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New predistorter using triangular memory polynomial for power amplifier of OFDM-based wireless broadband communication system
The Journal of China Universities of Posts and Telecommunications April 2012, 19(2): 43–47 www.sciencedirect.com/science/journal/10058885
http://jcupt.xsw.bupt.cn
New predistorter using triangular memory polynomial for power amplifier of OFDM-based wireless broadband communication system YU Cui-ping (), LIU Yuan-an, DU Tian-jiao, LI Shu-lan School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract A triangular memory polynomial (TMP) predistorter is presented in this paper to linearize a power amplifier’s nonlinear with memory effects. Compared with the traditional memory polynomial (MP) predistorter, the coefficients of TMP predistorter is reduced more than 75%, which can effectively decrease the implementation complexity. The coefficients of predistorter are directly extracted from an offline system identification process by an open-loop structure in our approach. Several signals with data rate 5 MHz, 10 MHz, 15 MHz and 20 MHz are used to verify the performance of the proposed predistorter. Experimental results show that the proposed TMP predistorter and the traditional MP predistorter almost have the same performance. Keywords
power amplifier, predistortion, memory effects, memory polynomial
1 Introduction In order to address the ever-increasing demand for spectrum efficiency, more wireless communication technology with non-constant envelope signals such as orthogonal frequency division multiplex (OFDM) have been adopted in the new and upcoming wireless communication standards. OFDM-based technology have higher peak-to-average power ratio (PAPR), which imposing stronger linearity requirements on radio frequency (RF) power amplifier (PA) [1–3]. Of all linearization techniques, predistortion is among the most effective and popular [4]. Several behavioral models of PAs have been proposed to model and linearize the PA’s nonlinearity with memory effects. Such as Volterra model [5–6], Wiener model [7–8], parallel-Wiener model [9], Wiener-Hammerstein model [10], MP model [4], some parallel-models [11] and neural network models [12–13] etc. A MP-based predistorter is shown to be a good predistorter [2] owing to its robust Received date: 20-06-2011 Corresponding author: YU Cui-ping, E-mail: [email protected] DOI: 10.1016/S1005-8885(11)60244-6
and low complexity, such as generalized memory polynomial (GMP) model [14], envelop-memory polynomial (EMP) model [15] and some parallel model including MP model [11,16]etc. But when long-term memory effects [17] are considered, MP model requires a large number of coefficients, and shows a slow convergence of root mean square by adding delay taps. While modeling a PA, these problems can be improved by using sparse delay taps MP introduced by Ref. [18]. In practical applications, linearization is the ultimate objective. In this paper, a predistorter with low complexity and high performance is suggested to efficiently predistort a PA’s nonlinearity with memory. For a predistorter usually, the sparse-delay memory polynomial model is unsuitable due to its high computational complexity in finding the optimum delay taps. To solve this problem, a TMP predistorter is proposed in our scheme. Instead of constant maximum nonlinear order in a MP predistorter, the proposed TMP predistorter has non-constant maximum nonlinear order. Compared with the traditional MP predistorter, the TMP predistorter can efficiently decrease the number of coefficients, especially when long-term memory effects are considered. Corresponding open-loop
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The Journal of China Universities of Posts and Telecommunications
structure [19] and identification algorithm are also detailed. Owing to the open-loop structure, the coefficients of the proposed predistorter can be directly extracted from the sampled input and output of a PA with a simple offline process. The linearization performance of a TMP predistorter is tested on a measure set-up. The experimental results show that the TMP predistorter can work as well as the traditional MP predistorter, but with fewer coefficients. This method also can be used for GMP model [14]EMP model [15] and some parallel model including MP model [11,16]etc. This paper is organized as follows: Sect. 1 is the introduction. Sect. 2 describes a new TMP model for predistorter. Sect. 3 is the open-loop structure and the coefficients extraction method. The experimental results are given in Sect. 4, with a conclusion in Sect. 5.
2
Triangular memory polynomial model
2012
nonlinearity order and maximum memory order, in the MP model, the number of coefficients increases linearly with the order of nonlinearity and maximum memory order. Yet when long-term memory effects are considered, the maximum memory order will be large, especially in OFDM-based wireless broadband communication system. This results in a large number of coefficients and high computational complexity. To reduce the number of coefficients, a TMP predistorter is proposed based on this phenomenon which the effects of nonlinear dynamics tend to fade with increasing order in many real PAs [6]. As shown in Fig. 1, the Kth order polynomial of x(n) represents a PA’s memoryless nonlinearity, the other’s polynomial of x(n − q) represent a PA’s memory nonlinearity, and the maximum nonlinear order of the past input decrease with the memory order. When Q>K, the maximum nonlinear order N of x(n − q) will equal to 1.
Considering a traditional MP predistorter with input x(n) and output y(n) as follows, K
Q
y (n) = ∑∑ akq x (n − q) | x (n − q) |k −1
(1)
k =1 q = 0
where K is the maximum nonlinearity order, Q is the maximum memory order. In (1), a Kth order polynomial of x(n − q ), (q = 0,1,..., Q) is used to represent its contribution to the output y(n). In another words, the maximum nonlinear order is constant for every input. Since the effects of nonlinear dynamics tend to fade with increasing memory order in many real PAs [6], we can try to adjust the maximum nonlinear order of the past input to decrease the number of coefficients and keep the linearity of the predistorter-PA chain. Let K=N, and N is defined as following: ⎧ K − q; q < K N =⎨ (2) ⎩1; qK then Eq. (1) becomes: Q
N
y (n) = ∑∑ akq x (n − q) | x (n − q) |k −1
(3)
q =1 k =1
where N is the maximum nonlinearity order, Q is the maximum memory order. In Eq. (3), the maximum nonlinear order N is non-constant and varies with memory order. We refer to Eq. (3) as the TMP model. A MP model is a truncation of the general Volterra model when only diagonal terms in Volterra kernels are considered. Unlike the classical Volterra model, where the number of coefficients increases exponentially with the
Fig. 1 Structure of TMP model when Q>K
3 System identification Fig. 2 is the coefficients extraction scheme of the proposed predistorter with open-loop structure [19]. Instead of establishing PA’s behavioral model, we suppose to build a new predistortion approach, which extracts the coefficients of the predistorter directly from the input and output data of a PA. This structure eliminates the real-time closed-loop adaptation requirement, and allows us to extract the parameters through a simple offline process.
Fig. 2
Structure of system identification
Issue 2
YU Cui-ping, et al. / New predistorter using triangular memory polynomial for power amplifier of…
As we know, the characteristic of a predistorter and the characteristic of a PA are inverse. In Ref. [5], it is shown that if one has a pth-order post-inverse of a general Volterra system, then the pth-order pre-inverse is identical. MP model is a special case of Volterra model [4]. Thus, for arbitrary order of approximation, predistortion is equivalent to postdistortion in our application. If the input and output data of a PA are represented by X and Y (scaled) respectively, then the characteristic of the corresponding predistorter can be extracted from X and Y. If the output of the predistorter is expected to be X, then Y should be its input. Now the output X and input Y of the predistorter are given. In order to extract the coefficients of the TMP predistorter, the TMP function is represented by a matrix equation. From the given input data Y and output data X in the time domain, we can define X = [ x(l ) x (l + 1) L x (l + L − 1)]T (4) and H = [ H0 L H q L HQ ]
(12)
4 Simulation and experimental results 4.1 Simulation The proposed TMP model and the traditional MP model were simultaneously used to model a Wiener-Hammerstein model PA, traditional MP model PA and parallel-wiener model PA, respectively. The simulation results are shown in Table 1. Compare with the traditional MP model [4], the proposed TMP model can decrease the number of coefficients by 43%–55%. This is very important for the realization of a predistorter. Let K=7 and Q=5, only odd order are considered, for traditional MP, in coefficients extraction step, the dimension of matrix H is N×24, but for TMP, the dimension of matrix H are decreased to N×12, this will decrease the memory consumption and predistortion latency. Tabel 1 PA model
(5)
where ⎡ h1,q (l ) ⎢ h1,q (l + 1) H q = ⎢⎢ M ⎢ ⎢⎣ h1,q (l + L − 1)
Xˆ = Ηaˆ
h2, q (l )
hN ,q (l ) ⎤ ⎥ h2,q (l + 1) L hN , q (l + 1) ⎥ ⎥ M M ⎥ h2,q (l + L − 1)L hN , q (l + L − 1) ⎥⎦
and hk , q (l ) =| y (l − q) |k −1 y (l − q)
L
(6)
(7)
45
Wiener-Hammerstein model Memory Polynomial model Parallel-Wiener model
Comparision of different predistorter The number The number NMSE of of coefficients coefficients (NMSE MP−NMSE TMP)/dB with TMP with MP 40
18
0.767 8
16
9
− 0.001 4
24
12
0.009 1
In order to prove the superiority of the TMP model, both the traditional MP method and the proposed TMP method were used to model a real PA. The simulation results were shown in Fig. 3.
Let the complex coefficients be represented as following: a = [a0 L aq L aQ ]T (8) there aq = [a1, q a2, q L aN , q ]
(9)
Eq. (3) with L consecutive time-domain data points can be represented with a matrix equation such as (10) X = Ha where X is an L×1 vector, H is an L × [(Q + 1)( K − Q / 2)] matrix (Q
Fig. 3 Difference of NMSEMP and NMSETMP vs. the nonlinear order K and the memory order Q
expected coefficients can be computed by the following equation: (11) aˆ = H −1 X −1 where H denotes the pseudoinverse matrix of H. aˆ is the least square root. Then
The positive number means the normalized mean square error (NMSE) attained by traditional MP predistorter is better than the proposed TMP predistorter. When maximum nonlinear order K varies from 7 to 13, the memory order varies from 1 to 15, the NMSE difference between the traditional MP and the proposed TMP
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The Journal of China Universities of Posts and Telecommunications
predistorter is less than 0.8 dB. At the same time, the number of coefficients can be reduced more than 75%. Fig. 4 shows the percent of coefficients decreased by TMP model versus the nonlinear order K and the memory order Q.
without predistortion. Trace b shows the output spectrum with the traditional memory polynomial predistortion with nonlinearity order K=11 and memory order Q=6 delay taps, and trace c shows the output spectrum with the proposed TMP predistorter using the same nonlinearity and memory order. The same conclusion can be drawn that the TMP predistorter can get as good performance as traditional MP predistorter with only 48% coefficients number. Tabel 2
ACPR performance of different predistorter
Data rate/MHz No predistorter MP predistorter TMP predistorter
Fig. 4 Percent of coefficients decreased by TMP model vs. the nonlinear order K and the memory order Q
2012
The percent of coefficients decreased by a TMP predistorter/%
5 − 36.86/ − 37.53 − 50.26/ − 48.20 − 50.43/ − 47.87
10 − 36.60/ − 37.53 − 49.42/ − 49.57 − 49.68/ − 49.97
15 − 37.56/ − 38.38 − 49.42/ − 48.53 − 49.28/ − 48.76
20 − 37.22/ − 37.39 − 49.31/ − 47.88 − 49.36/ − 47.87
48.57
48.57
48.57
52.38
4.2 Experiment Fig. 5 shows a block diagram of the experimental test setup. The predistortion algorithm is run in the PC. The Agilent vector signal generator E4438C and Signal analyzer N9030A are used to generate the predistorted signal and collect the PA response through networking with the PC.
Fig. 6
Experimental power spectrum
5 Conclusions Fig. 5
Measured set-up blocks
Both traditional MP predistorter and the proposed TMP predistorter were tested. The measured results as well as the number of coefficients are listed in Table 2. The second, third and fourth rows are the adjacent channel power ratio (ACPR) measured in the lower and upper adjacent channel slots. Finally, the last row shows the percent of coefficients reduced by TMP predistorter. It can be seen that the TMP predistorter can get almost the same ACPR performance as the traditional MP predistorter when the data rate varied from 5 MHz to 20 MHz. But the number of coefficients is reduced by more than 48% compared with traditional memory polynomial predistorter. Fig. 6 shows the output spectrum of the signal with 15 MHz data rate when different predistorter are applied. Trace a shows the spectral regrowth of the amplifier output
To linearize a PA’s nonlinear with memory effects, a new predistorter model with fewer coefficients and good performance is presented. By adjusting the maximum nonlinear order of the past input, the number of coefficients is reduced by up to 75%. An open-loop structure is used in the system identification, which allows us to extract the coefficients by a simple offline process. Based on the structure, we develop a prototype of the predistorter with data rate 5 MHz, 10 MHz, 15 MHz, and 20 MHz. Simulation results show that when maximum nonlinear order K varies from 7 to 13, the memory order varies from 1–15, the NMSE difference between the traditional MP predistorter and the proposed TMP predistorter is less than 0.8 dB. The ACPR performance is also validated by experiments. It can be seen from experimental results that the proposed TMP predistorter
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YU Cui-ping, et al. / New predistorter using triangular memory polynomial for power amplifier of…
performs almost same as the memory polynomial predistorter in terms of linearizing PAs. But the number of coefficients of TMP predistorter can be reduced by more than 50%. Acknowledgements This work was supported by the National Science and Technology Major Project (2010ZX03007-003-04).
10.
11.
12.
References 13. 1. Kwan1 A, Hammi O, Helaoue M, et al. High performance wideband digital predistortion platform for 3G+ applications with better than 55dBc over 40 MHz bandwidth. Proceedings of the 2010 IEEE MTT-S International Microwave Symposium (MTT-S’10), May 23−28, 2010, Anaheim, CA, USA. Piscataway, NJ, USA: IEEE, 2010: 1082−1085 2. Roblin P, Keun S, Chaillot D M, et al. Frequency-selective predistortion linearization of RF power amplifiers. IEEE Transactions on Microwave Theory and Techniques, 2008, 56(1): 65−76 3. Sung C J, Hammi O, Ghannouchi F M. Design optimization and DPD linearization of GaN-based unsymmetrical Doherty power amplifiers for 3G multicarrier applications. IEEE Transactions on Microwave Theory and Techniques, 2009, 57(9): 2105−2113 4. Lei D, Zhou G T, Morgan D R, et al. A robust digital baseband predistorter constructed using memory polynomials. IEEE Transactions on Communications, 2004, 52(1): 159−165 5. Schetzen M. The Volterra and Wiener theories of nonlinearsystems. New York, NY, USA: Wiley, 1980 6. Zhu A, Pedro J C, Brazil T J. Dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers. IEEE Transactions on Microwave Theory and Techniques, 2006, 54(12): 4323−4332 7. Isaksson M, Wisell D, Ronnow D. A comparative analysis of behavioral models for RF power amplifiers. IEEE Transactions on Microwave Theory and Techniques, 2006, 54(1): 348−359 8. Gilabert P, Montoro P, Bertran E. On the Wiener and Hammerstein models for power amplifier predistortion. Asia-Pacific Microwave Conference Proceedings (APMC’05): Vol 2, Dec 4−7, 2005, Suzhou, China. Piscataway, NJ, USA: IEEE, 2005: 4p 9. Silveira D, Gadringer M, Arthaber H, et al. RF-power amplifier characteristics determination using parallel cascade Wiener models and
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pseudo-inverse technique. Asia-Pacific Microwave Conference Proceedings (APMC’05): Vol 1, Dec 4-7, 2005, Suzhou, China. Piscataway, NJ, USA: IEEE, 2005: 4p Ding Y M, Sano A. Time-domain adaptive predistortion fornonlinear amplifiers. Proceedings of the 29th International Conference on Acoustics, Speech, and Signal Proceesing (ICASSP’04): Vol 2, Mar 17−21, 2004, Montreal, Canada. Piscataway, NJ, USA: IEEE, 2004: 865−868 Hammi O, Ghannouchi F M. Twin nonlinear two-box models for power amplifiers and transmitters exhibiting memory effects with application to digital predistortion. IEEE Microwave and Wireless Components Letters, 2009, 19(8): 530−532 Mkadem F, Boumaiza S. Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion. IEEE Transactions on Microwave Theory and Techniques, 2011, 59(4): 913−923 Rawat M, Rawat K, Ghannouchi F M. Adaptive digital predistortion of wireless power amplifiers transmitters using dynamic real-valued focused time-delay line neural networks. IEEE Transactions on Microwave Theory and Techniques, 2010, 58(1): 95−104 Morgan D, Ma Z, Kim J, et al. A generalized memory polynomial model for digital predistortion of RF power amplifiers. IEEE Transactions on Signal Processing, 2006, 54(10): 3852−3860 Hammi O, Ghannouchi F M, Vassilakis B. A compact envelope-memory polynomial for RF transmitters modeling with application to baseband and RF-digital predistortion. IEEE Microwave and Wireless Components Letters, 2008, 18(5): 359−361 Hammi O, Younes M, Ghannouchi F M. Metrics and methods for benchmarking of RF transmitter behavioral models with application to the development of a hybrid memory polynomial model. IEEE Transactions on Broadcasting, 2010, 56(3): 350−357 Santos R E, Carvalho N B, Gard K. The impact of long term memory effects in wireless QPSK modulated signals. Proceedings of the 2007 IEEE MTT-S International Microwave Symposium (MTT-S’07), Jun 3−8, 2007, Honolulu, HI, USA. Piscataway, NJ, USA: IEEE, 2007: 961−964 Hyunchul K, Kenney J S. Behavioral modeling of nonlinear RF power amplifiers considering memory effects. IEEE Transactions on Microwave Theory and Techniques, 2003, 51(12): 2495−2504 Yu C P, Feng Y S, Liu Y A, et al. Memory polynomial digital predistortion for power amplifiers. Proceedings of the International Symposium on Communications and Information Technologies (ISCIT’07), Oct 17−19, 2007, Sydney, Australia. Piscataway, NJ, USA: IEEE, 2007: 12−15
(Editor: ZHANG Ying)
http://jcupt.xsw.bupt.cn
New predistorter using triangular memory polynomial for power amplifier of OFDM-based wireless broadband communication system YU Cui-ping (), LIU Yuan-an, DU Tian-jiao, LI Shu-lan School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract A triangular memory polynomial (TMP) predistorter is presented in this paper to linearize a power amplifier’s nonlinear with memory effects. Compared with the traditional memory polynomial (MP) predistorter, the coefficients of TMP predistorter is reduced more than 75%, which can effectively decrease the implementation complexity. The coefficients of predistorter are directly extracted from an offline system identification process by an open-loop structure in our approach. Several signals with data rate 5 MHz, 10 MHz, 15 MHz and 20 MHz are used to verify the performance of the proposed predistorter. Experimental results show that the proposed TMP predistorter and the traditional MP predistorter almost have the same performance. Keywords
power amplifier, predistortion, memory effects, memory polynomial
1 Introduction In order to address the ever-increasing demand for spectrum efficiency, more wireless communication technology with non-constant envelope signals such as orthogonal frequency division multiplex (OFDM) have been adopted in the new and upcoming wireless communication standards. OFDM-based technology have higher peak-to-average power ratio (PAPR), which imposing stronger linearity requirements on radio frequency (RF) power amplifier (PA) [1–3]. Of all linearization techniques, predistortion is among the most effective and popular [4]. Several behavioral models of PAs have been proposed to model and linearize the PA’s nonlinearity with memory effects. Such as Volterra model [5–6], Wiener model [7–8], parallel-Wiener model [9], Wiener-Hammerstein model [10], MP model [4], some parallel-models [11] and neural network models [12–13] etc. A MP-based predistorter is shown to be a good predistorter [2] owing to its robust Received date: 20-06-2011 Corresponding author: YU Cui-ping, E-mail: [email protected] DOI: 10.1016/S1005-8885(11)60244-6
and low complexity, such as generalized memory polynomial (GMP) model [14], envelop-memory polynomial (EMP) model [15] and some parallel model including MP model [11,16]etc. But when long-term memory effects [17] are considered, MP model requires a large number of coefficients, and shows a slow convergence of root mean square by adding delay taps. While modeling a PA, these problems can be improved by using sparse delay taps MP introduced by Ref. [18]. In practical applications, linearization is the ultimate objective. In this paper, a predistorter with low complexity and high performance is suggested to efficiently predistort a PA’s nonlinearity with memory. For a predistorter usually, the sparse-delay memory polynomial model is unsuitable due to its high computational complexity in finding the optimum delay taps. To solve this problem, a TMP predistorter is proposed in our scheme. Instead of constant maximum nonlinear order in a MP predistorter, the proposed TMP predistorter has non-constant maximum nonlinear order. Compared with the traditional MP predistorter, the TMP predistorter can efficiently decrease the number of coefficients, especially when long-term memory effects are considered. Corresponding open-loop
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The Journal of China Universities of Posts and Telecommunications
structure [19] and identification algorithm are also detailed. Owing to the open-loop structure, the coefficients of the proposed predistorter can be directly extracted from the sampled input and output of a PA with a simple offline process. The linearization performance of a TMP predistorter is tested on a measure set-up. The experimental results show that the TMP predistorter can work as well as the traditional MP predistorter, but with fewer coefficients. This method also can be used for GMP model [14]EMP model [15] and some parallel model including MP model [11,16]etc. This paper is organized as follows: Sect. 1 is the introduction. Sect. 2 describes a new TMP model for predistorter. Sect. 3 is the open-loop structure and the coefficients extraction method. The experimental results are given in Sect. 4, with a conclusion in Sect. 5.
2
Triangular memory polynomial model
2012
nonlinearity order and maximum memory order, in the MP model, the number of coefficients increases linearly with the order of nonlinearity and maximum memory order. Yet when long-term memory effects are considered, the maximum memory order will be large, especially in OFDM-based wireless broadband communication system. This results in a large number of coefficients and high computational complexity. To reduce the number of coefficients, a TMP predistorter is proposed based on this phenomenon which the effects of nonlinear dynamics tend to fade with increasing order in many real PAs [6]. As shown in Fig. 1, the Kth order polynomial of x(n) represents a PA’s memoryless nonlinearity, the other’s polynomial of x(n − q) represent a PA’s memory nonlinearity, and the maximum nonlinear order of the past input decrease with the memory order. When Q>K, the maximum nonlinear order N of x(n − q) will equal to 1.
Considering a traditional MP predistorter with input x(n) and output y(n) as follows, K
Q
y (n) = ∑∑ akq x (n − q) | x (n − q) |k −1
(1)
k =1 q = 0
where K is the maximum nonlinearity order, Q is the maximum memory order. In (1), a Kth order polynomial of x(n − q ), (q = 0,1,..., Q) is used to represent its contribution to the output y(n). In another words, the maximum nonlinear order is constant for every input. Since the effects of nonlinear dynamics tend to fade with increasing memory order in many real PAs [6], we can try to adjust the maximum nonlinear order of the past input to decrease the number of coefficients and keep the linearity of the predistorter-PA chain. Let K=N, and N is defined as following: ⎧ K − q; q < K N =⎨ (2) ⎩1; qK then Eq. (1) becomes: Q
N
y (n) = ∑∑ akq x (n − q) | x (n − q) |k −1
(3)
q =1 k =1
where N is the maximum nonlinearity order, Q is the maximum memory order. In Eq. (3), the maximum nonlinear order N is non-constant and varies with memory order. We refer to Eq. (3) as the TMP model. A MP model is a truncation of the general Volterra model when only diagonal terms in Volterra kernels are considered. Unlike the classical Volterra model, where the number of coefficients increases exponentially with the
Fig. 1 Structure of TMP model when Q>K
3 System identification Fig. 2 is the coefficients extraction scheme of the proposed predistorter with open-loop structure [19]. Instead of establishing PA’s behavioral model, we suppose to build a new predistortion approach, which extracts the coefficients of the predistorter directly from the input and output data of a PA. This structure eliminates the real-time closed-loop adaptation requirement, and allows us to extract the parameters through a simple offline process.
Fig. 2
Structure of system identification
Issue 2
YU Cui-ping, et al. / New predistorter using triangular memory polynomial for power amplifier of…
As we know, the characteristic of a predistorter and the characteristic of a PA are inverse. In Ref. [5], it is shown that if one has a pth-order post-inverse of a general Volterra system, then the pth-order pre-inverse is identical. MP model is a special case of Volterra model [4]. Thus, for arbitrary order of approximation, predistortion is equivalent to postdistortion in our application. If the input and output data of a PA are represented by X and Y (scaled) respectively, then the characteristic of the corresponding predistorter can be extracted from X and Y. If the output of the predistorter is expected to be X, then Y should be its input. Now the output X and input Y of the predistorter are given. In order to extract the coefficients of the TMP predistorter, the TMP function is represented by a matrix equation. From the given input data Y and output data X in the time domain, we can define X = [ x(l ) x (l + 1) L x (l + L − 1)]T (4) and H = [ H0 L H q L HQ ]
(12)
4 Simulation and experimental results 4.1 Simulation The proposed TMP model and the traditional MP model were simultaneously used to model a Wiener-Hammerstein model PA, traditional MP model PA and parallel-wiener model PA, respectively. The simulation results are shown in Table 1. Compare with the traditional MP model [4], the proposed TMP model can decrease the number of coefficients by 43%–55%. This is very important for the realization of a predistorter. Let K=7 and Q=5, only odd order are considered, for traditional MP, in coefficients extraction step, the dimension of matrix H is N×24, but for TMP, the dimension of matrix H are decreased to N×12, this will decrease the memory consumption and predistortion latency. Tabel 1 PA model
(5)
where ⎡ h1,q (l ) ⎢ h1,q (l + 1) H q = ⎢⎢ M ⎢ ⎢⎣ h1,q (l + L − 1)
Xˆ = Ηaˆ
h2, q (l )
hN ,q (l ) ⎤ ⎥ h2,q (l + 1) L hN , q (l + 1) ⎥ ⎥ M M ⎥ h2,q (l + L − 1)L hN , q (l + L − 1) ⎥⎦
and hk , q (l ) =| y (l − q) |k −1 y (l − q)
L
(6)
(7)
45
Wiener-Hammerstein model Memory Polynomial model Parallel-Wiener model
Comparision of different predistorter The number The number NMSE of of coefficients coefficients (NMSE MP−NMSE TMP)/dB with TMP with MP 40
18
0.767 8
16
9
− 0.001 4
24
12
0.009 1
In order to prove the superiority of the TMP model, both the traditional MP method and the proposed TMP method were used to model a real PA. The simulation results were shown in Fig. 3.
Let the complex coefficients be represented as following: a = [a0 L aq L aQ ]T (8) there aq = [a1, q a2, q L aN , q ]
(9)
Eq. (3) with L consecutive time-domain data points can be represented with a matrix equation such as (10) X = Ha where X is an L×1 vector, H is an L × [(Q + 1)( K − Q / 2)] matrix (Q
Fig. 3 Difference of NMSEMP and NMSETMP vs. the nonlinear order K and the memory order Q
expected coefficients can be computed by the following equation: (11) aˆ = H −1 X −1 where H denotes the pseudoinverse matrix of H. aˆ is the least square root. Then
The positive number means the normalized mean square error (NMSE) attained by traditional MP predistorter is better than the proposed TMP predistorter. When maximum nonlinear order K varies from 7 to 13, the memory order varies from 1 to 15, the NMSE difference between the traditional MP and the proposed TMP
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The Journal of China Universities of Posts and Telecommunications
predistorter is less than 0.8 dB. At the same time, the number of coefficients can be reduced more than 75%. Fig. 4 shows the percent of coefficients decreased by TMP model versus the nonlinear order K and the memory order Q.
without predistortion. Trace b shows the output spectrum with the traditional memory polynomial predistortion with nonlinearity order K=11 and memory order Q=6 delay taps, and trace c shows the output spectrum with the proposed TMP predistorter using the same nonlinearity and memory order. The same conclusion can be drawn that the TMP predistorter can get as good performance as traditional MP predistorter with only 48% coefficients number. Tabel 2
ACPR performance of different predistorter
Data rate/MHz No predistorter MP predistorter TMP predistorter
Fig. 4 Percent of coefficients decreased by TMP model vs. the nonlinear order K and the memory order Q
2012
The percent of coefficients decreased by a TMP predistorter/%
5 − 36.86/ − 37.53 − 50.26/ − 48.20 − 50.43/ − 47.87
10 − 36.60/ − 37.53 − 49.42/ − 49.57 − 49.68/ − 49.97
15 − 37.56/ − 38.38 − 49.42/ − 48.53 − 49.28/ − 48.76
20 − 37.22/ − 37.39 − 49.31/ − 47.88 − 49.36/ − 47.87
48.57
48.57
48.57
52.38
4.2 Experiment Fig. 5 shows a block diagram of the experimental test setup. The predistortion algorithm is run in the PC. The Agilent vector signal generator E4438C and Signal analyzer N9030A are used to generate the predistorted signal and collect the PA response through networking with the PC.
Fig. 6
Experimental power spectrum
5 Conclusions Fig. 5
Measured set-up blocks
Both traditional MP predistorter and the proposed TMP predistorter were tested. The measured results as well as the number of coefficients are listed in Table 2. The second, third and fourth rows are the adjacent channel power ratio (ACPR) measured in the lower and upper adjacent channel slots. Finally, the last row shows the percent of coefficients reduced by TMP predistorter. It can be seen that the TMP predistorter can get almost the same ACPR performance as the traditional MP predistorter when the data rate varied from 5 MHz to 20 MHz. But the number of coefficients is reduced by more than 48% compared with traditional memory polynomial predistorter. Fig. 6 shows the output spectrum of the signal with 15 MHz data rate when different predistorter are applied. Trace a shows the spectral regrowth of the amplifier output
To linearize a PA’s nonlinear with memory effects, a new predistorter model with fewer coefficients and good performance is presented. By adjusting the maximum nonlinear order of the past input, the number of coefficients is reduced by up to 75%. An open-loop structure is used in the system identification, which allows us to extract the coefficients by a simple offline process. Based on the structure, we develop a prototype of the predistorter with data rate 5 MHz, 10 MHz, 15 MHz, and 20 MHz. Simulation results show that when maximum nonlinear order K varies from 7 to 13, the memory order varies from 1–15, the NMSE difference between the traditional MP predistorter and the proposed TMP predistorter is less than 0.8 dB. The ACPR performance is also validated by experiments. It can be seen from experimental results that the proposed TMP predistorter
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YU Cui-ping, et al. / New predistorter using triangular memory polynomial for power amplifier of…
performs almost same as the memory polynomial predistorter in terms of linearizing PAs. But the number of coefficients of TMP predistorter can be reduced by more than 50%. Acknowledgements This work was supported by the National Science and Technology Major Project (2010ZX03007-003-04).
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