Analysis on LUT based digital predistortion using direct learning architecture for linearizing power amplifiers
- Xiaowen Feng^{1, 2},
- Yide Wang^{1, 3},
- Bruno Feuvrie^{1, 4},
- Anne-Sophie Descamps^{1, 4},
- Yuehua Ding^{5, 3}Email author and
- Zhiwen Yu^{3, 6}
https://doi.org/10.1186/s13638-016-0628-y
© Feng et al. 2016
Received: 9 December 2015
Accepted: 29 April 2016
Published: 10 May 2016
Abstract
In modern wireless communication system, power amplifier (PA) is an important component which is expected to be operated at the region of high power efficiency, but in this region, PA is inherently nonlinear. Thus, the linearization of high power efficient PA is necessary. In this paper, direct learning architecture (DLA) and indirect learning architecture (ILA) are firstly compared. It shows that DLA is more robust than ILA. Then a baseband digital predistortion (DPD) method with DLA is proposed for power amplifier linearization based on combined look-up tables (LUT) and memory polynomial (MP) model. The main innovation is that a LUT-based approach is proposed to calculate directly the complex-valued predistorted signal. Moreover, some interpolation techniques are introduced to reduce the LUT size. The proposed DPDs are validated experimentally. Additionally, the influences of some important parameters in experimental setup, such as the number of bits of analog-to-digital converter (ADC) and the instrument bandwidth, are analyzed.
Keywords
1 Introduction
In modern wireless communication system, the energy consumption is an extremely important issue, especially for the transmitter. Power amplifier (PA) is a crucial component in the transmitter. Generally, for achieving a good power efficiency, PA must operate close to its compression region. Unfortunately, the high spectral efficiency signals used by today’s wireless communication systems are characterized by their non-constant envelopes and high peak-to-average power ratio (PAPR). Their amplitudes may overtop the compression region of the PA. The resulting nonlinear distortions, such as the spectral regrowth and degradation of error vector magnitude (EVM), disturb the transmission. Moreover, to support more users and provide higher data rates, the bandwidth of signal continues to increase. PA exhibits stronger memory effects with the increasing of the bandwidth of signal [1]. The research on high power efficient PA driven by a wide bandwidth signal is of great practical significance [2, 3]. To compensate PA nonlinearities, several linearization techniques are developed, such as feed-forward, feedback, linear amplification with nonlinear components (LINC) and predistortion techniques. Among these techniques, predistortion technique, particularly baseband digital predistortion (DPD), has been widely studied thanks to its ability of reconfiguration and simplicity of implementation.
DPD is one of the most effective linearization techniques. Its principle is to insert a digital predistorter (PD) in front of PA, which has the inverse nonlinear characteristics of that of the PA, so that the cascaded PD-PA system has a linear behavior. DPD can be realized using two architectures [4–6]: indirect learning architecture (ILA) and direct learning architecture (DLA). In ILA approach [7], a postdistorter model is first assumed, the measured output of PA is taken as the input of the postdistorter, and the measured input of PA is taken as the output of the postdistorter. Then, the postdistorter is estimated by an identification algorithm such as least squares (LS) method. Finally, the identified postdistorter is placed directly in front of PA as the predistorter. In DLA approach [8–10], a model of PA’s behavior is first defined, then its coefficients are identified, and finally the predistorter is found by reversing the identified PA model.
Among various DPD techniques, three solutions are popularly used. They are look-up table (LUT), polynomial model and neural network based DPDs. In [11, 12], several neural network-based DPDs have been proposed. The neural network has an excellent capability to accurately approximate nonlinear functions. Hence, it can be used to linearize the PA. But the training process of neural network is complex and time-consuming. Its hardware implementation is difficult in practical applications. LUT [13–16] based DPD has the advantage of simplicity, but its linearization performance depends on the LUT size. In order to improve the linearization performance with limited LUT dimension, some interpolated techniques are introduced in LUT-based DPDs. Polynomial [7, 8, 17] model-based DPD is also widely studied in the literature. They include the well-known Volterra series (VS) [18], memory polynomial (MP) [7, 8, 13], generalized memory polynomial (GMP) [19], other simplified VS variants [20] and so on. VS and GMP models are more accurate but also more complex. MP model has lower complexity and can closely mimic the nonlinear behavior of the PA with memory effects. It offers a good tradeoff between computational complexity and modeling accuracy.
In [7], a MP based DPD with indirect learning architecture is presented, where the MP model performs robustly and the model’s parameters are easy to extract. But compared with the DPD with direct learning architecture, the DPD with indirect learning architecture is less robust in the presence of noise [4]. In [10], a MP-based DPD with direct learning architecture is proposed, where it uses a root-finding method to calculate the predistorted signal. This DPD can achieve excellent linearization performance but the root-finding procedure is time-consuming. In [13], a MP/LUT DPD is proposed, where a conventional LUT is used instead of the root-finding procedure. The calculating time of DPD process decreases greatly but it requires a sufficiently large size of LUT.
In our previous work [21, 22], some interpolated LUTs are introduced based on MP/LUT DPD. Thanks to the interpolation techniques, the improved DPDs achieve good performance in terms of computational efficiency and LUT size. In [21], the linear interpolation is introduced based on MP/LUT DPD. In [22], the quadratic-interpolated LUT is combined with the non-uniform MP model. It is worth noting that, in [21, 22], LUTs are only used to determine the amplitude of the predistorted signal. While the predistorted signal’s phase must be calculated by another separated time-consuming process. In [23], the two interpolated LUTs are used based on non-uniform MP model. The linear-interpolated LUT is used to determine the amplitude of the predistorted signal. And, the quadratic-interpolated LUT is used to determine the phase of the predistorted signal. In this paper, we propose three LUT-based methods: LUT-based, LILUT-based, and QILUT-based methods. In the LUT-based method, the amplitude and phase of the predistorted signal both are calculated by a single classical LUT. In the LILUT-based method, the amplitude and phase of the predistorted signal both are calculated by a single linear-interpolated LUT. In the QILUT-based method, the amplitude and phase of the predistorted signal both are calculated by a single quadratic-interpolated LUT.
Additionally, in practical implementation, the linearization performance of DPDs is directly related to the number of bits of ADC (analog-to-digital converter) and the bandwidth of instruments [24]. This important issue is also studied in this paper.
The remainder of this paper is organized as follows. Section 2 presents the principles of ILA and DLA, and makes a comparison between them. The proposed DPD solution is presented in Section 3. Section 4 discusses some practical problems in the measurements, especially the influence of signal bandwidth. The experimental setup and results are presented in Section 5. Finally, Section 6 concludes the paper.
2 Predistortion architectures
In this section, the details of ILA and DLA are presented. And, the two architectures are compared by some simulations.
2.1 Indirect learning architecture
where (·)^{ H } denotes the complex conjugate transpose operation. After the identification of the postdistorter, the copy of the postdistorter is placed directly in front of PA as the predistorter.
2.2 Direct learning architecture
where Φ _{ pq }[x(n)]=x(n−p)|x(n−p)|^{2q }, P and 2Q+1 are the memory depth and highest nonlinearity order, respectively, and c _{ pq } are the model’s coefficients. The signals x(n) and y(n) are the input and output of PA, respectively. The coefficients c _{ pq } are extracted by LS method as mentioned before. Secondly, the identified model of PA is reversed for the determination of PD. In the following, the method in [10] to determine the PD with DLA is described.
2.3 Comparison of ILA and DLA
Two different DPD architectures (ILA and DLA) are presented in the above subsection. They both need to identify a pre-assumed model (MP model) with the measured input and output of PA. LS method is used in the model identification. From (3), it can be seen that the inverse of Z ^{ H } Z is required in LS algorithm. When solving the inverse problem, the condition number is usually used to measure how sensitive the solution is to changes or errors in the input. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.
where y(n) and v(n) are the output and input of Saleh model, respectively, and α _{ a }=20, β _{ a }=2.2, α _{ p }=2, β _{ p }=1 [26]. The input signal of PA is a WCDMA signal with 3.84 MHz bandwidth. The measured sequence has 1000 symbols (8000 samples). The ideal gain of this PA model is about 26 dB. The input power at 1 dB compression point is about −1 dBm.
From Figs. 3 and 4, it can be seen that the condition number of Z ^{ H } Z in DLA is always lower than that in ILA. It indicates that DLA is more robust than ILA with respect to perturbations. To further validate this result, the influences of the noise and quantization error of ADC on the modeling performance are analyzed.
In practical measurement, an ADC is required to realize the signal acquisition. The number of bits of ADC will affect the accuracy of the signal acquisition and then affect the performance of the model’s identification. Additionally, the measurement at the output of PA is noisy in practical application. The noise also affects the performance of the model’s identification. In the third simulation, these two DPD architectures are compared in terms of the number of bits of ADC in signal acquisition and the noise power at the output of PA.
For analyzing the influence of the noise at the output of PA, it assumes that complex white Gaussian noise is present at the output of PA as shown in Figs. 1 and 2. An original WCDMA signal x ^{′}(n) (bandwidth 3.84 MHz, power 0 dBm, sequence length 8000 samples) is given as the PA input. And the output y ^{′}(n) of PA is obtained by the Wiener model. The white Gaussian noise is added in the output signal y ^{′}(n) to get the noisy output y noise′(n). The input x ^{′}(n) and output y noise′(n) of PA are used for the model identification of (1) and (4). In this process, we take K=P=3 (memory depth = 3) and L=Q=2 (nonlinearity order = 5), respectively.
The original input x ^{′}(n) and output y ^{′}(n) of PA pass firstly the ADC, then the noise is added on the output signal of PA. The processed input and output signals are used for the model identification of (1) and (4). For ILA, the identified postdistorter model is directly placed in front of PA as the predistorter [7]. For DLA, the predistorter is determined by inverting the identified PA model [10].
3 Proposed LUT-based digital predistortion
Values of LUT
LUT input | LUT output |
---|---|
E(0) | R(0)e ^{ j θ(0)} |
… | … |
E(m) | R(m)e ^{ j θ(m)} |
… | … |
E(M) | R(M)e ^{ j θ(M)} |
where E(m) is the LUT input and θ(m) the phase of the term \(\sum _{q=0}^{Q}c_{0q}R(m)^{2q+1}\).
After the LUT is constructed, the predistortion algorithm is described in Algorithm 1.
where QILUT is the quadratic-interpolated LUT [22].
In this section, three DPD approaches are described. For convenience, the proposed DPDs based on simple LUT, LILUT and QILUT are called as LUT-based, LILUT-based, and QILUT-based, respectively. Among these three approaches, it is difficult to judge which one is the best, since they provide different degrees of tradeoff between the linearization performance, table size and time efficiency.
4 Discussions
In order to validate the proposed DPDs, experimental measurements are necessary. Before the measurements, some problems are discussed. In practical measurements, hardware conditions can not be ignored, such as the number of bits of ADC and instrument bandwidth. In the following, these parameters are analyzed by some simulations. In the simulations, the original input signal is a WCDMA signal with 3.84 MHz bandwidth. The input sequence is 1000 symbols. The input power is −5 dBm. The PA model is the Wiener PA model mentioned in Section 2.3. The DPD method used is the root-finding-based DPD [10].
Another problem is the bandwidth of instrument. In simulations, the signal bandwidth is only limited by the sampling frequency. In the measurement, except for the influence of the sampling frequency, the signal bandwidth is also affected by the bandwidth of instrument. When the bandwidth of instrument is narrower than that of the signal, the signal passing the instrument will be distorted. Especially, the signal bandwidth will increase after the predistortion. The bandwidth of the predistorted signal is wider than that of the original input signal. Thus, if the bandwidth of instrument is not sufficiently wide, the desired predistortion will be not achieved.
In order to evaluate the required bandwidth, the following simulation is made. It assumes that the sampling frequency of input signal is 50 samples/symbol. To simulate the instrument limitation, a lowpass linear-phase filter, with order 200 and a varying cutoff frequency, is used to limit the bandwidth of the predistorted signal. The limited bandwidth signal is finally applied to the Wiener PA model.
5 Experimental results
The proposed approach, LUT-based, LILUT-based, and QILUT-based DPDs, all are tested on this experimental testbed. The root-finding-based DPD in [10] is compared with the proposed three DPD approaches. The performance is evaluated in terms of the linearization capability, time efficiency and table size. The linearization capability is measured by two parameters. One is the NMSE between the predistorted signals by the three LUT based DPDs and the predistorted signal by root-finding-based DPD. The other is the measured ACPR at the output of linearized PA. The time efficiency refers to the consumed time of DPD process for obtaining one predistorted sample x(n) as shown in Algorithm 1. The table size refers to the chosen size of LUT.
NMSE of predistorted signals and time comparisons using different DPD methods
DPDs | NMSE (dB) | Time (us) |
---|---|---|
Root-finding-based DPD | −∞ | 103.75 |
LUT-based DPD (size 30) | –34.18 | 9.63 |
LUT-based DPD (size 1000) | –65.39 | 11.38 |
LILUT-based DPD (size 10) | –61.20 | 20.75 |
LILUT-based DPD (size 30) | –81.59 | 21.38 |
QILUT-based DPD (size 10) | –75.93 | 71.25 |
QILUT-based DPD (size 20) | –94.89 | 72.88 |
ACPR comparison using different DPD methods
ACPR (dB) | ||||
---|---|---|---|---|
Output power point | 17 dBm | 16 dBm | 15 dBm | 14 dBm |
Without DPD | –37.86 | –40.23 | –42.94 | –45.08 |
Root-finding-based DPD | –43.45 | –47.41 | –50.79 | –53.47 |
LUT-based DPD (size 30) | –39.53 | –44.47 | –45.70 | –45.90 |
LUT-based DPD (size 1000) | –41.76 | –47.58 | –51.06 | –53.59 |
LILUT-based DPD (size 10) | –39.33 | –45.72 | –50.91 | –53.60 |
LILUT-based DPD (size 30) | –43.33 | –45.75 | –51.12 | –53.53 |
QILUT-based DPD (size 10) | –41.59 | –46.08 | –50.84 | –53.19 |
QILUT-based DPD (size 20) | –43.34 | –47.52 | –50.69 | –53.86 |
6 Conclusions
Two classical DPD architectures (DLA and ILA) are compared in this paper. According to the comparison in terms of the condition number and considering the influence of the number of bits of ADC and noise in the signal measurement, it shows that DLA is more robust than ILA with respect to perturbations. The LUT-based, LILUT-based, and QILUT-based DPDs are then proposed for PA linearization based on MP model with DLA. These three DPDs allow some tradeoff between the linearization performance, time efficiency and table size. In different applications, a more appropriate DPD can be chosen to fit the actual situation. Moreover, the hardware condition of experimental setup is discussed. If a more accurate results are expected, a higher bits of ADC and a wider bandwidth of instrument are required.
Declarations
Acknowledgements
This work was supported by the China Scholarship Council, the grant from Science and Technology Planning Project of Guangdong Province, China (No. 2015A050502011), the grant from National Natural Science Foundation of China (No. 61401157) and the grant from the funds of central universities (No. 2015ZM127).
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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