Abstract â In this paper a low complexity behavioral model based on dynamic nonlinearity reduction is proposed for the behavioral modeling of power ...
Behavioral Modeling of Class-J Amplifier Driven by 100MHz LTEAdvanced Signal Using Dynamic Nonlinearity Reduction Oualid Hammi 1 , Souheil Bensmida 2 , and Kevin Morris 2 1
Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, 31216, Saudi Arabia 2
Centre for Communications Research, University of Bristol, Bristol, United Kingdom
Abstract — In this paper a low complexity behavioral model based on dynamic nonlinearity reduction is proposed for the behavioral modeling of power amplifiers driven by LTE-advanced signals. This allows for a reduction in the number of model coefficients’ without compromising its accuracy by independently minimizing the nonlinearity orders in each of the branches of the memory polynomial function. Experimental validation carried out on a class-J power amplifier driven by a 100-MHz LTE signal demonstrates the ability of the proposed model to accurately predict the amplifier’s output. Compared to the conventional twin-nonlinear two-box model, the dynamic nonlinearity reduction based twin-nonlinear two-box model reduces the number coefficients of the memory polynomial function from 75 to 30 while degrading the model’s NMSE by only 0.1dB. Index Terms — Behavioral modeling, class-J, LTE-A, memory effects, nonlinearity.
However, these results were reported for input signals with bandwidths of 10MHz [3], and 15MHz [4]. On the other hand, the study of power amplifiers nonlinearity under an LTE-A drive signal has been limited to mildly nonlinear PAs and Volterra series based predistorters [5][6]. In [5], a total of 314 coefficients were used for the band-limited Volterra series digital predistorter (DPD) with significant residual spectral regrowth due to the limited observation bandwidth. Accurate distortions cancellation was reported in [6] for 100MHz LTE-A signal with a computationally demanding 1026 coefficients based Volterra DPD. In this paper, the behavioral modeling of a class-J PA driven by a 100MHz wide LTE-A signal is reported. A low-complexity high-accuracy behavioral model, inspired from the twin-nonlinear two-box (TNTB) model [7], is derived by reducing the dynamic nonlinearity orders and taking advantage of the decaying impact of nonlinearity order as the memory order decreases [8][9]. In Section II, the experimental setup and the device under test (DUT) characteristics are briefly described. The proposed dynamic nonlinearity reduction (DNR) based TNTB model structure and performances are thoroughly discussed in Section III. Conclusions are reported in Section IV.
I. INTRODUCTION Emerging wireless communication systems are evolving toward the use of signals with wider bandwidths. For example, in long term evolution-advanced (LTE-A) standards, signals with bandwidths of up to 100MHz can be transmitted. Such signals result from the aggregation of several 20MHz LTE carriers either within the same or different frequency bands. Furthermore, these signals are modulated using highly compact constellations and have high peak to average power ratios (PAPR). Accordingly, the radiofrequency (RF) transmitter needs to be designed to handle such signals with the minimum distortions and highest power efficiency. The RF power amplifier (PA) is undoubtedly the key element that influences the performance of the RF transmitter. To cope with the bandwidth requirements of wireless systems, class-J PAs have recently received an increasing interest due to their ability to achieve high efficiency over a wide bandwidth [1][2]. In fact, the use of class-J PAs enables high power efficiency over a frequency range that spans over several wireless communication bands. Most of the prior work focuses on the RF design of class-J amplifiers with only a few attempts to model / linearize this class of amplifier [3][4].
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II. EXPERIMENTAL VALIDATION The DUT used in this work is a class-J PA prototype designed based on a commercial 10W gallium nitride (GaN) transistor [2]. The DUT has higher than 55% power efficiency over a frequency range spanning from 1.6 to 2.2GHz at the 2dB compression point. The test signal is a standard compliant LTE-A signal built using five contiguous 20MHz LTE carriers. The test signal has a total bandwidth of 100MHz and a PAPR of 12.8dB at a complementary cumulative distribution function of 0.01%. The DUT characterization was performed around a carrier frequency of 1800MHz using an arbitrary waveform generator (AWG) and vector signal analyzer (VSA) setup for the acquisition of the input and output complex baseband waveforms. To ensure wideband measurement
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capabilities, the AWG consisted of a baseband waveform generator and a modulator (AFQ100B and SGS100A from Rhode and Schwarz). A linear driver amplifier is used upstream of the DUT to boost the signal level and stimulate the DUT over its entire input power dynamic range without introducing any additional nonlinearities. The signal at the output of the class-J PA is attenuated and then demodulated using a vector signal analyzer (FSW26 from Rhode and Schwarz). The sampling rates at the signal generation and observation paths were 600Msps in order to properly acquire the DUT’s input and output baseband waveforms over a frequency range that covers up to the fifth order intermodulation distortions. The measured data was processed to extract the DUT’s AM/AM and AM/PM characteristics reported in Fig. 1. These curves illustrate the strong dynamic nonlinear behavior of the DUT and the significant dispersion observed in both AM/AM and AM/PM characteristics.
III. PROPOSED DYNAMIC NONLINEARITY REDUCTION BASED TWIN-NONLINEAR TWO-BOX MODEL The proposed DNR based twin-nonlinear model is built using the reverse TNTB structure reported in [7] by modifying its memory polynomial (MP) function. Indeed, in the conventional TNTB model, the MP’s input and output signals ( x ( n ) and y ( n ) , respectively) are related by: N
M
y ( n ) = ∑∑ aij ⋅ x ( n − j ) ⋅ x ( n − j )
i −1
(1)
i =1 j = 0
where aij are the model coefficients; and N and M represent the model’s nonlinearity order and memory depth, respectively. Accordingly, the total number of parameters in the MP function of (1) is N × M . Since strong memory effects are observed in the case of LTE-A signals due to their inherent broad bandwidth, the number of coefficients required for the MP function of the conventional TNTB model will increase linearly with the model’s memory depth. In order to mitigate such a fast rise in the model complexity, the MP function of the proposed DNR based TNTB model is re-written as: M
Nj
y ( n ) = ∑∑ aij ⋅ x ( n − j ) ⋅ x ( n − j )
i −1
(2)
j = 0 i =1
All parameters of (2) are similar to those used in (1) except for the nonlinearity order ( N j ) which is made dependant on the memory index ( j ). Based on the fact that the nonlinearity order of the high order memory effects are decaying, the following dynamic nonlinearity reduction constraint has been introduced in the proposed model:
(a)
for j1 < j2 ⇒ N j1 ≥ N j2
(3)
The DNR based reverse TNTB (RTNTB) model is identified according to the flow chart presented in Fig. 2. First, the RTNTB model is constructed. Then, the nonlinearity orders of the memory branches are successively reduced in an iterative fashion while satisfying the constraint of (3). To prevent degradation of the model accuracy, the nonlinearity order reduction at one iteration is conditional to the performances of the model obtained from the previous iteration. The performances of the proposed model were evaluated in terms of normalized mean square error (NMSE). Fig. 3 reports the minimum NMSE obtained versus the number of coefficients of the MP function for both the RTNTB and the DNR based RTNTB models. The DNR based RTNTB model was built from a RTNTB
(b) Fig. 1. Measured characteristics of the DUT under a 100MHz LTE-A test signal. (a) AM/AM, (b) AM/PM.
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model in which the nonlinearity order and memory depth of the MP function were initially set to 10 and 10, respectively. The results reported in Fig. 3 demonstrate the ability of the DNR based RTNTB model in drastically reducing the number of coefficients of the MP function from 75 to 30 while degrading the NMSE by only 0.1dB. Conversely, similar reduction in the number of parameters of the conventional RTNTB model would result in 1.3dB degradation in the NMSE.
driven by 100MHz LTE-A signal demonstrates the effectiveness of the proposed model as it reduces the number of coefficients by 60% while degrading the NMSE by only 0.1dB. ACKNOWLEDGEMENT The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum & Minerals (KFUPM) under Research Grant RG1220.
Identify TNTB Model
REFERENCES
j=1
Set Nj=Nj-1
Set Nj=Nj-1-1
Set j=j+1
END
Set Nj+1=…=NM=Nj
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Evaluate NMSE degradation
Is j
