An Improved Pre-Distortion Algorithm Based On Indirect Learning Architecture for Nonlinear Power Amplifiers Wei You, Daoxing Guo, Yi Xu, Ziping Zhang

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1 6 nd International Conference on Mechanical, Electronic and Information Technology Engineering (ICMITE 6) ISBN: An Improved Pre-Distortion Algorithm Based On Indirect Learning Architecture for Nonlinear Power Amplifiers Wei You, Daoxing Guo, Yi Xu, Ziping Zhang PLA University of Science and Technology, College of Communication Engineering Keywords: Pre-Distortion; Nonlinear Power Amplifier; Indirect Learning Architecture; Error Vector Amplitude Abstract. With the rapid development of wireless communication techniques, the main limitations of wireless communications lie in spectrum resource constraints and nonlinearity of high amplifier power (PA). Albeit exploring high-order modulation improves the spectrum efficiency significantly, however, the nonlinear distortion seriously degrades the performance especially when nonlinearity sensitive high-order non-constant envelop modulation signal pass through the saturate regime of PA. Due to the good performance in linearization, adaptive baseband digital pre-distortion has been widely developed and applied. Particularly, the optimization of the parameters for adaptive pre-distortion algorithm has a positive impact on linearization. In this paper, an improved algorithm is proposed to determine the optimum step by taking maximum error vector magnitude EVM improvement as the objective function. And thus the nonlinearity of power amplifier is compensated with indirect learning architecture and optimum step adaptive algorithm. Simulation results demonstrate that the constellations are well compensated and out-band power spectrum regenerations are significantly suppressed, which yields a satisfactory system performance linearization. Introduction With the rapid development of communication technology, diverse kinds of communication business are claimed by people. Nowadays, high-order signal modulation and transmission technologies are widely used to improve the utilization of spectrum resources. To this end, digital transmission technology with high spectral efficiency came into being, one of which is quadrature amplitude modulation (Quadrature Amplitude Modulation, QAM). Generally speaking, these new technologies have a non-constant envelope and high peak to average ratio, which will lead to more serious inner band distortion and outer band interference caused by nonlinearity of power amplifier. In order to maintain a linear relationship between the input and output of power amplifier, adaptive digital pre-distortion of baseband has been widely studied and applied. By inserting pre-distorter before power amplifier, the algorithm modifies the input signal automatically, which yields the linearity for power amplifier output signal. Moreover, characteristic variations of power amplifier caused by temperature, power supply variations, aging and other factors could be compensated adaptively. Particularly, the optimization of step factor has a positive impact on linearization compensation. In this paper, an improved algorithm is proposed to determine the optimum step by taking maximum error vector magnitude EVM improvement as the objective function. And thus the nonlinearity of power amplifier is compensated with indirect learning architecture [] and optimum step LMS adaptive algorithm []. The Nonlinear Model. Power Amplifier Model In order to model the nonlinearity of power amplifier, we use Saleh model for analysis. Based on statistics and analysis, Saleh model was established in accordance with input and output signal characteristics, which could describe the nonlinearity of power amplifier more accurately in a simple form. Saleh model explores two expressions to present the instantaneous amplitude of envelope to 49

2 show AM / AM and AM / PM characteristics, and the amplitude and phase expressions is, respectively, given by:.587 xt ( ) 4.33 xt ( ) Ax [ t], [ xt ( )] ().57 x( t) 9.7 x( t) The expression of output signal after power amplifier is: yt ( ) Axt [ ( )]exp j( [ xt ( )]) (). Pre-distorter Model Pre-distorter is essentially a non-linear model. In the paper, we use non-linear polynomial model to calculate and analyse the predistortion module, thus is expressed as: where K is the non-linear order. ( ) K k - k ( ) ( ) k = yn = å a xn xn (3) 3 The Improved Pre-Distortion Algorithm The selection and identification of the pre-distorter model are two key parts in pre-distortion system. When the model is determined, the extraction of model parameters affects the accuracy of pre-distortion system. We adopt indirect learning architecture for its simple structure as well as easily implement. 3. Indirect Learning Architecture Both simple structure and low complexity are advantages of indirect pre-distortion learning architecture[6]. Especially, there is no need to know specific model and parameters of power amplifier when estimating coefficients of pre-distorter. Figure shows the indirect pre-distortion adaptive learning architecture. With the adjustment of gain, the output signal of power amplifier zn ( ) is taken as input signal of pre-distortion learning and training network. By comparison between pre-distortion signal yn ( ) and output signal of training network yn ˆ( ), error en ( ) yn ( ) yn ˆ( ) is obtained as parameters which will be sent to the pre-distorter. If the algorithm converges,then en ( ), namely yn ( ) yn ˆ( ) and zn ( )/ G xn ( ). The indirect learning architecture adopts post inverse structure which reduces the sensitivity of signal parameters, and real-time closed-loop system as well as adaptive algorithm. x( n) z n en ( ) yn ( ) yn ˆ( ) G Figure. The indirect learning architecture for nonlinear compensation. 3. The Improved Pre-Distortion Algorithm: In accordance with the changes of estimation error, LMS adaptive algorithm adjusts tap coefficients of a finite impulse response filter automatically, so that the cost function could be 43

3 minimized. Suppose x( n ) denotes the input vector of FIR filter whereas yn ( ) denotes the output vector of filter, and tap coefficient of filter is represented by ( n). Thus, y( n) ( n) x( n). Assume dnincicates ( ) the desired signal,then the difference en ( ) between output signal of FIR filter y( n) and desired signal dncould ( ) be denoted by: T e n d n y n d n n x n d n x n n (4) The most common criterion in filter design is minimum mean square error criterion,(minimum Mean Square Error,MMSE)i.e., in order to minimize the mean square error between expected response and actual output of filter, we define the cost function as below: def ( ) = E{ ( ) } = E{ ( ) -w ( ) } J n e n d n x n (5) The aim of filter design is to find the appropriate filter coefficient matrix ( n) so that J ( n) can achieve its minimum. Solving by gradient descent method, hereafter: w( n) = w( n-) - m( n) ÑJ ( n- ) (6) where: * Ñ J( n) = - E{ u( n) d ( n) } + E{ u( n) u ( n )} w ( n) (7) The real gradient vector and instantaneous gradient vector are a pair of unbiased estimators: E{ ˆ ( )} E{ ( ) é * Ñ J n = - u n ( ) - ( ) w ( n- ) ù ëd n u n û} =ÑJ( n ) (8) Replace ÑJn ( -) by instantaneous gradient vector Ñ ˆ Jn ( - ),then: w( n ) = w( n - ) + m( n ) e( n) x( n ) (9) If m( n) is a constant, it is called fixed step LMS algorithm. Otherwise, we call it variable step LMS algorithm. Thanks to its easy calculation and well compensation performance, LMS adaptive algorithm has been widely used in engineering. owever, it is critical to select step factor. If it s set as a small value, the nonlinear distortion could not be well compensated. owever, if it is too large, the stability of system could not guarnteed. Since the constellation is merely a qualitative evaluation criterion, error vector magnitude EVM, which is used to describe power amplifier pre-distortion performance, is a remarkable quantitative index to measure amplitude and phase errors of modulated signal. Mathematical expression of EVM is shown as below[6]: N N i i i i i EVM y x x () where y i is a test vector signal, and x i represents the original reference signal. In this paper, an optimization criterion for step factor is put forward, that is, maximize EVM improvement to obtain optimal step factor: step max EVM EVM () opti PA PD step : size: step Therefore, the optimum step length for LMS algorithm is yielded based on the maximum of EVM improvement. 4. Simulation and Discussion In this section, we adopt 64QAM modulation signal as the simulation test signal with 5 symbols. The roll-off factor of shaping filter is.5 with 8 times the sampling, and the polynomial nonlinear order is 3. 43

4 EVM_improved The optimal value of EVM step factor Figure. The EVM improvement versus step factor based on LMS algorithm. From Fig. we can learn that the EVM improvement gradually rises and reaches to a peak with the increasing of step factor, but adaptive algorithm will be instable if step factor continues to increase. Therefore, the step factor corresponding to the maximum EVM improvement is what we need. Therefore, we set the step factor 3.35 for proceeding simulations. Therefore, further simulations are provided to verify the pre-distortion performance of system. Q component(v) without pre-distorter with pre-distorter ideal constellation Power spectrum density (db/rad/sample) linear channel with pre-distorter without pre-distorter I component(v) Normalized frequency( rad/sample) Figure 3. The constellation and PSD characteristics comparison for considered pre-distortion algorithm. Fig.3 shows the comparison of constellation and power spectral density plots, respectively, before and after pre-distortion. As can be seen from Fig.4, without pre-distortion, the radius of the constellation expands and constellation points diverge seriously due to the nonlinear distortion effects, which interferes with demodulating signal correctly. Nevertheless, after pre-distortion, the position offset of constellation vector is corrected obviously, and the suppression of nonlinearity performs remarkably. Under no pre-distortion circumstances, significant external expansion occurs in power spectrum of output signal, seriously interfering with adjacent channels. After pre-distortion, the regeneration out of band is significantly suppressed. The constellation and power spectral density simulation results well reveal that the nonlinear distortion is well compensated by the optimum step factor adaptive pre-distortion algorithm. 43

5 The angle of output signal (degree) The amplitute of output signal (V) The AM-PM characteristic without pre-distorter The AM-PM characteristic with pre-distorter 5.9 The AM-AM characteristic without pre-distorter The AM-AM characteristic with pre-distorter The amplitute of input signal (V) The amplitute of input signal (V).8.9 Figure 4. The AM-AM and AM-PM characteristics comparison for considered pre-distortion algorithm. Fig.4 obviously shows that without pre-distortion compensation, AM-AM characteristic of power amplifier performs significant nonlinearity. Similarly, AM-PM characteristic has a clear nonlinear distortion, too. After adaptive pre-distortion compensation, the AM-AM and AM-PM nonlinear characteristics of power amplifier have been significantly improved, which demonstrate that the nonlinear distortion of power amplifier has been well compensated by our proposed algorithm. 5 Conclusions In this paper, an improved algorithm is proposed to determine the optimum step by taking maximum error vector magnitude EVM improvement as the objective function. In proceeding, the nonlinearity of power amplifier is compensated with indirect learning architecture and optimum step adaptive predistortion algorithm. Simulation results demonstrate the effectiveness of our proposed algorithm and satisfactory system performance linearization is achieved. References [] Zhu A., Draxler P.J., Yan J.J., et al. Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series [J]. IEEE Transactions on Microwave Theory and Techniques, 8, 56(7): [] X. Dian and Z.B. Zeng. An Improved Adaptive Algorithm for Digital Predistortion [C]\\ International Conference on Computer Science and Electronics Engineering.. pp: [3] Saleh A.A.M., Salz J. Adaptive linearization of power amplifiers in digital radio systems[j].the Bell System Technical Journal,983, 6(4): 9-33 [4] Bo L., Jian-hua G., Bo A. A novel polynomial model for power amplifiers digital pre-distortion [C]\\ IEEE International Conference on Wireless Communications, Networking and Mobile Computing, 8. [5] R. Mondal, T. Rstaniemi, M. Doula. Genetic Algorithm Optimized Memory Polynomial Digital Pre Distorter for RF Power Amplifiers [C]\\ IEEE International Conference on Wireless Communications Signal Processing, angzhou, pp: -5, 3. [6] F. Li. Research on digital pre-distortion for RF power amplifiers [D]. University of Electronic Science and Technology of China, 3(in Chinese). 433

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