-alone unit or as a component directly inserted into the ADS circuit. 8 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 2 Preliminaries In this chapter, the basic theory about the RF signal and complex baseband signal presentation is explained. The three main linearization techniques are described as well as the basics of power amplifiers and nonlinear systems. In the end, Agilent’s design software ADS is presented. 2.1 The RF signal A signal is an entity capable of carrying some information. The basic information carrying signal is the baseband signal. The baseband signal carries analog information as voice, music or analog television signals or digital pulse code modulated signals. The baseband signal is normally a low frequency signal which is inconvenient to transmit on large distances. To be able to transmit the baseband signal in a power- and bandwidth efficient way it is modulated on a powerful high-frequency carrier signal. The RF signal is then presented as a sampled envelope on the RF carrier frequency. Modulation also allows us to move baseband signals to different ranges of frequency which makes it possible to send signals in any of a large number of frequency ranges without overlapping. 2.1.1 Modulation techniques The three basic modulation methods are; amplitude, frequency and phase modulation. Amplitude modulation (AM) samples the baseband signal on the carrier by adjusting the amplitude of the carrier. Although the amplitude modulation is commonly used it has some disadvantages, the variation of the amplitude requires a linear amplifier to correctly modulate the original signal on the carrier and it uses twice the bandwidth of the original signal because of the double-sideband transmission. Frequency modulation (FM) uses the continuous peak amplitude of the carrier signal and instead varies its frequency according to the modulated baseband signal. Frequency modulation, commonly used for radio broadcasts and mobile cellular telephony, offers some advantages over the AM. The FM signal can use more power efficient non-linear amplifiers because of the constant peak amplitude and the received signal-to-noise ratio does not degrade gradually as in AM but deteriorates suddenly, which improves the signal-to-noise ratio of the recovered baseband signal. A third advantage of FM is that when two interfering signals reach a receiver, the stronger captures the receiver so that the weaker is not heard. This phenomenon is important in mobile radio because we want to hear the nearest and strongest transmitter without the interference from more distant transmitters. (Pierce and Noll 1990) 9 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Phase modulation (PM) is used to change the phase of a signal among different phase states to represent a pattern of bits. The simplest phase modulation technique is the Binary Phase-Shift Keying (BPSK) where the change of the phase by 180 degrees represents the digits 0 and 1. The Quadrature Phase-Shift Keying QPSK has four different phase states, which can also be called 4QAM because of its constant amplitude. By combining AM and PM more phase states can be achieved to represent more binary digits and thus to increase the possible data transmission rate (Anderson 2003). Two examples are the 16QAM (Quadrature Amplitude Modulation) and the 64QAM which have 16 respectively 64 phase states. 2.1.2 Multiplexing Multiplexing is used for sending multiple signals in the same medium. Frequency-Division Multiple Access (FDMA) uses frequency shifting of individual single voice signals to produce a single signal of larger bandwidth that combines the individual signals. Each individual voice signal is carried over a single voice channel (Pierce and Noll 1990). FDMA has enhanced the efficiency of long-distance telephone networks and the early satellite communications. Time-Division Multiple Access (TDMA) is a more economical and more satisfactory multiplexing technique for short-distance transmissions over wires and for all transmissions over optical fiber. The TDMA works with the digital pulse code modulation signal and transmits several different signals over a single channel by sending them at different times. The individual signal is divided into small time slots which are sent as an intermittent signal together with other signals on the same frequency. The receiver then puts the time slots together and reconstructs the original baseband signal. The TDMA is a so called packet-switched network where the information is divided into smaller packets that are sent individually with a flexible route instead of a circuit-switched network like the FDMA where the path between the user and the destination node is set up at the time the connection is established, and any needed resources has to be reserved in the network until the connection is terminated. The packet-switched networks are therefore more efficient and flexible but also more complicated because data packets can take different paths and can be received out of order (Groe and Larson 2000). More about switching can be found in Signals, building blocks and networks (Carne 1995) TDMA is used in the 2G GSM cellular system. 10 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Code-Division Multiple Access (CDMA) is a spread-spectrum communication technique and a secondary modulation technique. The signal is first modulated by traditional amplitude, frequency or phase techniques. The individual message signals are then spread over a wide frequency with the ability to hop in the frequency range by multiply the message signal to a random carrier frequency. The spreading code are fundamental in the spread-spectrum communication. The spreading code enables synchronization of the transmitter and the receiver when the signal hops between different frequencies (Groe and Larson 2000). The advantage of the CDMA is that several transmitters can send information simultaneously over a single communication channel by frequency hopping and the use of spread codes. The fact that several signals are sent at the same time on very close spectrums also makes the CDMA technique sensitive to inter modulation distortion (IMD), this is explained further in chapter 3.5. Wideband CDMA (WCDMA) is the CDMA technique adapted for the UMTS mobile cellular network and currently used for the 3G and 4G cellular system. 2.1.3 Complex baseband signal representation The WCDMA signal that is fed into the DPD-PA-system is represented as a complex baseband signal since it is more convenient to handle than the traditional bandpass representation. When transmitting information, most systems operate by modulating an information bearing waveform onto a sinusoidal carrier. Hence, using complex baseband representation we can easily characterize and analyze communication signals independently of the carrier frequency. As an example, a two-tone bandpass signal can be written as: x c (t ) a cos( c t ) b cos( c 0 )(t ) (1) By using complex notation, we can re-write this expression as: x c (t ) Re a e j c t b e j ( c 0 )t Re a b e j ( c 0 )t e j c t Re I (t ) j Q(t ) e j c t I (t ) cos( c t ) Q(t ) sin( c t ) (2) 11 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers From (2) it is seen that a signal can be de-composed into a form containing orthogonal components. We also see that the signal can be split into a complex baseband signal (I + jQ) and a carrier component of frequency c. As in ordinary AC calculations, where we do not concern about the carrier frequency, we may omit this part and only deal with the complex baseband. The difference to single-sinusoidal AC representation will only be that now we have a time varying baseband component (Fitz 2007, p 4.4). The complex baseband signal may now be represented as: x BB (t ) I t j Qt (3) The treatment of nonlinearity of power amplifiers may be completely referred to this complex baseband signal described in (3) although the derivation may start at RF frequency. To see this we apply the mathematical representation of a nonlinearity as a polynomial power series. We postulate that the nonlinearity of a PA may be modeled in terms of the input signal as: x PA (t ) 0 xc t 1 xc t 2 xc t 2 N 1 3 (4) n xc t n n 0 From this we may insert the expression for xc(t) as in (2) to obtain the following expression referred to as the complex baseband signal: x PA (t ) Rex N 1 n 0 n BB (t ) e jwct n (5) This can be further expanded to get rid of the “Re”-function and to further later on also be able to drop the carrier frequency, as: 12 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers N 1 x PA (t ) n n 0 N 1 n n 0 1 * x BB t e j ct x BB t e j ct n 2 1 n n x BB t e j ct 2 n k 0 k x nk n * BB t e j t c k (6) k 1 n n nk * x BB t x BB t e jn 2k ct etc n 2 k 0 k n 0 So, we see from (6) that we obtain harmonic components at frequencies (n-2k)c in addition to just at the carrier frequency c. However, we are only interested in the components that are placed at exactly c, and therefore we will omit the other terms in the expansion. That is, we will only retain components where n-2 =1. Doing so, we arrive at the following expansion: N 1 n x PA (t ) Only wc components, (n - 2k 1) N 1 n n 0 N 1 n n 0 1 k k 1 n 1 2 k x BB t x BB * t e j1 ct n 2 k 0 k (7) 1 n 1 2 k 2k x BB t x BB t e j1 ct harmonics 2 n k 0 k We see from (7) that we will only retain “odd” power components of xBB. That is, we may express the output signal from the non-linear PA as an expansion in terms of the odd powers of xBB as: N 1 xPA,BB (t ) n xBB t xBB t 2n (8) n 0 However, it turns out that also the “even” components will contribute although they on the paper just give harmonics that lie outside the carrier frequency at higher harmonics, i.e. at 0 frequency and 2c. Therefore, we will write the complex baseband representation of the signal that comes out of the PA as: N 1 xPA, BB (t ) n xBB t xBB t n (9) n 0 13 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 2.2 Power Amplifiers A power amplifier (PA) is a circuit for converting dc-input power into a significant amount of RF/microwave output power. A transmitter consists of one or more PAs and usually auxiliary circuits like signal generators, frequency converters, modulators, signal processors, linearizers and power supplies. The most challenging part of designing modern PAs is to create both a high order of linearity as well as a power efficient unit. The old classical RF signals like the FM, FSK and the GMSK which had a constant envelope signal did not require linear amplification. Those signals were best produced by a high-level amplitude modulation RF PA. The modern RF signals which contains both amplitude and phase modulation such as QAM, QPSK and CDMA does though request a high linearity RF PA (Raab F, Asbeck P et al. 2002). RF PA:s are commonly designed as classes A-F which differ in methods of operation, efficiency and power-output capability. The following table gives the main characteristics of the different classes. Class Linearity Other characteristics A High High gain, operation close to transistor maximum frequency, often low output power. Constant power consumption. B High Power consumption proportional to input signal, thus significantly more power efficient than the class A, C Low Very power efficient and commonly used for high-level amplitude modulation D non-linear Switch-mode amplifier. Normally not used for frequencies over 300 Mhz. E non-linear Switch-mode amplifier. F non-linear Switch-mode amplifier. Table 1. PA classes. (Raab F, Asbeck P et al. 2002) To amplify a multicarrier signal with a non-constant envelope as the CDMA signal a class A or B amplifier must be used, or a mix of the two types (class AB) (Pothecary 1999, p 97). 14 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The class C amplifier has poor linear characteristics and the switch-mode amplifiers are not possible to use with bandwidth-efficient modulation schemes as for example the QPSK. 2.2.1 Nonlinear systems In a perfectly linear system, the output is a scalar function of its input, as: Vout (t)=K1 Vin (t) where Vout and Vin are the output respectively input voltage and K1 is a gain constant (Pothecary 1999, p. 43). However, when using a power efficient amplifier, it is not easy to amplify an input signal to the required levels for reliable transmission. It normally produces both amplitude and phase distortion, which get worse when approaching saturation. Moreover, the amplitude variation of an input signal also has a strong effect on the distortion of the output signal. Therefore, a PA is more sensitive to nonlinearities when using digitally modulated signals like WCDMA. More about how to model nonlinearities in PAs is discussed in chapter 3.1. A nonlinear PA causes two types of distortion products. First, those near the fundamental signals will interfere with the input signal itself and are called cross modulation. Second, the other type appears in form of new unwanted frequency components introduced at the output of the PA called intermodulation distortion (IMD). These cause spectral regrowth and interfere with adjacent channels making the information detection task in these channels difficult. The latter is significantly important in the WCDMA context, where channels are placed very close to each other. One of the most important nonlinearity measurements is the ACLR, see chapter 3.5, for which specific requirements are set in the 3GPP specification to restrict the power leakage into neighboring channels. Figure 2a) and b) new frequency components are introduced at the output of a nonlinear amplifier, causing spectral regrowth and IMD. 15 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 2.2.2 PA memory effects Any PA will show some dynamic deviations from its static characteristics. Those deviations are known as “memory effects”. Memory effects are an additional source of nonlinear behavior that is usually not accounted for in PA models. The memory effects can be categorized as dynamic thermal effects, unintentional bias modulation and trapping effects. Thermal effects can possibly be addressed to a physical based model but the other two are results of anomalous semiconductor and circuit effects and especially trapping effects defy analytical and even behavioral modeling. Unintentional bias modulation effects can be predicted in an extensive circuit simulator as the ADS-system, see chapter 2.5. Trapping effects on the contrary is hard to simulate and is best handled by choosing components which show none or very little of this affliction. The reducing of memory effects through the semiconductor process and circuit development and is an important area for ongoing research. (Cripps 1999) Because the memory effects are hard to include in the PA models characteristics they and can cause big problems in the developing of predistortion algorithms, see chapter 3.1.3. However, there are ways to include some of the memory effects in the algorithms. 2.2.3 Polynomial modeling without memory effects The nonlinear output of a memoryless amplifier modeled with a polynomial power series can be written as: y a0 a1 x a 2 x 2 ... a n x n Where x and y denote the input respective output signal, and complex coefficients. a0 a n - are However, such a simple polynomial model is insufficient to correctly characterize a power amplifier used in applications like WCDMA, since memory effects also must be taken into account. A system is said to suffer from memory effects when its output signal does not depend only on the instantaneous input values but also on previous ones. This is an undesired phenomenon that exists in most PAs and that makes it more difficult to model and to linearize the actual system. 16 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 2.2.4 Polynomial modeling with memory effects A polynomial power series with memory is best represented by a Volterra series because it provides a general way to model a non-linear system with memory. The Volterra series are however very complex and need much computational power to be calculated as the number of parameters to be estimated increases exponentially with the degree of nonlinearity and with the memory length of the system. More about Volterra series and non-linear systems can be found in Digital Pre-Distortion of Power Amplifiers (Spångberg 2002, p 14-15). A simpler version of the general Volterra series is the modified Volterra series which separates the static memoryless behavior of the PA from the purely dynamic behavior with memory effects. The two models are then mixed and calculated in a classical power series, also called memory polynomials. A nonlinear system with memory-depth of two can then be represented as follows: y (a 0 a1 x a 2 x 2 ... a n x n ) (b0 b1 x k b2 x k ... bn x k ) 2 n ... (c0 c1 x k m c 2 x k m ... c n x k m ) 2 n a a b b c c where 0 - n , 0 - n , and 0 - n are complex coefficients and x-i denote previous samples of the input signal, k is the sample delay, n is the polynomial order and m is the number of previous samples included. 2.3 Linearization techniques PA linearization is used to correct the nonlinearities of the PA and make the response more linear. This is done by comparing the output of the PA to the input and generate appropriate corrections. There are two main linearization techniques; input correction and output correction. Input correction is applied on the input signal of the PA to make the response linear. This technique does not increase the peak power and makes the input signal subjected to the non-linearity of the PA. The output correction is applied on the output signal and has to generate significant amount of power to perform its function. It will then physically increase the peak power of the linearized PA. When the PA saturates close to peak power additional power is added to the signal to keep a linear response. (Cripps 1999, p 399) 17 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Three main types of linearization techniques are commonly used on PAs in wireless communication systems and is here briefly explained; Feedback, Feedforward and Predistortion. 2.3.1 Feedback The feedback technique, which corrects the input signal, has been long used to eliminate unpredictable behavior of electronic devices. In a basic direct feedback amplifier the feedback signal is subtracted from the output source signal. The feedback signal is then scaled by a feedback factor and then reintroduced on the input source signal generating a different input signal which after amplifying should become more linear than the original output signal. This is called a closed feedback-loop. However basic direct feedback has a diminishing value as the signal frequency enters the GHz region due to oscillations at a nearby frequency and is not used on microwave amplifiers. Instead of using the feedback technique on the high-frequency carrier it can be used on the modulated baseband envelope. The Envelope feedback technique was well used on the early mobile communication systems but since the feedback signal only contains amplitude information it can just correct AM distortion and not phase distortion (Pothecary 1999, p 119). The Cartesian loop feedback technique can correct for both amplitude and phase distortion and has been widely used in solid state radio transmitters but is not suited for high-frequency microwave amplifiers. 2.3.2 Feedforward (FF) Feedforward is an output correction linearization technique. The basic feedforward correction loop subtracts a sample of the input signal and delays it. The subtracted input signal is then combined with a subtracted output sample of the main amplifier. This results in an RF error signal at the output of the combiner. The error signal is then amplified back to the original level by an additional amplifier and combined with the main amplifier output signal. If the output signal of the main amplifier has no gain or phase distortion the combined error signal will be of zero output and the additional amplifier will remain inactive. But when an error signal occurs the additional amplifier will produce an RF signal that theoretically fills the gap between the main amplifiers distortion properties and the requested linear output result. The combined output RF signal of the two amplifiers will be linearized and the enclosed system will have a capacity that exceeds the main amplifier because of the “help” from the additional amplifier. This is the basic principle behind the Doherty PA described in chapter 3.2.2. 18 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Feedforward is an instant correction technique that operates on the fully formatted RF signal and the correction process is only limited by the phase and amplitude tracking capability of the various components of the system. Great accuracy in gain and phase tracking throughout the system is inevitable to achieve a high precision in the operation, which must be maintained by the system and its single components over time, frequency and temperature. Nevertheless this technique has been well used and has been a key element in the mobile communications infrastructure. (Cripps 1999, p410) 2.3.3 Predistortion (PD) Predistortion is an input correction technique. The fundamental idea of predistortion is to introduce a nonlinearity, based on the known amplifier distortion, to the input signal which after it has been amplified provides a linear gain. Predistortion can correct for both amplitude and phase distortion. Both fixed and adaptive predistortion schemes can be applied where the latter is able to compensate for amplifier characteristics over time, for example, temperature. Predistortion normally provides good improvement in linearity near saturation of the PA and is very power efficient because it does not significantly reduce the efficiency of the amplifier (Pothecary 1999). Predistortion can be applied both in an analog or digital environment. Analog predistortion has a long history but hasn't really reached mainstream use but it is still in use for high power applications in the upper GHz frequency bands. Predistortion linearizers has been used in microwave links and satellite applications because of their relative simplicity, their wide band capacity and their ability to be added to existing amplifiers as stand-alone units (Katz 1999). Analog predistortion though has some negative sides, it will always create some additional high order distortion to the output signal that was not there in the beginning but is caused by the process (Cripps 1999, p401). The latest development of analog predistortion is to apply a second degree predistortion on baseband level. This has shown good results but due to the recent rapid development of digital predistortion (DPD) analog predistortion will probably remain as a limited linearization technique for some specific purposes but not for the big mainstream applications. 19 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 2.3.4 Digital predistortion (DPD) The working principle of the DPD technique can be understood when looking at Figure 3 below. In order to counteract the nonlinearity of the PA, a DPD preceding the PA is inserted into the signal path. The DPD function operates on the baseband input signal in such a way that its output is distorted in an inverse manner to the distortion generated by the PA. In another word, the DPD response compensates for the nonlinearity of the PA. Thus, when these two inverse nonlinearities are combined, it results in distortion cancellation and a desired linear response. Figure 3. The basic concept of the DPD-technique Figure 4. The DPD transfer function is the inverse of the PA transfer function. Mathematically, this can be described as followed: xˆ PA y y DPD x If xˆ x PADPD x x DPD x PA 1 x where x and y denote the input and output signal of the DPD-block. PA() and DPD() denote the transfer functions of the PA respectively DPDblock. To get the final result: xˆ x , DPD() must be the inverse of PA(). 20 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Hence, if the PA transfer function is F(x) then the DPD transfer function will be F-1(x). The problem here is that F(x) is often unknown and very difficult to determine. However, by using LMS adaptation technique it is possible to calculate F-1(x) directly without knowing F(x). More about this is explained in chapter 3.1. 2.4 Behavioral modeling or Component-based modeling There are several ways to model the nonlinearity of a system. Behavioral modeling, also called polynomial modeling, is one of the most common ways. Given the input and output signal, this method allows regenerated spectral components to be calculated analytically based on polynomial coefficients. This is called “black box” simulation because the simulation method is not depending on how the system actually works, it just finds the best representation of the output signal as a function of the input signal. Polynomial modeling is usually easy to implement on nonlinear memoryless systems but becomes very complex when introducing memory effects. Further reading about polynomial modelling with memory effects can be found in Modelling Power Amplifiers using Memory Polynomials (Kokkeler 2005) and Dynamic deviation reductionbased Volterra behavioural modelling of RF power amplifiers (Zhu, Pedro and Brazil 2006). Component-based modeling is a simulation of a complete system on component level. As contrary to the “black box” behavioral modeling this means we need to have the exact knowledge of every individual component and how they are connected in the enclosed system to be able to get an accurate result. This demands a powerful and complex simulation engine as well as detailed input of the simulated system. On the other side the results should give a very detailed picture of the system characteristics including memory effects. More about component-based modeling in ADS is described in chapter 3.2. 2.5 Advanced Design System (ADS) Advanced Design System (ADS) is an Electronic Design Automation (EDA) tool from Agilent Technologies. It is a software tool that offers a platform to design and simulate electronic circuits by using predefined components available in its component libraries. One of the biggest advantages when working in ADS is the possibility for RF designers to work with circuits of all levels, from top system level down to transistor level in the same simulation environment. 21 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers ADS is divided into two separate domains: The Digital domain and the RF/Analog domain. The RF-domain constitutes the main part of ADS and offers techniques such as Harmonic Balance and Circuit Envelope and SPICE-like time-domain simulation. These techniques will be discussed briefly in chapter 3.6. It is in this domain that most of wireless design work is carried out. The Digital domain works with data that is sampled at discrete time points suitable for digital signal processing. This domain has traditionally been uninteresting for most RF-designers but with rapidly increasing advances in today’s digital signal processors (DSP), its role in wireless design has become more and more important. In the next section, a description of the different simulation techniques that are available in ADS is given. The version ADS 2004A and ADS 2009A was used in conjunction with Matlab 6.5 and Matlab 7.0 throughout this work. Also see chapter 4.4. 3 Modelling of Power Amplifiers and Digital Predistortion In this chapter the system environment as well as some basic theories of the algorithms used is described. The two power amplifiers are explained and the integration of ADS and Matlab. 3.1 The Digital Predistortion algorithm This chapter presents the LMS algorithm on which the DPD technique in this report is based. The computation of coefficients in a polynomial expansion of the non-linearity can be done either by iterative adaptation on sample basis or on matrix inversion based on the whole signal vector. Both approaches will be tested to find the most efficient way to combine Matlab algorithms with ADS. A more detailed description of the LMS algorithm can be found in: ADS and Matlab to optimize predistortion of amplifiers (Elgeryd 2003) 3.1.1 Iterative solution on sample basis Adaptation of polynomial coefficients: In the LMS adaptation technique, a so-called indirect learning scheme is applied. It makes it possible to use the estimate of the polynomial coefficients α directly in the predistorter. The incoming data is predistorted according to the polynomial with the coefficients, which are updated for each sample. 22 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers In order to update the DPD coefficient α, a small fraction of the PA output is fed back, demodulated to baseband and compared to the original input signal, see chapter 3.3, sample by sample. It is understood that the reference signal has to be delayed in order to be time-aligned with the feedback signal. Let the input signal to the PA be x and α be the coefficient of the DPD: L1 (t1 ) L2 (t1 ) L3 (t1 ) L4 (t1 ) L (t ) L (t ) L (t ) L (t ) 2 2 3 2 4 2 1 2 L1 (t 3 ) L2 (t 3 ) L3 (t 3 ) L4 (t 3 ) L1 (t 4 ) L2 (t 4 ) L3 (t 4 ) L4 (t 4 ) Where L [y y. y 2 y. y 3 1 x(t1 ) x(t ) 2 2 3 x(t 3 ) 4 x(t 4 ) 4 y. y ] In matrix notation, this can be written as: L x Then α can be calculated by multiplying both left hand and right hand side of the equation by LH, which denotes the conjugate transpose of the Hermitian matrix L. LH L LH x By matrix inversion, the sought coefficient vector can then be solved by: ( LH L) 1 ( LH x) H * T * T Note that a matrix L is called Hermitian if L [ L ] , where [ L ] denotes the transpose of the complex conjugate of L. H 1 LH x W Updating : Let ( L L) M and such that ( M ) W The final matrix M and W are actually set up by the summations of all sub-matrices that are built up by each sample. For each new sample, M and W can therefore be updated by adding the new sub-matrix to the existing matrix as follows: M k 1 M k LH k Lk Wk 1 Wk LH k x 23 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 1 Finally we have: k 1 ( M k 1 ) Wk 1 where is set to a small number (e.g. 0.00001) just to avoid division by zero. While the matrix α is continuously built up for each signal sample, we take its instantaneous value after each sample to use as DPD coefficients. Then by applying these coefficients after each sample we may actually improve the DPD on a sample basis. In general, the method converges within 4000 iterations based on 4000 samples. 3.1.2 Iterative solution on matrix inversion basis The iterative solution on matrix inversion basis is a more efficient method based on the same ground as the sample-by-sample method. It compares the input and output signal to determine the polynomial coefficients using matrix inversion. Here, alpha is updated for the whole matrix instead of after each sample. Given the relationship below: L1 (t1 ) L2 (t1 ) L3 (t1 ) L4 (t1 ) L (t ) L (t ) L (t ) L (t ) 2 2 3 2 4 2 1 2 L1 (t 3 ) L2 (t 3 ) L3 (t 3 ) l 4 (t 3 ) L1 (t 4 ) L2 (t 4 ) L3 (t 4 ) L4 (t 4 ) 1 x(t1 ) x(t ) 2 2 3 x(t 3 ) 4 x(t 4 ) Then: L x L\x Note that the backslash operator is the Matlab notation for solving LMSproblems. Using this operator, the problem of possible singular matrix is eliminated. 3.1.3 With memory effect Memory effect can be taken into account both on sample and matrix basis by expanding the L-polynomial such that it also includes one or several previous input samples, as earlier described in chapter 2.2.4. For example, with one previous sample included the L-polynomial becomes: 4 2 3 4 2 3 L y y. y y. y y. y y n 1 y n 1 . y n 1 y n 1 . y n 1 y n 1 . y n 1 Here, we have a fourth order polynomial consisting of two tables: one for the instantaneous input sample and one for the sample right before that. The previous samples can be delayed by an arbitrary number of samples compared to the instantaneous one. 24 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Parameters that can be varied are the polynomial order, the number of tables (how many previous samples to include) and the sample delay. 3.2 Component-based PA-modeling in ADS As previously described in chapter 2.4 behavioral modeling are commonly used in high-level system designs thanks to their ability to reduce the system simulation time. Nevertheless, one should retain that this method is used at the expense of the result accuracy. In order to compute an accurate DPD transfer characteristic, which is actually the inverse transfer characteristic of the PA, we need to model the PA as realistically as possible. In this master’s thesis, we will consider and evaluate the reliability and robustness of component-based modeling in ADS as an alternative to polynomial modeling. Two RF PAs are completely modeled in ADS with input matching network, output matching network and bias network and tested in this study: a highly linear MRF5S21 PA and a power efficient Doherty PA. These amplifier models are designed by Freescale and are described below. 3.2.1 The MRF5S21 PA (PA1) An MRF5S21 PA that has been designed in ADS using a LDMOS 130W transistor from Freescale (former Motorola) is biased to 28V. It has a 19 dB gain and 50 dBm saturated power. Figure 5 shows the PA in its simulation environment. Figure 5. The MRF5S21 PA top level. 25 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The PA simulation environment, which is created in the RF-domain of ADS consists of the PA block, a load of 50 Ohm, several variable definitions and a Circuit Envelope simulator. The Envelope simulator is the only simulator in the RF-domain that is suitable for digital modulated signals as concluded in chapter 3.6. The ports are used to receive and to output signals. In the simulation results this PA is referred to as PA1. Pushing into the device under test (DUT) we can see the sublevel that actually constitutes the PA as it is defined in ADS with input and output matching networks, see Figure 6. The LDMOS 130W transistor used here is designed especially for WCDMA base station applications at frequencies between 2140 and 2170 MHz. Note that the same DUT is also employed in the Doherty PA. Figure 6. Schematics of the MRF5S21 PA at transistor level. Pushing further down into the sublevels, we have the matching networks consisting of microstrip lines, inductors and capacitors. See Appendix 2. 3.2.2 The Doherty PA (DPA) The DPA tested here consists of a main amplifier, an auxiliary amplifier with the same LDMOS 130W transistor as for the single PA design. It also consists of a quarter-wave transmission line that combines the outputs of the two amplifiers, see Figure 7 below. Both the main amplifier and the auxiliary amplifier use the same DUT with the schematics already shown in Figure 6. Yet, they are biased differently so that the auxiliary amplifier turns on only when the main amplifier saturates. The auxiliary PA are sometimes called peak PA. The system benefits then from a loadpulling effect and can achieve a maximum power efficiency of 78 %. 26 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The Doherty PA offers a higher efficiency than traditional power amplifiers but it also suffers from reduced linearity. Thus, combining DPA with DPD technique can result in both high power efficiency and linearity. In the simulation results the Doherty PA is referred to as DPA. Figure 7. Block diagram of a DPA. Figure 8. Output power of the two PAs. This DPA has a 15 dB gain and 51 dBm saturated output power, its simulation environment is shown in Figure 9 and Figure 10 below: 27 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 9. The DPA top level. Figure 10. A Doherty structure with main PA, peak PA and /4transmission line. 28 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 3.3 System overview, Matlab-ADS integration With the understanding of how the PA and the DPD work independently as systems, a simulation environment which combines these two subsystems can be created. The goal is to linearize RF-PAs modelled in ADS by using DPD-algorithms developed in Matlab. In the following chapters the integration and the interface between the digital domain that is simulated in Matlab and the RF/analog domain that is simulated in ADS are explained. The main structure of the simulation system is shown in Figure 11. Note that the DPD block and the DPDalgorithm blocks are implemented in Matlab while the rest is modeled in ADS. Figure 11. The flow-chart of the linearizer-PA system The WCDMA signal enters the digital predistorter (DPD) in the form of complex base band and is represented by the two real valued signals I and Q. The DPD predistorts the input signal by multiplying it with the values of alpha, attained from the DPD-algorithm. In this particular case, polynomial DPD functions are used, as described in chapter 3.1. A further explanation of the complex baseband representation is given in detail in chapter 2.1.3. 29 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Having passed the DPD, the predistorted signal is then applied to an RF carrier (2.14 GHz) through a QAM-modulator incorporating a Local Oscillator (LO). Thereafter, the signal is passed to the PA where it is amplified and distorted by the nonlinearities of the PA. In the feedback path, a small fraction of the PA output is down-converted back to base band by a demodulator before entering the DPD-algorithm where it is compared to the reference signal. By using the LMS algorithm, the inverse characteristic of the PA is then calculated and the polynomial coefficients can be updated and passed to the DPD. These coefficients, which are used to predistort the baseband input signal in the DPD as described above, are updated by the LMS algorithm for each firing as the iteration continues. The final result is an output signal with less distortion. 3.4 Matlab-ADS integration methods An interface between Matlab and ADS must be created so that signals and variables can be passed between the two software tools. The two possible solutions are presented below. 3.4.1 Approach 1: Iterative solution on sample basis In this method, polynomial coefficients are calculated and updated for each data point using the LMS-algorithm described in chapter 3.1. Two Matlab-components are inserted directly into the ADS environment. During the simulation ADS calls on Matlab each time a Matlabcomponent is evoked. Produced data is saved in a special catalog in ADS called “Data”, see Figure 13, which is accessible even by Matlab. The DPD-algorithm couples the input signal and the output signal from the feedback path to determine alpha as described previously. Alpha is saved in the “Data” catalog and then fetched in the next firing by the adaptation block called DPD, which is placed before the PA. Figure 12 illustrates the idea. 30 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 12. Block diagram: sample-by-sample iteration. The DPD and DPD-algorithm blocks can be incorporated in an ADS schematic by special Matlab-components which are available in the component library of ADS. These are called on by ADS in each firing. Figure 13. Alpha is saved in the “Data” catalog in ADS, accessible by both softwares. 31 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Implementation: In this approach, Matlab is directly integrated in the ADS simulation, which eliminates the trouble of shifting between Matlab and ADS. Here, simulation for the whole combined system can be carried out in one single step. Though, this is a time-consuming method due to the process of ADS calling on Matlab in each firing. To get a better speed, the faster Matlab component MatlabliblinkCx can be used on one condition: the Matlab scripts in use have to be pre-compiled and placed in a special library. Pre-compiling must be redone as soon as there is any change in the Matlab code. For this purpose, a Matlab script which takes care of the pre-compiling task was developed. In fact, this script is one essential part in the integration of Matlab and ADS, since it functions like a bridge between these two software tools. Figure 14. Top level in Approach 1. See Appendix 3 for detailed charts of the different set ups. Picture note: With two Matlab components, “MatlabLibLinkCx”, integrated in the ADS test bed, the whole simulation takes place in ADS. When the whole signal of 16000 samples has passed, the final output signal is then read into Matlab for further analyse. 32 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Working principle: 1) 2) 3) 4) Place the two Matlab files (DPD and DPD-alg.) in the “Data” library in ADS. Pre-compile them by running the script mcc. Simulate in ADS. Signal processing in Matlab for plotting and ACRL calculation. If changes are needed in the Matlab-files: click ”Stop and release simulation”, recompile the files and simulate again. Produced data such as simulations outputs are saved in the ADS-format “.tim”, which is not compatible with Matlab. Hence, before the signal can be read back into Matlab for further processing, the signal format has to be converted. Even for this purpose, Matlab scripts were developed. 3.4.2 Approach 2: Matrix inversion basis with post-distortion The vector processing technique handles data in large matrices instead of processing single data points and is therefore an efficient method for numerical calculations. By using this iterative solution on matrix inversion basis, we can take full advantage of the capabilities possessed by the signal processor. A drawback is that this method only works under the condition that the circuit does not contain any feedback path, since the result computation does not take place until the whole matrix has passed through the circuit. In our case, since the DPD-algorithm must adapt to the PA characteristic, which varies due to changes in temperature, voltage and time etc, a feedback path to make the algorithm adaptive is necessary. However, one solution that allows both adaptation and matrix processing is to apply post-distortion and to execute the amplification part and the DSP part separately. The whole signal is first passed through the PA which is modeled in ADS, and then the signal is processed in Matlab for linearization using the matrix inversion technique. To get a good result, at least two iterations are required. 33 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Implementation: The simulation consists of three steps as described below: Step 1 (ADS): Let the input signal (x) pass through the PA to get the amplified but distorted output (y). Save then y in a large matrix where it is accessible to Matlab. This is done totally in the RF-domain of ADS. Figure 15. Step 1: amplification in ADS. Step 2 (Matlab): Both the input and output signals are read into Matlab as two vectors. Now, efficient computations can be applied to calculate the polynomial coefficients using the matrix inversion LMS-algorithm. The input signal is then multiplied by these coefficients to make a new, distorted input signal (New-x), which will be fed to the PA. Figure 16. Step 2 and 3: signal processing in Matlab followed by amplification in ADS. Step 3 (ADS): The new, distorted signal passes through the PA for a linear amplification. The output should now be linearized but if not, more iteration can be carried on by repeating Step 2 and Step 3. Finally, the output can be read into Matlab again for further signal processing, for example computing the ACLR and plotting the DSP. In practice, these steps are followed: 1) 2) 3) 4) 5) First ADS simulation with x-org as input signal. Signal processing in Matlab. Run read(1). Second ADS simulation with newIQ as input signal. Matlab: Run read(2). Repeat step 3 and 4 for additional iterations. 34 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Here, x-org is the original input signal to the PA, while newIQ is the predistorted input signal that we get after linearization in Matlab. The commands read(1 ) and read(2) starts the signal processing with x-org and newIQ respectively as input signal in the DPD-algorithms. ADS-implementation: The solution in ADS consists of several levels. In the top level, a design kit with parameters for the modelled PA, some variables and the DataFlow controller are defined as showed in the picture below. The modelled PA is included in the schematics as a sublevel which in turn has sublevels for Input matching networks etc. In the PA top level, the controller is used. Figure 17. Top level in Approach 2, using DataFlow as simulation controller. The chart shows ADS-simulation without Matlab. See also Appendix 3. The I and Q parts of a WCDMA signal are stored as .txt files which are compatible with Matlab. These are read by the ReadFile components, and then converted to a complex signal, amplified digitally, converted back to timed signals, passed through a QAM-modulator before passing through the PA. The amplified and distorted signal is then passed through a QAMdemodulator, several signal conversions and finally put out as .txt files by the Printer components to be used in Matlab. The output from the NumericSink component is useful for analyzing directly in ADS. 35 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The advantages with this simulation setup are the faster simulation speed since ADS does not have to call on Matlab while executing and the possibility to easily switch among different DPD-algorithms without interfering with the simulation in ADS. Two iterations are enough to get a good result. Scheduled iteration The many steps in Approach 2 can be avoided by using a feature called “simulation sequencer” that is available in ADS. This feature allows users to schedule the simulation of different blocks. In fact, it simulates several blocks automatically one after the other in the order specified by the user, using data produced by the previous block. By inserting Matlabcomponents in ADS, we can make a block that takes care of Step 2 above. Placing these three steps as three blocks in a top level schematic using the “sequencer controller”, the whole simulation can be started by just one click. Figure 18. Block diagram of scheduled simulation. This could be a flexible method but unfortunately it cannot be done in ADS today. The “sequencer” feature works well but it does not support co-simulation of RF and DSP blocks. Since Step 2 is done in the DSPdomain and the rest is in RF, we will have to wait until Agilent Technology has found a way to support co-simulation with this feature. 3.5 Intermodulation distortion and the ACLR Intermodulation distortion (IMD) is unwanted frequency components introduced at the output of the PA that does not belong to the actual signal. These cause spectral regrowth and interfere with adjacent channels making the information detection task in these channels difficult, see chapter 2.2.1. Further reading about intermodulation distortion can be found in Digital Pre-Distortion of Power Amplifiers (Spångberg 2002). IMD is normally measured by using the ACLR requirements. 36 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Adjacent Channel Power Leakage Ratio (ACLR) is one of the most important linearity requirements in today’s communication systems. In the past, it was called ACPR (Adjacent Channel Power Ratio) and was defined as the power in an adjacent channel relative to the power in the main channel. However, this definition was considered insufficient and has been modified to also take into account the sensitivity for power leakage of the receiving filter in a neighboring receiver. This sensitivity is defined by the roll-off factor in the root raised-cosine filter (RRC) used in receivers (Pothecary 1999, p 71ff). According to the 3GPP specifications, the ACLR value of 3G base stations must be higher than 45 dBc at 5 MHz frequency offset and 50 dBc at 10 MHz offset (3GPP TS 25.104, p 6.6.2.2.1). Considering the contribution of other components in the TX-chain to the distortion (for example the demodulator), the PA itself must be designed to meet even higher requirements. To evaluate the level of nonlinearity, ACLR calculations are made using a RRC filter with a roll-off factor of 0.22 throughout this thesis. To simplify the results a mean value for ACLR1 up (+5 MHz) and ACLR1 low (-5 MHz) has been used in the charts to represent the ACLR1 value, the same has been done for ACLR2. Figure 19. The ACLR1 and ACLR2 37 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 3.6 ADS-simulators In the RF/analog domain, three different simulators are available in ADS: SPICE, Harmonic Balance and Circuit Envelope. The working principles of these simulators are presented below. The Ptolemy Data Flow controller is used as a bridge between the digital and RF domain and enables simulations of the whole system. SPICE-like time domain simulation Working in time-domain, this simulator solves nonlinear differential equations by integration. It can simulate systems that contain both baseband and RF-circuits. Nevertheless, to avoid the effect of aliasing, the chosen time step has to be small enough to maintain the signal waveform. This imposes a big problem for wireless applications since the difference between the frequency of the RF-carrier and the BB-signal is very large. Therefor the simulated time steps has to be very vast to get an accurate and result the SPICE simulation will be very time consuming (Yap 1997). Harmonic Balance (HB) Harmonic Balance (HB) is on the other hand a nonlinear frequencydomain simulator which does not suffer from a large difference in frequency like the SPICE-simulator. It computes the steady-state response of a circuit by calculating the Fourier coefficients of the output solution. HB is considered an efficient and accurate method except for one drawback: it works only when the signal can be represented by a small number of sinusoidal components (Kundert 1997). Thus, it is not adequate to represent the continuous spectrum of non-periodic signals, as the WCDMA signal, and can therefore not be represented accurately by HB. Circuit Envelope (CE) Circuit Envelope simulation does not suffer from a large frequency difference like SPICE and it can also deal with non-sinusoidal signals. Working in both time and frequency domain, it combines SPICE and HB by performing a HB simulation at each time step. In Circuit Envelope, the RF-carriers are separated from the signal and only the modulation envelope is sampled. The sampling requirement is thus reduced to represent only the low-frequency baseband-signal instead of the highfrequency RF carrier. The modulation information is represented as a baseband time-varying complex envelope riding on the RF carriers (Yap 1997). The result is a time-varying HB analysis that can be applied to circuits with time-varying complex modulated signal, and even though Circuit Envelope employs HB as part of the solution process, the matrix size remain reasonable for simulation on even personal computers. 38 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Ptolemy Data Flow in ADS In the baseband processing models, the Ptolemy Data Flow controller is used. The Ptolemy engine in ADS is mainly a framework for synchronizing simulations with each other. The Ptolemy Data Flow controller consists of two domains; the Synchronous Data Flow domain (SDF) used for purely numeric simulations and the Timed Synchronous Data Flow domain (TSDF) used for RF/analog simulations. ADS Ptolemy thus acts like a bridge between the digital design or signal processing simulation environment (SDF) and the RF/analog simulation domain (TSDF) and is able to simulate both environments in an enclosed system. The Ptolemy controller also allows other external simulation technologies to run concurrently with native simulation domains like for example Matlab, which will also be used in this thesis. Simulation model chosen Having studied the different simulators, it is concluded that the only simulator that is suitable for simulation of circuits with time-varying complex modulation in the RF domain is Circuit Envelope. This simulator is chosen to enable the co-simulation with the digital domain where Ptolemy Data Flow is used. 4 Simulation and evaluation This chapter focuses on the simulation environment and the schematics in practice. The used simulation variables are described as well as the simulation results. 4.1 ADS-Matlab integration in practice Matlab blocks are imported in the ADS simulation environment through the ADS Ptolemy engine. In the latest version of ADS (2004A), a new feature named ‘MatlabLiblink’ was introduced to shorten the simulation time of circuits with inclusion of Matlab components. This feature can operate in three different modes: Script Mode, Compile and Auto. Script mode The Script mode is very slow and time-consuming. It works in the same way as the traditional Matlab-component, and interprets the Matlab script step-by-step. 39 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Auto mode The Auto mode works with already compiled Matlab files, which are placed in a special library. Organizing the Matlab-files in this way makes it significantly easier for Ptolemy to parse them. Hence, the simulation speed is increased to be 20 times faster compared to the Script mode. One inconvenience is the requirement of recompiling the Matlab-files whenever a change is made to the code. Pre-compiling is also required when using the faster component MatlabLiblinkCx. For pre-compiling, ADS (version 2004A) only works with Compiler 3.0 provided in Matlab 6.5 Release 13. The latest version of Compiler in Release 14 cannot be used since there are some changes in Matlab that are not updated in the software of ADS. Compile mode In the Compile mode, there is no need to pre-compile the scripts since ADS would call on the Matlab compiler itself and therefore simulations with Matlab files would be greatly simplified. However, this last feature does not yet work in ADS 2004A. Due to different reasons, the communication between ADS and the Matlab compiler somehow cannot be established. Thus, the Auto mode is a natural choice. 4.2 How the simulations were executed Regardless simulation approach, these first steps are required to create a test bed in ADS: Step 1: Choose ADS-mode: RF/analog or DSP, here both. Step 2: Create the top level schematic using DF-simulator (DataFlow). See Figure 20. Step 3: Add Design Kit on the top level. Note that it should only be placed here. (Here, FSL_TECH_INCLUDE is used). Step 4: Include PA-schematics in sublevels, using Circuit Envelope on the PA top level. See Figure 21. Step 5: Specify the simulation time and other variables, for example sampling frequency etc. The simulation time should be long enough to give an accurate spectrum. The DefaultNumericStop specifies the number of values of a certain variable to be saved. The sampling frequency is set to 61.44 MHz. 40 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 20. Test bed in ADS with top level DF-simulator Figure 21. ADS schematics, Approach 1: Iterative solution on sample basis. Figure 22 and Figure 23 shows enlargements of the digital respectively the analog domain. In digital domain MatlabLibLink is used to call on pre-compiled Matlab scripts placed in a special library which contain the DPD-algorithm. At the end of the chain the new alpha-value is extracted. 41 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 22. Enlargement of the digital domain with DPD and extraction of alpha-value. The two MatlabLiblinkCx components runs the files “DPD” respectively “DPD-alg” From the digital domain the signal is transferred to the analogue domain in ADS through the Ptolemy engine. The simulation is synchronized by time-steps. One part of the amplified output signal is redirected to a demodulator and feed back to the digital domain in Figure 22. Figure 23. Enlargement of the analog domain with PA and modulators and demodulators 42 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 4.3 Simulation variables As described in the scope of this thesis each PA is simulated on both sample and matrix inversion basis for comparison between the different methods. In addition to those four main cases several other variables have been tested in each case throughout the simulations to get an authentic result. These variables are the gain, the polynomial degree of the signal representation and the memory-depth. These factors are explained below. 4.3.1 PA gain The linearity of the power amplifier is dependent of the gain as the nonlinearity of the PA increases near saturation. To test the DPDalgorithms ability to linearize the output signal the PA must be driven close to and above saturation. Different gains are therefore fed into the PA in the simulations to analyze its behavior. For PA1 the following gainlevels has been simulated; 20, 24, 26 and 28. For DPA the following gainlevels have been simulated; 20, 25, 30, 34. The relation between gainlevels and output effects are shown in Table 2. PA 20 Mean power 22,8 W Maximum output power 123 W 24 33,5 W 182 W 26 39,1 W 215 W 28 43 W 223 W 20 14,6 W 80 W 25 22,9 W 125 W 30 32,2 W 170 W 34 40,1 W 215 W Gain-level PA1 (sample) DPA (sample) Table 2, Relation between gain-level and output effect 4.3.2 Polynomial degree The polynomial degree is important to get a correct representation of the baseband signal in the digital domain. With higher degree a better representation of the signal was performed. But with higher degree polynomials the amount of data to be calculated also increases. Therefore it is of interest to analyze if there is an optimal polynomial degree for simulation to which further increasing of the polynomial degree shows little improvement to the resolution of the signal. In the simulations performed, the polynomial degree has been varied between from 4 to about 12-15. 43 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 4.3.3 Memory-depth One of the purposes of this thesis is to analyze if ADS can simulate memory effects. As described in chapter 2.2.4, a formula to compensate for memory effects has been implemented in the Matlab scripts. In addition to calculation of the current signal the formula also takes into account the last one or two signals passing the DPD-loop. If the output signal becomes more linear after compensating for the possible memory effects, it will be taken as proof that memory effects exists in the simulation. If the output signal show no visible difference, with or without compensation for memory effects or gets even more distorted, memory effects does probably not exists in the simulations. Memorydepths used in the simulations are: M1, M2 and M3, where M1 is without any compensation= no memory, M2 compensates for the last signal and M3 compensates for the last two signals. 4.4 Simulation results In the following chapters the simulation results will be displayed and analyzed. We will focus on how the results differ in linearization effect depending on PA output effect, the polynomial degree, the matrix or sample method and of memory-depth. In chapter 5 the results will be summarized and conclusions will be drawn. In year 2005 the main simulations were made in ADS2004A for the sample and matrix method. But the simulations with the matrix method were not convincing and did not show the expected results. For example the PAs did not seem to saturate at any gain-level, as must be the case. In spite of much troubleshooting nothing wrong with the simulations could be determined. In the year 2010 the matrix method was again simulated with the newest version of ADS at the time, ADS 2009A. This time the results were more plausible and matched the results from the sample method. The following simulation results are therefor from 2005 for the sample method and from 2010 for the matrix method. 44 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Non-linear and linearized signal As the PA gain increases the non-linear behavior is augmented and linearization of the input signal becomes necessary. Figure 24 shows the concept of linearization, the non-linearized signal suffers from substantial inter modulation distortion (IMD) that may distort the adjacent channels. After linearization the IMD in the example has been suppressed about -10 to -15 dB and with compensation for memory effects some -10 dB further. dB 4.4.1 Figure 24. An example of the concept of linearization. Figure 25 shows the difference between a non-linearized and a linearized signal for amplifier PA1 and DPA. In both cases the IM-level is suppressed about -10 to -20 dB compared to the non-linear signal. Both examples also show that the effect of linearization decreases as the gain increases, this will be discussed further in chapter 4.4.3. 45 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Nonlinearized signal compared to linearized signal (ACLR1, PA1 and DPA without memory effect) 70 65 60 dBc -dB 55 Sample PA1 Non-linear 50 Sample DPA Non-linear 45 Sample PA1 M1 Sample DPA M1 40 35 30 25 DPA20/PA1 20 DPA25/PA1 24 DPA30/PA1 26 DPA34/PA1 28 Figure 25. Non-linearized compared to linearized signal for PA1 and DPA sample without memory effect. 4.4.2 ACLR1 and ACLR2 The simulations show that the ACLR2 level very much follows the ACLR1 level. In Figure 26 the ACLR2 noise levels are about 5 dB lower than the ACLR1 for all gain levels. This meets the specification for the 3GPP standard very well because the minimum suppression of noise level for ACLR1 is 45 dBc and 50 dBc for ACLR2, which also means a 5 dB difference between the levels. The simulations also show that the PA1 exceeds the 3GPP specifications for gain levels 20, 24 and 26 but not for 28 which becomes too distorted and thus non-linear. 46 Linköping University Master’s thesis dBc ADS and Matlab to Optimize Predistortion of Amplifiers Figure 26. ACLR1 compared to ACLR2, PA1 sample. Linearization relative to gain-levels Does the linearization effect drop when gain-levels rise? This is the expected behavior because a more non-linear signal from the PA is more difficult for the predistorter to linearize. In the following charts this behavior is analyzed. Linearization relative to effect (PA1 sample without memory effect) 250 70 60 200 50 150 40 30 100 -dB dBc (W) effect output PAPA effect output 4.4.3 PA1 Effects ACLR1 20 50 10 0 0 PA1 20 PA1 24 PA1 26 PA1 28 Gain Figure 27. ACLR-value relative to output effect, PA1 sample. 47 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 27 shows an increasing non-linear behavior of the signal as the output effect of the PA increases. This is a likely result because a higher gain brings the PA closer to saturation where the non-linearities of the PA become too significant for the predistorter to handle. Linearization relative to effect (DPA sample with memory effect) 250 80 70 200 50 150 40 100 30 DPA Effects -dB dBc (W) effect output PAPA effect output 60 M1 M2 M3 20 50 10 0 0 DPA 20 DPA25 DPA30 DPA34 Gain Figure 28. ACLR-value relative to output effect with memory effect, DPA sample. The DPA show a similar result as the PA1. In Figure 28 the memory effects are included and they follow the same dropping trend when the gain increases. The linearity of the DPA does not drop as fast the PA1 at high gains. The matrix solutions show almost the same result, see Figure 29 and Figure 30. The linear behavior is dropping with higher gain-levels. The PA1 seems to drop more rapidly than the DPA at higher gain-levels, as was the result with the sample method. An explanation is that the auxiliary PA increases the linearity of the DPA near saturation. 48 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Linearization relative to effect (PA1 matrix with memory effect), sim 2010 200 70 180 65 160 60 55 120 50 100 Effekter -dB dBc effect output (W) effect output PA PA 140 M1 45 M2 80 40 60 35 40 30 20 0 25 PA1 20 PA1 24 PA1 28 Gain Figure 29. ACLR-value relative to output effect with memory effect, PA1 matrix. 140 75 120 70 65 100 60 80 55 60 DPD Effects -dB dBc effect(W) output PAoutput effect PA Linearization relative to effect (DPA matrix with memory effect), sim 2010 M1 M2 50 40 45 20 40 0 35 DPA20 DPA25 DPA30 Gain Figure 30. ACLR-value relative to output effect with memory effect, DPA matrix. 49 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Polynomial degree (N-value) It is of interest to study how the polynomial degree of the DPD-algorithm affects the linearization of the output signal. A higher N-value should give a more linear result because of better resolution of the signal frequency spectrum. The drawback is that a high N-value will need a higher processing capacity of the DPD to calculate the compensated signal. To optimize linearization compared to processing capacity we would like to find the ideal polynomial degree and to see if the results settle at any point. Linearization effect PA1 sample (ACLR1 without memory) 65 60 55 PA1 20 dBc -dB 4.4.4 50 PA1 24 PA1 26 45 40 35 4 5 6 7 8 9 10 11 12 N Figure 31. ACLR-value as function of polynomial degree, PA1 sample. The highly linear amplifier PA1 shows a typical and expected response to the polynomial degree. A clear improvement in linearization from low Nvalues until the effect settles after a certain point of about N=7-8. The effect levels out at higher polynomial degree. The different gain-levels also shows an expected result with a more non-linear behavior at higher output effects that to a certain level can be compensated with a higher polynomial degree. This result indicates that a more non-linear signal can be compensated for with a powerful DPD. 50 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Linearization effect DPA sample (ACLR1 without memory) 70 65 60 DPA 20 dBc -dB 55 DPA25 DPA30 50 DPA34 45 40 35 44 55 66 77 88 99 10 1 11 1 12 1 13 1 14 1 15 1 N Figure 32. ACLR-value as function of polynomial degree, DPA sample. The power efficient DPA does not show the same characteristics as the PA1. At the gain-level 20 the signal peaks and thereafter declines but with higher gain the linearization effect never really settles and levels out. The Doherty PA uses the feedforward technique which in itself compensates for non-linear behavior with its auxiliary PA. The first simulated gainlevel of 20 does probably not activate the auxiliary PA, as the other levels must do, and therefore have the characteristics of a normal PA. Except for gain 20, the DPA is not as linear as the PA1 and does not reach over 60 dBc for ACLR1. 51 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Linearization effect PA1 matrix (without memory), sim 2010 65 60 55 PA1 20 dBc -dB 50 PA1 24 45 PA1 28 40 35 30 3 4 5 6 7 8 9 10 11 12 N Figure 33. ACLR-value as function of polynomial degree, PA1 matrix. The matrix method for PA1 shows a graph with more deviation but with a similar trend line as the sample method. After about N=6 the polynomial degree does not seem to improve the linearity of the signal substantially, at least not for gain 20. Linearization effect DPA matrix (without memory), sim 2010 70 65 60 dBc -dB 55 DPA20 DPA25 DPA30 50 45 40 35 4 5 6 7 8 9 N Figure 34. ACLR-value as function of polynomial degree, DPA matrix. 52 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The DPA matrix simulations show a similar outcome as the sample method. Gain 20 has a decreasing behavior after N=5 and with higher gain the trend is increasing over the chart but from a lower starting point. As for the sample method the IM-level does not reach over 60 dBc for ACLR1. Memory effects In the following results the effect of the memory algorithm described in chapter 2.2.4 is analyzed. The memory algorithm is applied in the Matlab script to simulate the DPD in the digital domain. The M1 results are the predistorted signal without compensation for memory effects. The M2 signal includes compensation for the last processed signal and the M3 signal includes compensation for the last two signals. If ADS includes memory effects in the simulations the compensated signals should show a more linear result than the non-compensated signal. Memory effect PA1 20 sample (ACLR1) 67 65 63 M1 dBc -dB 4.4.5 61 M2 M3 59 57 55 4 5 6 7 8 9 10 11 12 N Figure 35. PA1 sample, gain 20 with memory effect 53 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers From Figure 35 we can see that applying the memory algorithm to the signal results in a more linear output. The non-compensated signal (M1) has an ACLR1-value of about 62 dBc while the M2 signal has an average of about 63 dBc. The M3 signal is even better for some N-values. From this result we can conclude that ADS actually simulates memory effects. If ADS did not simulate memory effects, the M2 and M3 signal would almost certainly not have shown any improvements or the results would have been more distorted than the M1 signal. Memory effect PA1 24 sample (ACLR1) 64 62 dBc -dB 60 M1 58 M2 M3 56 54 52 50 4 5 6 7 8 9 10 11 12 N Figure 36. PA1 sample, gain 24 with memory effect With gain-level 24 the compensation for memory effects has less effect than gain 20. At higher gain-levels the signal get more distorted and harder to linearize, thus the memory algorithm also gets less effective. 54 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect PA1 26 sample (ACLR1) 60 58 56 54 dBc -dB 52 M1 50 M2 M3 48 46 44 42 40 4 5 6 7 8 9 10 11 12 N Figure 37. PA1 sample, gain 26 with memory effect At gain 26 the compensation for memory effects shows no improvements, instead we get the opposite result. The signal is too distorted and the memory algorithm can't tribute to the result. In this case the output signal for M2 and M3 is actually worse than the non-compensated M1-signal. 55 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect DPA 20 sample (ACLR1) 75 73 71 69 dBc -dB 67 M1 65 M2 M3 63 61 59 57 55 4 5 6 7 8 9 101 N Figure 38. DPA sample, gain 20 with memory effect For the DPA amplifier at gain-level 20 the compensation for memory effect shows a huge improvement in linearization. Figure 38 shows that the M2 signal has about 4 dBc less distortion than M1 and the M3 signal has up to 8 dBc less distortion than the non-compensated signal. According to the results the DPA amplifier suffers from far more memory effects than the PA1 amplifier. On the other hand the DPA amplifier reaches a 65 dBc IM-level before compensation for memory effects while the PA1 amplifier only reaches about 62 dBc IM-level at the M1 signal. 56 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect DPA 25 sample (ACLR1) 65 60 55 dBc -dB M1 M2 M3 50 45 40 4 5 6 7 8 9 10 11 12 13 14 15 N Figure 39. DPA sample, gain 25 with memory effect Memory effect DPA 30 sample (ACLR1) 54 52 dBc -dB 50 M1 48 M2 M3 46 44 42 40 4 5 6 7 8 9 10 11 12 13 14 15 16 N Figure 40. DPA sample, gain 30 with memory effect 57 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Figure 39 and Figure 40 show a similar result for the DPA amplifier as for the PA1 on higher gain-levels. When distortion increases and the PA saturates the linearization algorithm loses its effect and cannot compensate for memory effects. At gain-level 25 the compensation for memory effect shows no improvement and at level 30 the result is slightly worse than the non-compensated signal. Memory effects in matrix method The compensation for memory effects in the matrix method does not show the same clear improvement as in the sample method. For PA1, as shown in Figure 41 and Figure 42 below, a slight improvement for gain 20 can possibly be observed with memory effects which correlate with the result of the sample method. For gain 24 a slight improvement can maybe also be seen but due to the big deviations of the memory-less signal it is hard to say if that really is the case. Memory effect PA1 20 matrix (ACLR1), sim 2010 70 65 60 dBc -dB M1 M2 55 50 45 3 4 5 6 7 8 9 10 11 12 13 14 N Figure 41. PA1 matrix, gain 20 with memory effect 58 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect PA1 24 matrix (ACLR1), sim 2010 70 65 -dB dBc 60 M1 M2 55 50 45 3 4 5 6 7 8 9 10 11 12 13 14 N Figure 42. PA1 matrix, gain 24 with memory effect The memory-algorithm applied to the DPA at gain 20 shows the same big improvement as for the sample method, see Figure 43. While the M1 curve is dropping with higher N-values the M2 curve levels out on about 74 dBc. This behavior is further analyzed in chapter 4.4.4. 59 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect DPA 20 matrix (ACLR1), sim 2010 75 70 dBc -dB 65 M1 M2 60 55 50 44 5 5 66 77 88 99 10 1 11 1 12 1 13 1 N Figure 43. DPA matrix, gain 20 with memory effect With higher gain-levels the compensation for memory effect loses its effect and does not contribute to the linearization. The same results were observed in the DPA sample simulations. Figure 44 and Figure 45 show no improvement compared to the memory-less signal. The output signal of the PA is significantly more non-linear at higher gains, as can be seen in the charts, thus the memory-algorithm is not effective. 60 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Memory effect DPA 25 matrix (ACLR1), sim 2010 65 60 dBc -dB 55 M1 50 M2 45 40 35 4 4 55 66 77 88 9 9 10 1 11 1 121 N Figure 44. DPA matrix, gain 25 with memory effect Memory effect DPA 30 matrix (ACLR1), sim 2010 65 60 dBc -dB 55 M1 50 M2 45 40 35 4 5 6 N Figure 45. DPA matrix, gain 30 with memory effect 61 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Sample and Matrix simulation From the results we can conclude that there are no big differences between the sample and matrix method in linearizing a signal. In Figure 46 both the non-linear and the linearized appearance for PA1 is almost identical between the sample and matrix result. From the charts in chapter 4.4.4 and 4.4.5 we can see that the sample results are generally smoother than the matrix diagram plots. This is a plausible result because the sample method builds up the matrix sampleby-sample thus constantly tuning the linearization algorithm while the matrix method estimates a convenient average alpha-value to update the whole matrix using the LMS-algorithm. The sample method therefore provides a more accurate result than the matrix method but to the cost of more comprehensive calculations. The average simulation time in ADS for the sample method was approximately 20 minutes/simulation. For the matrix method it was about 10 minutes/iteration, with three iterations the overall simulation time was about 30 minutes. dBc 4.4.6 Figure 46. Comparison between non-linear and linearized signal PA1 for different gain-levels, without memory 62 Linköping University Master’s thesis dBc ADS and Matlab to Optimize Predistortion of Amplifiers Figure 47. Comparison between non-linear and linearized signal DPA for different gain-levels, without memory As for the PA1, the result for DPA shows the same characteristics regardless of if the sample or matrix method was used. The overall efficiency of the linearization technique is obvious when looking at Figure 46 and Figure 47 above. For gain-levels 20-24, for PA1, respectively 20-25, for DPA, the linearized signal shows a significant suppression of the IM-level by -20 to -25 dB for ACLR1, which very well exceeds the 3GPP standards. And as shown in chapter 4.4.5 that reduction can be further enhanced by compensation for memory effects. 63 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers 5 Summary and conclusions The simulation results show that digital predistortion is a very powerful and efficient way of linearizing the output signal and suppress IMD of a power amplifier. At the best, IMD was suppressed up to -24 dB for PA1 at gain 24 and -24 dB for DPA at gain 20. With compensation for memory effect IMD was suppressed up to -26 dB for PA1 and -33 dB for DPA. An integrated simulation environment for ADS and Matlab was successfully created within the work of this thesis. Matlab scripts could easily be used for predistortion algorithms in the digital domain together with analog simulations of component-based PA models by using the ADS Ptolemy engine with MatlabLiblink. The total simulation time was approximately 20 minutes for the sample method and 30 minutes for the matrix inversion method. The sample method proved to be the most accurate linearization algorithm. This method provided the expected results without much deviation. The matrix method did not show the same good results as the sample method as it suffered from substantial deviation in the results. The lack of a feedback path caused longer overall simulation time than the sample method because at least three iterations hade to be executed. In most cases it was also possible to find an optimal polynomial degree of the linearization-algorithm. As expected, the linearization effect did level out at a certain polynomial degree, making further polynomial modeling of the signal irrelevant and time-consuming. At low gain-levels it was apparent that ADS was able to simulate memory effects in the analog domain. The applied memory-algorithms to the linearization-algorithm showed a great improvement to the linearization of the output signal of the PA. These results would have been unlikely if memory effects did not exist in the simulations. At higher gain-levels though, the compensation for memory effects lost their efficiency which also was expected because the big non-linearitys of a saturated PA makes the memory effects a small part of the linearization problem. The PA1 proved to be the easiest power amplifier to linearize but saturated very sharply when exposed to high gain-levels. The Doherty PA could hang on a little longer at high gain-levels due to its auxiliary PA. 64 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers References Literature Anderson Harry, Fixed broadband wireless system design, Wiley, Chichester, U.K, 2003 Carne Bryan E, Telecommunications Primer: Signals, building blocks and networks, IEEE press, New York, U.S.A, 1995 Cripps Steve C, RF Power Amplifiers for Wireless Communications, Artech House, Boston, Massachusetts, U.S.A, 1999. Fitz Michael P, Fundamentals of Communications Systems, McGraw-Hill Companies, U.S.A, 2007 Groe John and Larson Lawrence, CDMA -Mobile Radio Design, Artech House, Boston, Massachusetts, U.S.A, 2000. Pierce John and Noll Michael, Signals -the science telecommunications, Scientific American Library, U.S.A, 1990 of Pothecary Nick, Feedforward Linear Power Amplifiers, Artech House, Boston, Massachusetts, U.S.A, 1999. Articles/Master Thesis/Papers Elgeryd T, Master Thesis: ADS and Matlab to Optimize Predistortion of Amplifiers, KTH, Stockholm, Sweden, 2003. Katz Allen, SSPA Linearization, Linearizer Technology Inc, Microwave Journal, U.S.A, 1999 Kokkeler A.B.J, Modeling Power Amplifiers using Memory Polynomials, University of Twente, Enschede, Netherlands, 2005 Kundert Ken, Simulation Methods for RF Integrated Circuits, Cadence Design Systems, San Jose, California, U.S.A, 1997 Raab F, Asbeck P et al. Power Amplifiers and Transmitters for RF and Microwave, Green Mountain Radio Research Company, Vermont, U.S.A, 2002 65 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Spångberg D, Master Thesis: Digital Pre-Distortion of Power Amplifiers, Uppsala University, Uppsala, Sweden, 2002 Yap How-Siang, Designing to Digital Wireless Specifications Using Circuit Envelope Simulation, HP Eesof Division, Hewlett-Packard, Asia Pacific Microwave Conference 1997 Zhu A, Pedro J. C. and Brazil T. J, Dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers, IEEE Transactions on Microwave theory and techniques, Vol 54, No 12, 2006 Technical Specifications 3GPP TS 25.104 v9.2.0, 3rd Generation Partnership Project; Technical Specification Group Radio Access Network (Release 9), 2009-12 66 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Appendix 1. Schematics of the PA1 and DPA The PA1 PA1- and DPA-DUT 67 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers The Doherty PA (DPA) Doherty structure 68 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Appendix 2. Schematics of the input and output matching networks Designing the input and output matching networks is an important part of the PA design. The goal is to find the matching networks that maximize the power delivered to a 50-Ohm load, which means a minimized reflection coefficient. By using the Smith chart and S-parameter simulations a matched amplifier can be found. The figures below give an idea of how a matching network can look like. 69 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers PA input-matching network 70 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers PA output-matching network 71 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Appendix 3. Top level schematics Sample PA1 top level 72 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Sample DPA top level 73 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Matrix PA1 top level 74 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Appendix 4. Schematics of modulators QAM-modulator QAM-demodulator 75 Linköping University Master’s thesis ADS and Matlab to Optimize Predistortion of Amplifiers Appendix 5. The WCDMA test signal There exist several different test models of WCDMA signals for different test purposes. The Test Model 1 (TM1) is employed in this thesis since according to the 3GPP specifications it should be used for ACLR measurements, which are central in this study. The WCDMA signal used here has a bandwidth of 5 MHz and a peak-to-average-ratio (PAR) of 7 dB. Its sampling frequency is chosen to be 61.44 MHz, which is equal to 16 times a chip rate of 3.84 MHz. 76

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertising