On the use of digital predistortion for power line communications

On he Use o Digi al P edis o ion o Powe Line Communica ions
Pe e L. Gilabe
Dep . o Signal Theo y and Communica ions, Uni e si a Poli ècnica de Ca alunya.
pe e.lluis.gilabe @upc.edu
Abs ac
This con ibu ion p e ends o highligh he bene i s o including digi al p edis o ion (DPD) linea iza ion in
he digi al on -end o Powe Line Communica ions (PLC).
In oduc ion
PLC ne wo ks encoun e majo challenges due o noise, a enua ion, and in e e ence om elec ical
appliances. A key app oach o enhancing PLC pe o mance is powe ampli ica ion, which s eng hens
signal obus ness agains hese dis up ions. Howe e , powe ampli ie s (PAs) mus balance e iciency and
linea i y, as achie ing bo h simul aneously is di icul . Typically, PA design p io i izes maximizing powe
e iciency a high back-o le els o accommoda e he high peak- o-a e age powe a io (PAPR) o OFDM
signals, while linea i y is managed a he sys em le el using linea iza ion echniques. In addi ion o il e ing
and noise cancella ion me hods o in e e ence mi iga ion, digi al p edis o ion linea iza ion can
compensa e o dis o ion in oduced by PAs and add ess impedance misma ches ha signi ican ly
deg ade signal quali y in PLC sys ems.
Theo e ical Backg ound
The p inciples o p edis o ion a e depic ed Fig. 1. A nonlinea sys em called a p edis o e is placed be o e
he PA o compensa e o i s nonlinea cha ac e is ics. The e o e, he p edis o e 's goal is o ideally
eplica e he in e se nonlinea beha io o he PA, he eby achie ing linea ampli ica ion a he PA's
ou pu .
Fig. 1. P inciples o p edis o ion linea iza ion o powe ampli ie s.
DPD is implemen ed wi hin he baseband p ocessing o he digi al on -end. To cha ac e ize and
compensa e o he nonlinea dis o ion and memo y e ec s o PAs, ma hema ical desc ip o s a e
essen ial. Unlike physical models, which equi e de ailed knowledge o he PA’s elec onic componen s,
hei cons i u i e ela ions, and he heo e ical p inciples go e ning hei in e ac ions, PA and DPD
beha io al models a e de i ed solely om inpu -ou pu obse a ions. As a esul , hei accu acy is highly
dependen on he chosen model s uc u e and pa ame e ex ac ion me hod [Gil25].
Polynomial-based models, including simpli ied e sions o he Vol e a se ies such as he memo y
polynomial (MP) [Kim01] and he gene alized memo y polynomial (GMP) [Mo 06], a e among he mos
widely used beha io al models in he li e a u e. Addi ionally, piecewise beha io al models like he
decomposed ec o o a ion (DVR) model [Zhu15] and look-up able (LUT) implemen a ions [Mol07],
[Gil18] ha e been p oposed o add ess s onge nonlinea PA beha io by le e aging he locali y o
piecewise unc ions. While hese models a e nonlinea , hey emain linea in hei pa ame e s, allowing
o e icien ex ac ion using he leas squa es (LS) me hod. Mo e ecen ly, a i icial neu al ne wo ks
(ANNs) ha e eme ged as a p omising app oach o PA beha io al modeling and DPD linea iza ion,
pa icula ly in he con ex o wideband B5G modula ed signals and highly e icien ye nonlinea PAs
[Fis23], [Lop22]. This app oach aims o su pass he limi a ions o con en ional single-s age DPD models in
e ms o linea iza ion pe o mance. Howe e , he imp o ed accu acy o ANNs comes a he cos o a
signi ican ly la ge numbe o pa ame e s, aising conce ns abou powe consump ion and esou ce
u iliza ion. As an al e na i e, cascaded (CC) beha io al models and composi e a chi ec u es ha e been
p oposed o DPD applica ions, d awing inspi a ion om he mul is age s uc u e o ANNs. These models
a e designed o handle complex nonlinea i ies and wideband ope a ing condi ions wi h s ong memo y
e ec s, whe e adi ional single-s age DPD models s uggle o mee linea i y equi emen s [C i25].
Conside ing he PLC applica ion, whe e he signal bandwid h emains wi hin ens o MHz, he GMP model
o e s a balanced ade-o be ween compu a ional complexi y and linea iza ion pe o mance.
Addi ionally, i p o ides he lexibili y needed o compensa e o unwan ed misma ched impedance
e ec s.
The GMP model is an ad anced ex ension o he MP, inco po a ing bi-dimensional ke nels ha accoun
o c oss- e m in e ac ions be ween he complex signal and bo h lagging and leading en elope e ms. This
enhancemen imp o es modeling accu acy bu comes a he cos o a highe numbe o pa ame e s
compa ed o he MP. The low-pass equi alen PA inpu -ou pu ela ionship using he GMP beha io al
model is exp essed as ollows,
𝑦𝑦�[𝑛𝑛]=� � 𝑎𝑎𝑘𝑘𝑘𝑘𝑥𝑥[𝑛𝑛−𝑙𝑙]|𝑥𝑥[𝑛𝑛−𝑙𝑙]|𝑘𝑘
𝐿𝐿
𝑎𝑎
−1
𝑘𝑘=0
𝐾𝐾
𝑎𝑎
−1
𝑘𝑘=0
+ � � � 𝑏𝑏𝑘𝑘𝑘𝑘𝑘𝑘𝑥𝑥[𝑛𝑛−𝑙𝑙]|𝑥𝑥[𝑛𝑛−𝑙𝑙−𝑚𝑚]|𝑘𝑘
𝑀𝑀𝑏𝑏
𝑘𝑘=1
𝐿𝐿𝑏𝑏−1
𝑘𝑘=0
𝐾𝐾𝑏𝑏
𝑘𝑘=1
+ � � � 𝑐𝑐𝑘𝑘𝑘𝑘𝑘𝑘𝑥𝑥[𝑛𝑛−𝑙𝑙]|𝑥𝑥[𝑛𝑛−𝑙𝑙+𝑚𝑚]|𝑘𝑘
𝑀𝑀𝑐𝑐
𝑘𝑘=1
𝐿𝐿𝑐𝑐−1
𝑘𝑘=0
𝐾𝐾𝑐𝑐
𝑘𝑘=1
(1)
wi h 𝑦𝑦�[𝑛𝑛] and 𝑥𝑥[𝑛𝑛] being he es ima ed PA ou pu and PA inpu complex baseband signals, espec i ely.
The complex coe icien s desc ibing he PA model a e 𝑎𝑎𝑘𝑘𝑘𝑘, 𝑏𝑏𝑘𝑘𝑘𝑘𝑘𝑘 and 𝑐𝑐𝑘𝑘𝑘𝑘𝑘𝑘. The nonlinea o de o he
polynomials a each o he b anches is de e mined by Ka, Kb and Kc, while he memo y dep h is de e mined
by La, Lb and Lc. Finally, he leading and lagging e ms o he en elope de ining he c oss-p oduc s is gi en
by Mb and Mc. The numbe o coe icien s o he GMP model is 𝑂𝑂=𝐾𝐾𝑎𝑎𝐿𝐿𝑎𝑎+𝐾𝐾𝑏𝑏𝐿𝐿𝑏𝑏𝑀𝑀𝑏𝑏+𝐾𝐾𝑐𝑐𝐿𝐿𝑐𝑐𝑀𝑀𝑐𝑐.
DPD coe icien s adap a ion
Figu e 2 p esen s he block diag am o he adap i e DPD subsys em, which ollows a di ec lea ning
closed-loop app oach [Gil25].
Fig. 2. Block diag am o a di ec lea ning DPD adap a ion a chi ec u e.
In he o wa d pa h, he inpu -ou pu ela ionship wi hin he DPD block can be exp essed using ma ix
no a ion as ollows,
𝒙𝒙=𝒖𝒖−𝑼𝑼𝑼𝑼 (2)
whe e u is he Nx1 inpu ec o and N is he numbe o samples (i.e., n=0,1,···,N-1)), x is he Nx1
p edis o ed ec o and w is he Ox1 ec o o coe icien s. The NxO da a ma ix U con aining he GMP
basis unc ions desc ibed in (1), is de ined as
𝑼𝑼=(𝝋𝝋𝑢𝑢[0], 𝝋𝝋𝑢𝑢[1], … , 𝝋𝝋𝑢𝑢[𝑁𝑁−1])𝑇𝑇 (3)
whe e
[]
u
nφ
is he Ox1 ec o o basis unc ions
[]
u
j
n
ϕ
, o j = 1,···,O, a ime n.
𝝋𝝋𝑢𝑢𝑇𝑇[𝑛𝑛] = (𝜑𝜑1
𝑢𝑢[𝑛𝑛], 𝜑𝜑2
𝑢𝑢[𝑛𝑛], ⋯,𝜑𝜑𝑂𝑂
𝑢𝑢[𝑛𝑛]) (4)
These basis unc ions can be pa icula ized by any nonlinea beha io al model ha is linea in pa ame e s.
Then, ollowing he di ec lea ning app oach depic ed in 2, he Ox1 ec o o DPD coe icien s (w) a e
ex ac ed i e a i ely inding he LS solu ion as ollows,
𝑼𝑼𝑖𝑖+1 =𝑼𝑼𝑖𝑖+𝜇𝜇�𝑼𝑼𝑯𝑯𝑼𝑼�−1𝑼𝑼𝑯𝑯𝒆𝒆 (5)
wi h 𝜇𝜇 (0 < 𝜇𝜇< 1) being a weigh ing ac o and e being he Nx1 ec o o he esidual es ima ion e o ,
de ined as
𝒆𝒆=𝒚𝒚
𝐺𝐺0−𝒖𝒖 (6)
whe e 𝐺𝐺0 de e mines he desi ed linea gain o he PA and whe e y and u a e he Nx1 ec o s o he PA
ou pu and he ansmi ed inpu , espec i ely.
Simula ion En i onmen
Conside ing a wo-po unma ched ne wo k (see Fig. 3), he ou pu s and he inpu s a e composed o a
ec o o wo signals.
Fig. 3. Block diag am o a gene al wo-po unma ched ne wo k.
The wo ou pu s, y1 and y2, a e independen om each o he , bu each ou pu is he esul o nonlinea
combina ion and in e ac ion o he wo inpu s, x1 and x2. The e o e, he ou pu y1 can be de ined as
𝒚𝒚𝟏𝟏=𝑓𝑓(𝒙𝒙𝟏𝟏,𝒙𝒙𝟐𝟐) (7)
A GMP beha io al model, de i ed om eal measu emen s, was implemen ed o eplica e he PA’s
nonlinea dis o ion and memo y e ec s. Addi ionally, impedance misma ch was simula ed by
inco po a ing e lec ed wa e o ms. The e alua ion es signal consis ed o a 16-QAM OFDM wi h a 10
MHz bandwid h, while impedance misma ch was emula ed using a e lec ed wa e wi h a ol age s anding
wa e a io (VSWR) o 3.
Fo DPD pu poses he GMP model has been conside ed. The mos ele an basis unc ions o he GMP
DPD model a e selec ed using he doubly o hogonal ma ching pu sui (DOMP) algo i hm desc ibed in
[Bec18]. The e o e, om an o iginal con igu a ion o 563 basis, wi h 𝐾𝐾𝑎𝑎= 8, 𝐿𝐿𝑎𝑎=11,𝐾𝐾𝑏𝑏= 5, 𝐿𝐿𝑏𝑏= 8,
𝑀𝑀𝑏𝑏= 5, 𝐾𝐾𝑐𝑐= 5, 𝐿𝐿𝑐𝑐=11 𝑎𝑎𝑛𝑛𝑎𝑎 𝑀𝑀𝑐𝑐= 5 in (1), a e he DOMP selec ion, only 200 coe icien s we e
conside ed o pe o m DPD.
Resul s
Figu es 4 and 5 illus a e he 16-QAM cons ella ions and powe spec a, espec i ely, a he PA ou pu
unde bo h well-ma ched and misma ched impedance condi ions. As seen in he powe spec um ( ed
line) in Figu e 5, impedance misma ch in oduces a s onge equency dependence. The ou -o -band
(OOB) spec al eg ow h becomes mo e asymme ical compa ed o he well-ma ched case, as e lec ed
in he adjacen channel powe a io (ACPR) alues in Table I. Addi ionally, his unwan ed equency
esponse impac s he in-band signal, leading o a mo e signi ican deg ada ion in e o ec o magni ude
(EVM), as shown in Table I. In he well-ma ched scena io, he EVM is 5.2%, whe eas he misma ched
condi ion esul s in a much highe in-band dis o ion, wi h an EVM o 26.4%.
Fig. 4. 16-QAM cons ella ion conside ing: PA nonlinea dis o ion and memo y e ec s (le ); and PA
nonlinea dis o ion, memo y e ec s and impedance misma ched ( igh ).
Fig. 5. 16-QAM cons ella ion conside ing: PA nonlinea dis o ion and memo y e ec s (le ); and PA
nonlinea dis o ion, memo y e ec s and impedance misma ched ( igh ).
Table I. ACPR and EVM alues o di e en scena ios.
ACPR (dB)
Lowe Band/Uppe Band
EVM (%)
Nonlinea PA
-29.7 / -28.8
5.2
Nonlinea and misma ched PA (VSWR=3)
-35.6 / -28.0
26.4
NL and Misma ched w. DPD (VSWR=3)
-49.2 / -45.6
1.1

Figu es 6, 7, and 8 show he 16-QAM cons ella ions, powe spec a, and AM-AM cha ac e is ics,
espec i ely, a he PA ou pu unde a misma ched impedance condi ion, bo h wi h and wi hou DPD
linea iza ion. As seen in Fig. 7 and Table I, he ou -o -band dis o ion is e ec i ely compensa ed wi h DPD,
esul ing in an ACPR imp o emen o app oxima ely 14 dB in he lowe band and 17 dB in he uppe band,
e en in he challenging case o misma ched nonlinea PA beha io . Addi ionally, as shown in Fig. 6 and
Table I, he in-band dis o ion is also mi iga ed, wi h he EVM imp o ing by mo e han 25 pe cen age
poin s compa ed o he misma ched nonlinea PA. Finally, he AM-AM cha ac e is ic in Fig. 8
demons a es he success ul linea iza ion and compensa ion o memo y and impedance misma ched
e ec s using he GMP DPD model.
Fig. 6. 16-QAM cons ella ions be o e (blue) and a e ( ed) DPD unde misma ched condi ion.
Fig. 7. PA ou pu powe spec a be o e (blue) and a e ( ed) DPD unde misma ched condi ion.
Fig. 8. PA AM-AM cha ac e is ic be o e (blue) and a e ( ed) DPD unde misma ched condi ion.
Conclusion
The esul s demons a e he e ec i eness o he GMP DPD model in mi iga ing nonlinea dis o ions and
memo y e ec s, e en unde challenging impedance misma ched condi ions, which a e pa icula ly
ele an in PLC. The selec ion o he mos ele an basis unc ions using he DOMP app oach enabled an
e icien implemen a ion o DPD, signi ican ly educing bo h in-band and ou -o -band dis o ions. As
shown in Table I, he p oposed me hod achie ed up o 17 dB imp o emen in ACPR and educed he EVM
om 26.4% o 1.1%, highligh ing i s capabili y o enhance signal in eg i y in PLC sys ems whe e impedance
misma ches a e common due o a ying line condi ions. Fu he mo e, he AM-AM cha ac e is ic
e idences he success ul compensa ion o memo y and misma ch e ec s, ensu ing imp o ed linea i y and
obus ness in signal ansmission. These indings alida e he impo ance o adap i e DPD echniques in
main aining spec al e iciency and eliable communica ion pe o mance in nonlinea and impedance-
misma ched PLC en i onmen s.
Re e ences
[Gil25] Gilabe , P.L. and Mon o o, G. (2025). Digi al P edis o ion o Powe Ampli ie s. In Encyclopedia o RF and
Mic owa e Enginee ing, K. Chang (Ed.). h ps://doi.o g/10.1002/0471654507.e me422
[Kim01] J. Kim and K. Kons an inou, Digi al p edis o ion o wideband signals based on powe ampli ie model wi h
memo y, Elec on. Le . 37: 1417–1418 (No . 2001).
[Mo 06] D. R. Mo gan, Z. Ma e al., A gene alized memo y polynomial model o digi al p edis o ion o RF powe
ampli ie s, IEEE T ans. Signal P ocess. 54(10): 3852–3860 (Oc . 2006).
[Zhu15] A. Zhu, “Decomposed ec o o a ion-based beha io al modeling o digi al p edis o ion o RF powe
ampli ie s,” IEEE T ans. Mic ow. Theo y Tech., ol. 63, no. 2, pp. 737–744, Feb. 2015.
[Mol17] A. Molina, K. Rajamani, and K. Azade , “Digi al p edis o ion using lookup ables wi h linea in e pola ion
and ex apola ion: Di ec leas squa es coe icien adap a ion,” IEEE T ans. Mic ow. Theo y Techn., ol. 65, no. 3, pp.
980–987, Ma . 2017.
[Gil08] P. L. Gilabe , A. Cesa i, G. Mon o o, E. Be an, and J.-M. Dilhac, “Mul i-lookup able FPGA implemen a ion
o an adap i e digi al p edis o e o linea izing RF powe ampli ie s wi h memo y e ec s,” IEEE T ans. Mic ow.
Theo y and Techn., ol. 56, no. 2, pp. 372–384, 2008.
[Fis23] A. Fische -Bühne , L. An ila, M. D. Gomony, and M. Valkama, “Phase-no malized neu al ne wo k o
linea iza ion o RF powe ampli ie s,” IEEE Mic ow. Wi eless Tech. Le ., ol. 33, no. 9, pp. 1357–1360, 2023.
[Lop22] D. López-Bueno, G. Mon o o and P. L. Gilabe , "T aining Da a Selec ion and Dimensionali y Reduc ion o
Polynomial and A i icial Neu al Ne wo k MIMO Adap i e Digi al P edis o ion," in IEEE T ansac ions on Mic owa e
Theo y and Techniques, ol. 70, no. 11, pp. 4940-4954, No . 2022
[C i25] R. C iado, W. Li, W. Thompson, G. Mon o o, K. Chuang and P. L. Gilabe , "Model-O de Reduc ion o
Mul is age Cascaded Models o Digi al P edis o ion," in IEEE Jou nal o Mic owa es, ol. 5, no. 1, pp. 137-149, Jan.
2025.
[Bec18] J. A. Bece a, M. J. Made o-Ayo a, J. Reina-Tosina, C. C espo-Cadenas, J. Ga cia-F ias, and G. A ce, “A doubly
o hogonal ma ching pu sui algo i hm o spa se p edis o ion o powe ampli ie s,” IEEE Mic ow. Wi eless Compon.
Le ., ol. 28, no. 8, pp. 726–728, Aug. 2018.
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