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Pre-Distortion Based Linearisation Technique for Power Amplifiers of Wideband Communication Systems Sangeeta Bawa, Maninder Pal, Jyoti Gupta

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Pre-Distortion Based Linearisation Technique for Power Amplifiers of Wideband Communication Systems Sangeeta Bawa, Maninder Pal, Jyoti Gupta International Journal of Scientific & Engineering Research, Volume 4, Issue 5, May-2013 726 ISSN 2229-5518 Pre-distortion Based Linearisation Technique for Power Amplifiers of Wideband Communication Systems Sangeeta Bawa, Maninder Pal, Jyoti Gupta Abstract— The high power amplifiers (HPAs) for CDMA and OFDM telecommunication systems need to be highly linear. However in practise, the response of HPA is non-linear which introduces distortion in signals being amplified. This response can be made linear using various linearization techniques. In this paper, an adaptive pre-distortion based linearization technique is introduced. It is based on adding pre-distortions into signals, which will result in cancellation of non-linear distortions appearing in power amplifier. The characteristics of this non-linear adaptive linearizer are represented by an analogue polynomial. In this paper, the coefficients of this polynomial are adjusted automatically in a manner that the output of linearizer when fed to an amplifier, the final output becomes error free and the whole system behaves like a linear amplifier. This helps reducing the distortion in power amplifiers, resulting in a better linearised output. Index Terms— Pre-distortion, High power amplifier, Linearization, Non-linear amplifier, Adaptive Linearizer, Perturbation based method. —————————— —————————— 1 INTRODUCTION ECENTLY, modern communication services such as OFDM form will contain the original sine wave and its harmonic distor- R and WCDMA have created a huge demand for highly linear tion products [4]. The harmonics can be eliminated by filtering high power amplifiers [1-2]. It is primarily because these and do not pose a problem except for wideband communication services require high power amplifiers supporting wideband applications requiring wide bandwidth. However, when more communications. In addition, these services also involve the than one carrier is present, additional new signals known inter- transmission of multiple signals and/or large quantities of infor- modulation distortions (IMDs) are produced in the vicinity of mation at high data rates. In HPAs, distortion of signals is usually input signals. The IMDs are located at frequencies above and be- produced by its non-linear response. This distortion is usually low the input carriers, and at frequency intervals equal to the sep- measured in terms of amplitude, although it also includes associ- arations of input carriers. Filtering cannot easily eliminate IMD ated abnormalities in phase [3]. For phase, the associated distor- products, as these are located on the same frequency or near to tion is called phase non-linearity. The term amplitude non-linearity the desired input signals. Therefore, a wide frequency range of can be considered as a measure of deviation from the desired operation of linearizer and high power amplifier is highly desira- straight-line behaviour and canIJSER be represented by the following ble. power series: 2 3 n Vout= K1Vin+ K2Vin + K3Vin ....+ KnVin (1) 2 LINEARIZATION TECHNIQUES Linearization can be referred as a procedure for reducing signal Where, K1, K2, K3,...,Kn are the coefficients of non-linear poly- distortions produced by the non-linear response of an amplifier. nomial, and Vin and Vout are the respective input and output of Several engineers and researchers have proposed and designed HPA. In situation, when a single carrier input signal, (say, a sine many models of linearizers such as feed-forward [3], feed back- wave), is substituted into this expression (1), the output wave- ward [5], envelope feedback system [6], cartesian feedback system [7] and predistortion [7-9]. However, these are associated with ———————————————— several drawbacks. The most common of these drawbacks in- • Sangeeta Bawa is currently pursuing Masters degree program in Electronics & Communication Engineering in Department of Electronics & Communica- clude: phase delay, reduction of the achievable bandwidth, deg- tion Engineering, of MM university, Mullana, Ambala, INDIA. radation of gain and phase margin, and low power efficiency for Email: [email protected]. low input signals [10]. Among the above mentioned linearization • Maninder Pal did his B.Tech in Electronics & Communication Engineering techniques, pre-distortion is the most commonly used. It is based from NIT, Kurukshetra, India in 2000 and MS in Digital Communication from Loughborough University in 2004. He carried out his research work in on the concept of inserting a nonlinear module between the input the area of signal processing and was awarded PhD in 2008 by Loughborough signal and power amplifier [11-12]. The nonlinear module gener- University. He worked for several years on various international projects in ates IMD products that are in anti-phase with the IMD products the domain of acoustics and signal processing. Presently, he is senior faculty produced by the power amplifier. These anti-phase IMD signals and research member in Electronics Department of MMU, Mullana, India. ideally cancels the IMDs produced by HPA; and thus, resulting in • Jyoti Gupta received the B.Tech degree in Electronics & Communication a better overall linearised behavior of the whole system. In this Engineering from Kurukshetra University, Kurukshetra, in 2004 and the paper, an adaptive linearizer is implemented using perturbation M.Tech degree from Rajasthan Vidyapeth University, Udaipur in 2006. She is working as an Asstt. Professor in MM University, India since 2008. Her re- based method; whereby, the characteristics of linearizer are repre- search interests include Speech Communication and power amplifier lineariza- sented by non-linear polynomials. tion techniques. IJSER © 2013 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 4, Issue 5, May-2013 727 ISSN 2229-5518 3 ADAPTIVE LINEARIZER ment, which varies the envelope of input signal (Vin) resulting in the signal (Vdout). This Vdout signal is fed to the amplifier such that The principle of an amplifier with an adaptive linearizer is ex- error(t) can be minimized. In this adaptive linearization tech- plained in Fig. 1. The output of non-linear amplifier is fed back to nique, perturbation based method is used to adjust the coeffi- the error detector after attenuating through a fixed attenuator. cients of polynomials in such a way that the error approaches to The error, due to non-linearity of amplifier, is calculated by taking zero and the output of an overall system (amplifier and linearizer) the difference of the attenuated output of the non-linear amplifier becomes closely to linear. and input signal. This error is fed to the adaptive linearizer ele- Fig. 1. Block diagram of a high power amplifier using the perturbation based adaptive linearization technique. The transfer characteristics of a HPA and adaptive linearizer characteristics of linearizer can be expressed as: shown above in Fig. 1 can be expressed as polynomial. In general, = + +3 +5 + + 2*N− 1 for any input x, the polynomial of nth order is given by: Vdout a0 a 1 Vin a3 ( Vin ) a5 ( Vin ) ... a2*N − 1 ( Vin ) (5) The coefficients of this polynomial (expression 5), representing IJSERN 2 3 N −1 N i the characteristics of adaptive linearizer are adjusted in such a yxwwxwxwx() =0 + 1 + 2 +3 +... + wxN −1 + wxN = ∑ wxi i=0 (2) way that the characteristics of adaptive linearizer are inverse to that of the non-linear amplifier. If the output signal from such a where, w0, w 1 , w 2 ,..., wN are the coefficients of polynomial. linearizer is fed to the non-linear amplifier; then it will give a line- According to the pre-distortion linearization theory, the response arised output. The value of the coefficients a0, a1, a3,... of the adap- of linearizer is made equal in amplitude and antiphase of the tive linearizer are calculated using the algorithm based on pertur- IMDs generated by the amplifier [9]. As shown in Fig. 1, the char- bation based approximation method, mentioned below and as acteristics of HPA represents closely to tangent hyperbolic func- shown in Fig. 2. tions; which can be represented in polynomial form (say, up to 5th order) as: 4 Algorithm 3 5 Tanh(t) =0.9971*t -0.3076*t + 0.0725*t (3) 1. Start if there is an error i.e. error~0. Calculate the Error for one It can be interpreted from (3) that it comprises only of odd terms complete cycle and take this as the initial error (Error_initial). The and the coefficients of each of the alternate terms after the third cycle time depends upon the input signal time period. order term change the sign alternatively. Therefore, the general 2. Increment the first coefficient of adaptive linearizer polynomial, expression for characteristics (as shown in Fig. 1) of HPA can be a1 by ∆ i.e. a1 →a1 + ∆, where, ∆ is the step size (Initially, a1 =1 represented as: and all other coefficients are zero). 3. Calculate the error (Error′) per cycle of the input waveform. V= w + w( V )+ w ( V )3 + w ( V )5 + ... + w ( V )2*N− 1 out 0 1 dout 3 dout 5 dout 2*N− 1 dout Compare this error with the initial error (Error′_initial). N (4) = + (2*i− 1) w0 ∑ w(2*i− 1) () V dout 4. If this error (Error′) is less than the initial value (Error_initial), i=0 i.e. initial error, then consider this error as the reference error where, Vdout and Vout are respectively the input and output of the (Error_Reference) and value of a1 remains the same (as in step 2) non-linear amplifier shown in Fig. 1. As the characteristics of line- else if the Error′ is increased, then the steps 2 to 4 is repeated by arizer in Fig. 1 is anti-phase to nullify the effect of higher order- decrementing the value of a1 by 2∆, i.e. a1 → a1-2∆. terms in (expression 4); therefore, the polynomial representing the IJSER © 2013 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 4, Issue 5, May-2013 728 ISSN 2229-5518 5.
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