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Nonlinear RF Power Amplifier Behavioural Analysis of Wireless OFDM Systems
Máirtín O’Droma1 and Yiming Lei 2
1Telecommunications Research Centre, University of Limerick, Ireland. Mairtin.ODroma@ul.ie
2School of Electronics Engineering & Computer Science, Peking University, Beijing, China
Abstract
Four signal representation approaches are combined with a Bessel-Fourier PA envelope behavioural model of a GaN memoryless
nonlinear power amplifier (PA) to reveal insights into the nonlinear amplification of multicarrier OFDM signals. Isolating and
analyzing different orders of intermodulation product (IMP) impairment, the impact of higher order IMPs on ACPR degradation in
the second and higher adjacent channel bands and how that is the determining factor for the PA’s upper limit operating point and
power conversion efficiency, rather than the ACPR in the first adjacent band or the inband EVM degradation, may be shown.
1. Introduction
NONLINEAR distortion is a source of major degradation of modulation fidelity in multicarrier systems, such as
orthogonal frequency division multiplexing (OFDM) systems. Compared with conventional single carrier
communication systems, OFDM signals significantly improve spectrum efficiency and reduce frequency selective
fading problems [1]. However their consisting of large numbers of independent QAM subcarriers, means the
composite signal’s peak to average power ratio (PAPR) can be significant. This is what makes them so sensitive to
nonlinear distortion. The primary source of this nonlinear distortion is the RF transmitter power amplifier (PA) [2-7].
Accurate and efficient behavioural modelling of these multi-carrier signals through nonlinear amplification
processes is not a trivial problem. The PA modelling and signal representation techniques require careful selection.
Here the memoryless form of the Bessel-Fourier (BF) model (Section 2) is used for the nonlinear PA modelling
because of its particular suitability for handling multicarrier signals, its adaptability for different signal-representation
approaches, and of course its large dynamic range modelling accuracy potential [4, 7-9].
The fundamental band of the RF nonlinear PA transmitter system output for an OFDM signal input is
composed of large numbers of inter-modulation products (IMPs) superimposed on the inband amplified ‘wanted’
OFDM subcarriers and appearing in adjacent channels as spurious out-of-band emissions. The same is the case for the
harmonic bands which, however, with well tuned and well matched PA output circuitry, should be thoroughly
attenuated. Nonetheless if for some reason there are exceptions here, such as the use of selected low power, high
harmonic band, PA output signals for generating adaptive PA linearisers control signals, the BF model is fortunately
powerful enough to handle this with very little adjustment, i.e., it can re-create the un-attenuated behavioural
responses at any or all harmonics.
The IMP impairment of the inband signal modulation fidelity is typically measured by error vector magnitude
(EVM) figures of merit (FOMs). The out-of-band IMP interference in adjacent channels may be measured by the
output spectrum behaviour set against spectrum masks, by adjacent channel power ratio (ACPR) measures or other
such like FOMs [3-10]. Particular air-interface standards normally set the FOM criteria to be satisfied.
In Section 3 the behavioural performance of an L-band GaN PA amplifying an IEEE 802.11a OFDM WLAN
signal, with its 48 data sub-carriers –here with16-QAM– and 4 BPSK pilot sub-carriers [11] is examined and analysed
as an example. Particular emphasis is given to extracting and assessing the impairment contributions of different IMP
components and the factors determining the upper limits to the PA operating point and power efficiency. Together
with the BF model we combine the powers of four signal representation approaches with their different attributes and
modelling efficiencies and effectiveness to achieve this.
The GaN amplifier device was supplied by Ferdinand-Braun-Institut (FBH), Berlin. The measured AM/AM
(g) and AM/PM (Φ) envelope characteristics were extracted in collaboration with Prof. Kompa’s microwave research
laboratory at the University of Kassel, Germany. Those at the chosen frequency are shown in Figure 1. They were
found to be effectively memoryless over the band of interest. The input backoff (IBO) and output backoff (OBO)
powers in decibels are the input and output powers (Pin and Pout resp.) normalized to their respective saturation powers,
which are defined as the powers at the point “P0.1” where dPout/ dPin [dBm] first reaches 0.1 with Pin increasing, [12,
978-1-4244-6051-9/11/$26.00 ©2011 IEEE
13]. It is notable that the AM/PM distortion has a negligible variation of <3 degrees over the dynamic range to the 1dB
compression point (P1), rising to 4.5 degrees over the 5dB less IBO beyond this; cf., [14].
2. BF modelling of the GaN PA
An Lth order BF model of the envelope characterisation of the GaN PA may be extracted using [4]:
∑
=
Φ⋅==
L
k
ik
Aj
ii kAJbeAgAF i
1
1
)( )().()(
α
(1)
where is the input and output measured envelope samples are Ai , g(Ai) & Φ(Ai); bk are the model coefficients; Jn
represents a Bessel function of the first kind of order n; and α may be shown to be inversely proportional to the
model’s dynamic range (D), i.e.,
α
=2π/D. To ensure the model’s dynamic range is greater than the measured dynamic
range,
α
< 1 [4]. The number of coefficients required to create a model which is indistinguishable from the measured
data may vary from device to device and also be a function of the device’s modelled dynamic range. Seven or more
coefficients should be plenty for almost all circumstances. Here a BF(10, 0.6) is used, i.e., 10 coefficients and
α
=0.6.
Figure 1. The GaN amplifier’s AM-AM & AM-PM n ormalized
envelope characteristics at 2.15GHz.
Figure 2. Power density spectrums of various orders IMPs. MFTD,
DTD and Stat signal representation approaches are used. PA operating
point is 3dB OBO. Frequency is in OFDM subcarrier spacing units.
3. Analysis of nonlinear OFDM signal
For any OFDM PA input signal the BF model may be readily programmed to extract all IMPs of given order in
any band. There are different ways to do this –different combinations of BF model forms and signal representation
techniques– depending on the analysis goals. The signal representation techniques, each with its own attributes may be
combined, as here, to yield particularly insightful behavioral analysis, such as the results shown in Figures 2 and 3.
In Figure 2, the power spectra of the zonal band wanted sub-carrier components and of the 3rd, 5th, 7th and 9th
IMPs as yielded by the BF model are shown. The PA operating point is set at 3dB OBO. The former are produced
using the mixed frequency-time domain modelling approach (MFTD) [8, 15] which effectively constructs the
amplified subcarriers one at a time. Computing-time it is relatively slow but this is tolerable with just 52 subcarriers
and importantly, it preserves the modulation information, presenting it exactly as it should be after PA amplification,
depending of course on the model accuracy. The latter IMP spectra are calculated by using computing-time efficient
statistical signal representation (Stat approach) [8, 15]. Summing these signals will yield a good estimate of the
amplified signal with inband and out-of-band IMP impairment present. A full output power spectrum snapshot with
IMPs of all orders present, not just up to the 9th is included to provide a useful comparison reference particularly for
inband and in the first adjacent channel regions. Such a spectrum may be efficiently found using the direct
time-domain (DTD) signal representation approach [8, 15]. While DTD preserves modulation information it has poor
ability to prevent aliasing errors. If the sampled bandwidth is sufficiently wide their effect in the inband region or in
the first adjacent channel bands may be made relatively negligible. Such is the case here with an oversampling rate of
8 applied. However the significantly reduced rate of fall-off of this full DTD spectrum in the region beyond the
immediate adjacent channel bands is noticeable and here its accuracy cannot be relied on, all because of the presence
of greater aliasing errors.
Immediately helpful here is to notice which orders of IMPs are contributing impairments in which spectral
regions. Clearly in-band distortion will be dominated by 3rd order IMPs, as will the first adjacent channel interferences
although 5th order IMPs begin to have an impact in the outer quarter of these adjacent band edges. However in the 2nd
adjacent bands, 5th and 9th order products dominate, with the 9th alone being the dominant distortion for virtually the
whole of the second half of these bands (relative to the wanted band) –a region where the density of 5th order products
rapidly dies away. It is noticeable in this Figure that the 7th order IMPs have negligible presence, being a constant ~20
dB (approximately) below the 9th order over the frequency range show.
Moving from the 3dB OBO power spectra snapshot, the ‘swept-operating-point’ graphs of likely behavioural
performance are shown in Figure 3. These are derived using the Stat signal representation approach. Powers are
normalized relative to Po at the P0.1 saturation point.
Figure 3. Powers of fundamental signal and IMPs located wanted
sub-carriers, and Stat approach is used.
Figure 4. GaN PA output EVM and ACPR at 11MHz and 20MHz
frequency offsets for an IEEE 802.11a OFDM signal.
Interesting observations may be deduced from Figure 3. Firstly, the signal to total IMP impairment noise ratio
(SINR) degrades as would be expected as the PA is driven into the nonlinear region. This degradation is clearly
dominated by the 3rd order IMP to such an extent that 3rd order IMP generation would be sufficient to yield good
estimates of inband IMP signal distortion, i.e., of the degradation of the EVM FOMs, at least from 8 to 1 dB OBO.
Secondly there are regions where the 7th and 9th order IMP power exceeds the 5th order IMP power, viz. in the 6.5 to 4
dB OBO operating region, and the 9th IMP power exceeds the 7th IMP power, viz. 11 to 9 dB OBO and 4 to 2.5dB
OBO. Although for the latter both are significantly suppressed in this region, nonetheless its clear that in the higher
adjacent channel regions performance analysis should take account of the impact of higher order IMP powers and also
be aware that their values can be quite dependent on the PA operating point. While generally WLAN systems operate
with a constant transmitter power, OFDM LTE systems will have transmit power control systems for reasons inclusive
of seeking more linear operation, higher bit rate density (spectral efficiency) and ‘green IT’ aimed at reducing energy
usage and loss in wireless network access point transmitter systems and base stations. Thirdly the presence of IMP
‘sweet spots,’ where the IMP power drops rapidly into a trough, in different locations for the different orders: for this
PA, the 3rd manifests none, the 5th one, and the 7th and 9th two each. It is possible to exploit these sweet spots,
especially of the higher order IMP powers to reduce out-of-band emission problems, and sometimes circumstances
may demand this. However as the location of the sweet spots are PA specific, good knowledge of the individual PA
characteristics is required, or an adaptive IMP sweet spot lineariser may be incorporated.
The EVM and ACPR FOM results for this system are shown in Figure 4, graphed over the 11dB OBO dynamic
range (16 dB IBO range), with the IEEE 802.11a specification limits indicated. These results are extracted by using an
MFTD-modified Stat (MS) approach [8] with 200 OFDM IFFT blocks. Besides their degradation with increasing PA
drive, it is interesting to note that the system’s upper operating point limit, at 2.4 dB OBO, is determined by the ACPR
degradation in the 2nd adjacent channel. Nonetheless, the upper limits to the operation point dictated by these three
FOMs fall within 0.5 dB OBO of each other. This is because of the harmonious definitions of these FOMs in the
specification [11]. These operating point limits also notably fall in the mildly nonlinear region, and thus power
conversion efficiency, which normally peaks beyond the PA’s P1 point, cannot be optimised without breaching inband
and out-of-band performance specifications. Finally considering the usually high PAPR of the input OFDM signal,
instantaneous IMP impairment corresponding to these peak input power points, will produce degradations exceeding
these standard specifications.
4. Conclusion
Combining the benefits of multiple signal representation approaches together with the BF PA behavioural
model is shown to be effective in yielding insightful and useful behavioural analysis of the nonlinear amplification of
high-density multicarrier systems such as OFDM systems used in WLAN, WiMAX, 4G LTE and DVB systems. In
particular it is shown that 3rd IMP impairment dominates the inband distortion to the exclusion of all other IMP
distortion, while the spurious emissions caused by higher order IMPs, 7th and 9th order especially, and present in bands
beyond the first adjacent channels, can be the determining factor for the upper limit to the PA’s operating point and
power conversion efficiency. How this may be ameliorated by exploitation of order-based IMP sweet spots is also
presented.
5. Acknowledgments
This work was supported in part by TARGET – Top Amplifier Research Groups in a European Team – a
European Union (EU) Sixth framework Information Society Technologies Programme (IST-FP6), IRCSET (Irish
Research Council of Science, Engineering, and Technology) under EMBARK Postgraduate Research Scholarship.
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