Adv. Radio Sci., 4, 189–195, 2006
www.adv-radio-sci.net/4/189/2006/
© Author(s) 2006. This work is licensed
under a Creative Commons License.
Advances in
Radio Science
IQ-imbalance and its compensation for non-ideal analog receivers
comprising frequency-selective components
M. Mailand, R. Richter, and H.-J. Jentschel
Dresden University of Technology, Institute of Traffic Information Systems, 01062 Dresden, Germany
Abstract. Within current implementations of mobile terminals, more and more analog components are replaced by
appropriate digital processing. On the one hand, the analog front-ends become less complex. On the other hand,
more digital signal processing is required to compensate
for the spurious effects of the front-end. In this article, the frequency-selective imbalance of the in-phase and
quadrature-phase signals is addressed. A closed representation of arbitrary signals being processed by an arbitrary imbalanced analog front-end is provided. The analysis is valid
for both, direct conversion and intermediate frequency (IF)
reception. With the consideration of practical variations of
amplitude and phase impairments, the influence of only the
frequency-dependent portions of the impairments is investigated. It is shown, that the compensation of the quasilinear impairments is sufficient and complex deconvolutive
IQ-regeneration procedures are not stringently required to
obtain sufficient signal qualities.
1 Introduction
In modern mobile communication receivers, more and more
analog components are replaced by digital building blocks.
One the one hand, this leads to less circuitry effort (chip
size, power consumption, etc.) in the analog domain. On the
other hand, additional digital signal processing is required in
order to remove spurious effect of the sub-optimum analog
front-end.
In this article, we investigate a certain type of analog signal distortions, i.e. the in-phase (I) and quadraturephase (Q) imbalance. For heterodyne or intermediate frequency (IF) reception, IQ-imbalance causes the well-known
image problem. There, the respective image channel mixes
Correspondence to: M. Mailand
([email protected])
partially onto the wanted signal during the IF-down conversion, (Valkama et al., 2001). Within an homodyne, direct conversion or zero-IF reception, IQ-imbalance leads to
a distortion of the IQ-signals themselves within the respective wanted channel. For both frequency down conversion
concepts, the IQ-imbalance is a serious issue degrading the
reception performance. This spurious effect occurs mainly
due to amplitude- and phase-impairments between the local
oscillator paths as well as due to mismatches between the
respective IQ-branches after the analog down conversion.
For the case of wideband transmission, the anyway distorting IQ-imbalance mixing becomes an IQ-imbalance convolution, due to the frequency selectivity of the analog frontend components after the down conversion. Thereby, especially different impulse responses of filters and IF- or
baseband-amplifiers have significant influence.
For direct conversion and IF-conversion, we will show
for transmissions utilizing wideband signals, that the impact
of the IQ-imbalance convolution or the frequency selectivity of the components, respectively, has not to be considered
stringently. Mainly, the mean values of the phase- and amplitude impairments of the IQ-imbalance convolution cause
most of the signal distortions. Therefore, it will be sufficient
to compensate for the frequency-selective IQ-imbalance convolution with methods primarily developed for ‘simple’ IQimbalance compensation, e.g. by utilizing blind source separation (BSS) algorithms, (Cardoso et al., 1996).
2
Receiver front-ends
The technique of direct down conversion (DDC) transforms
the RF-signal directly down to baseband. For that purpose,
the LO is set to the carrier frequency ωLO = ωRF of the
wanted channel. Due to temperature dependencies, production imperfections etc., the analog components in the I- and
Q-path can not be perfectly matched. The amplitude as well
Published by Copernicus GmbH on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
190
2
M. Mailand
al.: IQ-imbalance
its compensation
for non-ideal
analog
receivers
Marko Mailand
et al.: et
IQ-Imbalance
and itsand
Compensation
for Non-ideal
Analog
Receivers
...
analog
z’I (t)
Frequency
DownConversion
sRF (t)
LO
ADC
ŝI (k)
BPF/LPF
DSP
(Mixing incl.
Amplitude & Phase
Errors of the LOPaths)
LNA
digital
z’Q (t)
ŝQ (k)
ADC
BPF/LPF
cos(ωRF t)
90°
M1
a)
M1
b)
(·)²
M2
(·)²
M3
(·)²
φ1
φ2
g1
g2
φ1
φ2
φ3
g1
g2
g3
Fig.
multiplicative mixing
mixing
Fig. 1.1. General
GeneralDDC
DDCfront-end
front-end utilizing
utilizing (a)
a) multiplicative
or
additive mixing;
mixing; with
with imbalance
imbalance of
of the
the LO-signal
LO-signal and
and path
path
or (b)
b) additive
mismatches.
mismatches.
ideal
changes
into
as
theLO-signal
actual phase
of the
respective LO-signal to the I- or
Q-path will differ from the respective optimal values result= gϕ1 · cos(ω
) −imbalances.
j g2 · sin(ωLO
t + ϕ2 ) (1)
sLO
LO t + ϕ1g
ing
in (t)
phase
Therefore,
the
i and amplitude
i
ideal
LO-signal
changes
into
for the distorted paths (see Fig. 1).
of the respective
front-end architecture, there
s LOIndependent
(t) = g1 · cos(ω
LO t + ϕ1 )
will be different signal paths for the I-signal and the Q-signal.
−j g2 · sin(ω
t + ϕ2 ) in the
(1)
These signal paths are also expected
to beLO
unmatched
realistic
case. Hence,
they Fig.
influence
by
for
the distorted
paths (see
1). the IQ-components
th
anIndependent
additional scaling,
i.e.
path
mismatch
M
for
the
i
path.
i
of the respective front-end architecture,
there
wethe
assume
thatand
anythe
type
of rewillFor
be further
differentinvestigations,
signal paths for
I-signal
Q-signal.
ceiver being regarded comprises some direct current (DC)
These
signal paths are also expected to be unmatched in the
offset cancellation.
realistic case. Hence, they influence the IQ-components by
The influence of flicker noise or 1/f -noise which is an
an additional scaling, i.e. path mismatch Mi for the i th path.
additional serious problem especially for CMOS implemenFor further investigations, we assume that any type of retations of DDC receivers is not addressed in this paper.
ceiver being regarded comprises some direct current (DC)
offset
cancellation. Mixing
2.1 Multiplicative
The influence of flicker noise or 1/f -noise which is an
additional
serious
problem
for implementation
CMOS implemenMultiplicative
mixing
is theespecially
conventional
of
tations
of DDC
receiversHere,
is notthe
addressed
in is
this
paper. by
direct down
conversion.
RF-signal
multiplied
the original LO-signal within one path (in-phase signal, I)
2.1
Multiplicative
and by
a 90◦ rotatedmixing
LO-signal in a second path (quadraturephase signal, Q), i.e. in principle x(t) = LPF{sRF (t) ·
Multiplicative
is the branch
conventional
implementation
sLO (t)}. Themixing
upper signal
is assumed
not to be
of
direct
down
conversion.
Here,
the
RF-signal
is path
mulmatched to the second path. This leads to a relative
tiplied
by
the
original
LO-signal
within
one
path
(inmismatch M1 . In Fig. 1a), the receiver front-end with the
◦ rotated LO-signal in a secphase
signal,
I)
and
by
a
90
respective impairments is shown. After mixing, the low pass
ond
signal,higher
Q), frequency
i.e. in principle
filterpath
(LPF)(quadrature-phase
suppresses the unwanted
terms.
x(t)
=
LPF{s
(t)
·
s
(t)}.
The
upper
signal
is asThus, almostRF
only theLO
IQ-signals of interest will branch
be digitized.
sumed
not
to
be
matched
to
the
second
path.
This
leads
According to Fig. 1a) and considering all the impairments,to
awe
relative
get: path mismatch M1 . In Fig. 1a, the receiver frontend with the respective
impairments is shown. After mixing,
1
0
thezlow
pass
filter
(LPF)
suppresses the unwanted higher fre(2)
I (k) = g1 M1 · sI (k) cos(ϕ1 ) + sQ (k) sin(ϕ1 )
2 Thus, almost only the IQ-signals of interest
quency terms.
1
0 be digitized.
will
According
to 2Fig.
andcos(ϕ
considering
all
zQ
(k) = g2 · −s
) + s1a
(3)
I (k) sin(ϕ
Q (k)
2) .
2
Adv. Radio Sci., 4, 189–195, 2006
Inimpairments,
general, the equations
the
we get: (2) and (3) can be rewritten in a
matrix form to consider
all possible, linear imbalances
(ex1
cept
DC-offsets):
zI0 (k)
= g1 M1 · sI (k) cos(ϕ1 ) + sQ (k) sin(ϕ1 )
(2)
2
z 0 (k)
A1 B1
sI (k) 0 1
0
A2 s· =−sI 0I(k) sin(ϕ
= 2) +
(4)(3)
zQ
(k) z= = g
sQ (k) cos(ϕ
2) . .
z
(k)
A
B
s
2
2
Q (k)
Q
2
general,tothe
Eqs.
(2) andgain
(3) can
rewritten
in a maWe In
consider
have
arbitrary
and be
phase
impairments
trix form
all possible,
imbalances
(except
within
eachtoofconsider
the IQ-paths,
althoughlinear
a relative
IQ-imbalance
DC-offsets):
was
sufficient, (Valkama et al., 2001). Hereupon, we define
0
ratio (SIR)
for the IQ-branches:
the signal-to-interference
z (k)
A1 B1
sI (k)
z0 = A s = 0I
=
. |B |
(4)
zQ (k) | A1 | A2 B2
2
sQ (k)
, SIRQ = 20 · log10
. (5)
SIRI = 20 · log10
| B1 |
| A2 |
We consider to have arbitrary gain and phase impairments
2.2
Additive
within
each ofMixing
the IQ-paths, although a relative IQ-imbalance
was sufficient, (Valkama et al., 2001). Hereupon, we define
Direct
down conversion byratio
additive
a lot of
the signal-to-interference
(SIR)mixing
for thegained
IQ-branches:
attention in the recent years. Usually, the six-port technology is applied. In the use
| Bthe
| A1as| communication receiver
2 | for, aSIR
· log10 Fig. 1b)
. (5)
· logreduced
Q = 20
I = 20was
10
merSIR
six-port
to
five-port
structure.
| B1 |
| A2 |
shows the general architecture for additive DDC utilizing
Additive
mixing
a2.2
five-port.
Clearly,
the mixers (multiplicative elements in
Fig. 1a) ) are replaced by appropriate summing elements folDirectby
down
conversion
by additive
mixing
gainednonlinear
a lot of atlowed
a square-law
device
(in general,
a simple
tention
in
the
recent
years.
Usually,
the
six-port
technology
component, e.g. a diode). The advantages compared to the
is applied. concept
In the use
as communications
the formixer-based
are e.g.,
better robustnessreceiver
for RF-signal
mer
six-port
was
reduced
to
a
five-port
structure.
Figure
power level fluctuations, DC-offsets can be cancelled more1b
showsand
theit general
architecture
for broadband
additive DDC
utilizing
easily
is possible
to implement
receivers
in
a
five-port.
Clearly,
the
mixers
(multiplicative
elements
in
a comparably simple manner, (Ratni et al., 2002).
Fig.
are replaced bysignal
appropriate
summing elements
folThe1adown-converted
before analog-to-digital
conlowed by
a square-law
devicecan
(in generally
general, abesimple
nonlinear
version
(A/D)
of the front-end
denoted
with
component,
e.g.
a
diode).
The
advantages
compared
to the
2
zi0 (t) = gi2 M
· (se.g.,
+ s2Q (t))
(6)
i + Miare
I (t) better
mixer-based
concept
robustness
for
RF-signal
|
{z
}
power level rectified
fluctuations,
DC-offsets
wave including
DC-offsets can be cancelled more
in
easily and+it2isMpossible
to
implement
broadband receivers
i · sI (t) gi cos(ϕi ) + sQ (t) gi sin(ϕi )
| simple manner, (Ratni
{z et al., 2002).
}
a comparably
wanted signal components
The down converted signal
before analog-to-digital conversion
(A/D) ofshift
the front-end
with
The phase
elementscanϕgenerally
and be
thedenoted
attenuai
tion/amplification
components 2gi within the five-port
zi0 (t) = gi2 Mi + Mi · (sI2 (t) + sQ
(t))
comprise
| known, wanted
{z values as }well as impairments.
Hence, they
contribute
to the DC-offsets
indeterminacy of the front-end
rectified
wave including
transmission
due
to
spurious
effects.
+ 2 Mi · sI (t) gi cos(ϕi ) + sQ (t) gi sin(ϕi )
(6)
The rectified
wave which comprises
the DC-offsets
|
{z
} can be
components
easily removed by awanted
simplesignal
front-end
calibration (Hentschel
, 2004) or by the implementation of an appropriate front-end
The phase shift elements ϕi and the attenuaarchitecture (Mailand et al., WCNC 2005).
tion/amplification components gi within the five-port
Therefore, we obtain measurements which consist only
comprise known, wanted values as well as impairments.
of linear mixtures of the IQ-signals, i.e. zi0 (k) = 2 Mi ·
Hence, they contribute to the indeterminacy of the front-end
sI (k) gi cos(ϕi ) + sQ (k) gi sin(ϕi ) in (6). In consetransmission
due to spurious effects.
quence, the transmission of the DDC front-end with additive
The rectified wave which comprises the DC-offsets can be
mixing is determined by
easily removed by a simple
calibration
front-end
(Hentschel,
2004) or0 by the implementation
of
an
appropriate
zI0 (k)
A1 B1
sI (k) front-end
z = As = 0
=
.
(7)
architecture (Mailand
zQet
(k)al., WCNC
A2 B2005).
s
2
Q (k)
Therefore, we obtain measurements which conThe
∈ [0, 2π)ofhave
different ofi.e.
sist phase
only parameters
of linearϕimixtures
theto be
IQ-signals,
s (t),
each
other,
to
assure
a
possible
separation
of
s
(t)
and
0
I
Q
zi (k) = 2 Mi · sI (k) gi cos(ϕi ) + sQ (k) gi sin(ϕ
in
i)
i.e. to guarantee a nonsingular mixing matrix A.
www.adv-radio-sci.net/4/189/2006/
4
Marko Mailand et al.: IQ-Imbalance a
Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ...
3
M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers
191
the o
which is centered at ωRF and covers a bandwidth B (Fig. 2). IQ-fr
S (ω)
analog
digital
The operation (·)∗ denotes complex conjugation of its argu- rejec
x (t)
z’ (t)
SIF*
ment. In (8)
H (f )
H (f )
ADC
SIF
ŝ (k)
*
imag
SIM
SIM
S0*
S0
s (t)
DSP
z(t) = s0 (t) + sIF (t) exp(jωIF t) + sIM (t) exp(−jωIF t) can n
z’ (t)
x (t)
addit
ŝ (k) (9)
ADC
(f )
H (f )
= zI (t) + j · zHQ (t)
the o
φ
ω
is the general multichannel baseband signal.
-(ω + ω ) -ω
-(ω -ω )
ω -ω
ω
ω +ω
M
LO
Without the g loss of general validity, the analog com- signa
B
ponents: LO-paths
within the frequency down-conversion
90°
cos(ω t)
stage, branch filters and amplifiers, analog-to-digital conFig.2. 2.Schematic
Schematicfrequency
frequencydomain
domain illustration
illustration of the
Fig.
the RF-signal
RF-signal Fig. verters
(ADC) contribute
to the considering
respectivefrequencyfrequency3. 3. Imbalanced
front-end
frequencyFig.
Imbalanced
front-end model;
model;
considering
comprisingthree
threechannels
channelscentered
centeredat
at ωωRF
comprising
RF..
independent
orfrequency-selective
frequency-selective
IQ-imbalances.
Hence,
independent
andand
frequency-selective
IQ-imbalance;
multiplicative
independent
IQ-imbalance;
multiplicative
we can combine
several components what leads to a more With
frequency-conversion
utlized.
frequency
conversionthe
utilized.
general front-end model. In Fig. 3, the amplitude and phase HQ (
Eq.
In consequence,
the transmission
DDC
The(6).
composition
of the base-band
signals of
or the
front-end
impairments
are modelled by the relativeZ(errors
g and ϕ, re- ances
*
a)
Z (-ω)
ω)
front-end withxadditive
mixing is determined by
translated
deconvolution
the
measurements
i (k) is systematically a mixture of I-signals
spectively,into
within
the mixingmethods
stage. which
HN OMconsider
(ω) represents
e.g. (
mixing.
Utilizing
frequency-selectivity
of the imbalance.
and Q-signals zfor
additive
multiplicative
0 (k)
the
(LPF)
functionality
which
rejects
* nominal* low-pass-filter
Ho
A1 B1
sI (k)
SIF (-ω)
(ω)
S0 (-ω)
I
z0 = Athe
s =IQ-mixture
.
(7)
Therefore,
we need*components
a general description
ofdown-conversion.
theSIFwideband
0 (ω)
mixing,
zi0 (k) is due
0 (k) =within one measurement
the
high frequency
after Sthe
zQ
A2 B2
sQ (k)
by th
SIM (-ω)
SIM (ω)
signal
being the
affected
by amplitude/phase
impairments
to front-end impairments.
Therefore,
complex
signal after the nominal
LPFand
of the fects
path
mismatches.
Following
the
explanations
in
(Valkama
Nevertheless,
although
analog
processing
is signifiThe
phase parameters
ϕi the
∈ [0,
2π ) have
to be different
of
branches is:
tive f
et al., 2001), we consider
signal
n a multichannel received
o
each different,
other, to assure
a possible
separationofofdirect
sI (t) down
and sQcon(t),
cantly
the general
description
tions
x(t) = LP FNnOM sRF (t) · sLO
o (t)
i.e. to guarantee
a nonsingular
mixing
matrix A.
version
transmission,
considering
spurious
effects, is the
of (2
ω
ω
-ω
-ω
ω
ω
IF
IF
IF
IF
sRF (t) = 2 · < z(t)exp(j ωRF t)
of the baseband
signals or
front-end
measameThe
forcomposition
both, multiplicative
and additive
mixing.
Furthering m
=
z
(t)
+
j
·
g
cos(ϕ)
z
(t)
−
g
sin(ϕ)
z
(t)
I
Q
I
surements
xi (k) isofsystematically
a mixture for
of I-signals
and
more,
an analysis
the interrelationships
IF-reception
= z(t) exp(j ωRF t) + z∗ (t) exp(−j ωRF t) (8)
cesse
Q-signals
for additive conclusions.
mixing. Utilizing
multiplicative
leads
to comparable
With
respect tomixIQ- b)
=
x
(t)
+
j
·
x
(t)
.
I
Q
Z’(
ω
)
insuf
ing, the IQ-mixture
one measurement
zi0 (k) is
due to
which is centered at ωRF and covers a bandwidth B (Fig. 2).(10)
imbalance,
the analogwithin
front-end
can be modelled
indepenis ne
front-end
The operation (·)∗ denotes complex conjugation of its argudently
fromimpairments.
the utilized technology.
As
Nevertheless,
analog
processingthe
is original
signifiThe transfer
functions HI (ω) and HQ (ω) stand for the actual
ment.
In Eq. (8)
The
problem to although
be solvedthe
is how
to regenerate
tain
t
cantly different,
general description
of direct
down conmismatch due to the frequency-selective differences of the
IQ-signals
withoutthe
knowledge
of the front-end
transmission,
Adap
z(t) = scomponents
ωI F t) + and
s I M (t)
ωI F t)
version transmission, considering spurious effects, is the
analog
ofexp(j
the in-phase
theexp(−j
quadrature-phase
0 (t) + s I F (t)
i.e. the mixing matrix A. For that purpose, adaptive filtersame for both, multiplicative and additive mixing. Furtherbranch,
respectively.
With
the
use
of
(10),
we
obtain
the
=
z
(t)
+
j
·
z
(t)
(9)final calib
ω
ω
I
Q -ωIF
IF
ing and blind source separation algorithms can be applied
more, an analysis of the interrelationships for IF-reception
(Win
IQ-imbalanced
signal
mixture
as:
(Valkama et al., 2001) as well as several calibration proceleads to comparable conclusions. With respect to IQis
the
general
multichannel
baseband
signal.
Fo
4.0 Schematic description of (a) a general multichannel signal
dures
(Hentschel
, 2004)front-end
for both can
of the
front-end indepenarchitec- Fig. Z
(ω) = H
Xof
+ j · validity,
HQ (ω) Xthe
imbalance,
the analog
be modelled
I (ω)
I (ω)
Q (ω)
Without
the
loss
general
analog
compoconv
and (b) the respective
resulting0 IQ-imbalanced mixture.
tures.
dently from the utilized technology.
nents: LO-paths
down conversion stage,(11) tion
= ZI0 (ω)within
+ j ·the
ZQfrequency
(ω)
The problem to be solved is how to regenerate the original
branch filters and amplifiers, analog-to-digital converters
But,
= HI (ω) ZI (ω)
IQ-signals without knowledge of the front-end transmission,
respective frequency-independent or and
and(ADC) contribute to the 3 i.e.IQ-Imbalance
- Effects
of that
Amplitude/Phase
Impairthe mixing matrix
A. For
purpose, adaptive
filterfrequency-selective
IQ-imbalances.
we can combine
+ j · HQ (ω)
· g cos(ϕ) ZHence,
Q (ω) − g sin(ϕ) ZI (ω)
tions
ments
and Path
Mismatches
ing
and blind
source
separation algorithms can be applied
the several components
what leads to a more
1
general frontable
G2 (ω)
= · Fig.
A (ω)
− AQ (ω) and phase impairments
(Valkama et al., 2001) as well as several calibration proceend
model.
= 2In
HI (ω)I3,
− the
j Hamplitude
Q (ω) g sin(ϕ) · ZI (ω)
(15)
imba
(Hentschel,
2004) for
of thetofront-end
architecare modelled
relative errors g and ϕ, respectively,
Indures
the previous
sections,
we both
assumed
have only
quasi1 by the
=
·
H
(ω)
−
H
(ω)
g
exp(j
ϕ)
.
I HQ (ω)
Qcos(ϕ)
tures.impairments. In reality, the amplitude and phase imwithin the mixing
HNgOM
(ω) represents
ZQ (ω) the nominal
linear
2+ j · stage.
–
low-pass-filter (LPF) functionality which rejects the high frepairments have a frequency dependent characteristic. Hence,
=the
AIoverlapping
(ω) · Zafter
+ jshown
· AQ (ω)
ZQ (ω)
(12)
I (ω)the
down
conversion.
Therefore,
Fig. 4,components
is
of ·Z(ω)
and
Z ∗ (−ω)
different parts (at different frequencies) of a single chan- Inquency
IQ-imbalance
effects of amplitude/phase
impairsignal(12)
afteristhe
of the
branches
is:in(7)
tocomplex
theequation
IQ-imbalance
as
given
inLPF
(13).
This
nel3 will
be affected- differently.
Usually, this effect
be- duethe
Thus,
thenominal
generalized
version
ofresults
(4) and
0
ments
and
path
mismatches
n
o
the
imbalanced
multichannel
baseband
observation
Z
(ω)
comes more serious with wider bandwidths. In such cases,
and can be used for the description of any type of imbalanced
–
=
LP
F
s
(t)
·
s
(t)
x(t)
N
OM
RF
LO
in Fig. 4(b).front-end.
In general, there are two possible imbalthe known techniques of IQ-regeneration will have to be shown
IQ-processing
In the previous sections, we assumed to have only quasifor
the
and
the2001),
desiredthe
translated into a deconvolution methods which consider the ance scenarios:
With
the +simplifications
in(t)
(Valkama
etzIal.,
= zI (t)
j · IF-reception,
g cos(ϕ) zQ
−image
g sin(ϕ)
(t)
linear impairments. In reality, the amplitude and phase imsignal
mix
onto
each
other
(S
and
S
)
or,
within
frequency-selectivity of the imbalance.
down-converted
and
generally
imbalanced
signal
can
bedi-deIF
IM
pairments have a frequency dependent characteristic. Hence,
=
x
(t)
+
j
·
x
(t)
.
(10)
I
Q
rect
conversion,
the
desired
signal
is
distorted
by
a
complex
noted
as
Therefore,
we (at
need
a general
descriptionofofa the
wideband
different
parts
different
frequencies)
single
chancomplex
conjugated
of
itself
Fursignal
being
amplitude/phase
and scaled
–
nel will
be affected
affected by
differently.
Usually,impairments
this effect beThe and
transfer
HI (ω) andversion
H+Q (ω)
stand
the0 ).
actual
0 functions
∗ (S
(ω) = Gmentioned
G2 (ω)
· Zfor
(−ω)
(13)
1 (ω) · Z(ω)
it Z
should
that
IQ-imbalance
not
path
mismatches.
Following
thebandwidths.
explanationsIninsuch
(Valkama
comes
more serious
with wider
cases, thermore,
mismatch
due to be
the frequency-selective
differencesdoes
of the
et the
al., known
2001), we
considerofa multichannel
received
signal
the components
distortions of the
thein-phase
channeland
affecting
the respective
analog
the quadrature-phase
techniques
IQ-regeneration
will have
to be equal
with
IQ-signals
in
general.
On
the
one
hand,
for
zero-IF
recep
n
o
1
·
A
(ω)
+
A
(ω)
G
(ω)
=
=
s
(t)),
the
general
imbalance
description
(13)
tion
(z(t)
I
Q
1
sRF (t) = 2 · < z(t) exp(jωRF t)
0
www.adv-radio-sci.net/4/189/2006/
Adv. Radio Sci., 4, 189–195, 2006(14)
2
–
shows comparable1transmission behavior as the RF-channel.
= z(t) exp(jωRF t) + z ∗ (t) exp(−jωRF t) (8) Hence, in this case,
= · one
HIcould
(ω) + include
HQ (ω) gthe
exp(−j
ϕ)
IQ-regeneration
2
within the channel equalization, at least partly. But, on
RF
Frequency
Down-Conversion
I
NOM
I
I
I
RF
Q
Q
NOM
RF
IF
RF
RF
IF
RF
IF
RF
RF
IF
RF
Q
Q
90°
cos(ωRF t)
SIR =
|G1 (ω)|2
.
|G2 (ω)|2
(16)
Fig. 3. Imbalanced front-end model; considering frequencyindependent and frequency-selective IQ-imbalance; multiplicative
192
M. Mailand et al.: IQ-imbalance
its compensation
non-ideal analog
Withoutand
a mismatch
of the for
IQ-branches,
i.e. receivers
HI (ω) =
frequency-conversion utlized.
a)
*
Z (-ω)
SIF* (-ω)
Z(ω)
S0*(-ω)
ωIF
-ωIF
*
SIM
(-ω)
SIM (ω)
ω
b)
S0 (ω)
-ωIF
SIF (ω)
ωIF
ω
Z’(ω)
ωIF
-ωIF
ω
Fig.
Fig. 4.
4. Schematic
Schematic description
descriptionof
of(a)
(a)aageneral
generalmultichannel
multichannelsignal
signal
and
and (b)
(b) the
the respective
respective resulting
resultingIQ-imbalanced
IQ-imbalancedmixture.
mixture.
branch,
respectively. With the use of Eq. (10), we obtain the
and
final IQ-imbalanced
signal mixture as:
1 G
(ω)
=
·
A
(ω)
−
A
(ω)
2
I
Q
2 XI (ω) + j · HQ (ω) XQ (ω)
Z 0 (ω) = HI (ω)
(15)
0 1
0
= ZI=(ω) ·+ jH·IZ
(ω)
(11)
(ω)
.
Q − HQ (ω) g exp(j ϕ)
2
= HI (ω) ZI (ω)
In Fig. 4, the overlapping
is shown of Z(ω) and Z ∗ (−ω)
+
j
·
H
(ω)
·
g
cos(ϕ)
Z
(ω)
−
g
sin(ϕ)
Z
(ω)
Q
I
due to the IQ-imbalance
as givenQ in (13). This results
in
observation Z 0 (ω)
the imbalanced
multichannel baseband
= H (ω) − j HQ (ω) g sin(ϕ) · ZI (ω)
shown in Fig.I 4(b). In general,
there are two possible imbal
ance scenarios:
for
IF-reception,
and the desired
+ j · HQ (ω) g cos(ϕ)theZimage
Q (ω)
signal mix onto each other (SIF and SIM ) or, within di= AI (ω) ·the
ZI desired
(ω) + j signal
· AQ (ω)
· ZQ (ω) by a complex
(12)
rect conversion,
is distorted
scaled and complex conjugated version of itself (S0 ). FurThus,
Eq. (12)
is thebegeneralized
of Eqs. (4) does
and (7)
thermore,
it should
mentionedversion
that IQ-imbalance
not
and
can
be
used
for
the
description
of
any
type
of
imbalanced
equal the distortions of the channel affecting the respective
IQ-processing
front-end.On the one hand, for zero-IF recepIQ-signals in general.
With
the
simplifications
in (Valkama
et description
al., 2001), (13)
the
imbalance
tion (z(t) = s0 (t)), the general
down
converted
and
generally
imbalanced
signal
can
be
deshows comparable transmission behavior as the RF-channel.
noted
Hence,as in this case, one could include the IQ-regeneration
within
equalization,
least partly. But,
on
0
Z
(ω) =the
G channel
(ω) · Z(ω)
+ G (ω) · Zat∗ (−ω)
(13)
1
2
with
1 · AI (ω) + AQ (ω)
2
1 = · HI (ω) + HQ (ω) g exp(−j ϕ)
2
G1 (ω) =
(14)
and
1 · AI (ω) − AQ (ω)
2
1 = · HI (ω) − HQ (ω) g exp(j ϕ) .
2
G2 (ω) =
Adv. Radio Sci., 4, 189–195, 2006
(15)
HQ (ω), (16) turns into the relation for quasi-linear imbalances
which
already been
depicted
in various
In Fig.
4, thehas
overlapping
is shown
of Z(ω)
and Z ∗articles,
(−ω)
e.g.to(Valkama
et al., 2001),
(Windisch
al., 2004),
due
the IQ-imbalance
as given
in Eq.et(13).
This etc.
results
0 (ω)
However,
in (13)
and Fig. 4,baseband
the termobservation
Z ∗ (−ω) isZcaused
in the
imbalanced
multichannel
by theinimbalances
represents
aliasing
general,
there the
are image
two possible
im-efshown
Fig. 4b. Inand
fects. scenarios:
Therefore, for
weIF-reception,
lose the separability
thetherespecbalance
the imageofand
detive signal
frequency-signals.
analog
sired
mix onto eachWith
otherpractical
(SI F and
SI M )implementaor, within
tions conversion,
of receiver front-ends,
SIRis isdistorted
usually by
in the
range
direct
the desired the
signal
a comof (20
. . . 40)dB.
For theconjugated
most of currently
utilized
plex
scaled
and complex
version of
itself receiv(S0 ).
ing methods it(zero-IF,
low-IF,
wideband-IF)
and usually
proFurthermore,
should be
mentioned
that IQ-imbalance
does
cessed
modulation
schemes/orders,
this image
attenuation
not
equal
the distortions
of the channel
affecting
the re- is
spective
IQ-signals
in general.
On the one for
hand,
for zeroinsufficient.
In principle,
a compensation
IQ-imbalance
IFis reception
needed. (z(t) = s 0 (t)), the general imbalance descriptionAs
(13)
showsmentioned,
comparablethere
transmission
liketothe
already
are severalbehavior
techniques
obRF-channel.
Hence,
in this case,
oneforcould
include mixtures.
the IQtain the required
separation
matrix
quasi-linear
regeneration
within
the algorithms
channel equalization,
at least partly.
Adaptive filters,
blind
as well as test-signal-based
But,
on the other
hand,
IF-reception
with state-of
the2001),
art
calibration
methods
arean
state
of the art (Valkama
et al.,
analog
IQ-front-ends,
can(Mailand
not guarantee
sufficient
(Windisch
et al., 2004),
et al., aIST
2005). imagechannel-rejection
before
the first
conversion.
For the task of
retrieving
thefrequency
original signal
out ofAsthe
result,
the image
channel
will overlap
ontodifferent
the desired
chanconvolved
mixture
as depicted
in (13),
deconvolunel,
can notwere
be compensated
for (Cardoso
by channel
tionwhich
algorithms
proposed, e.g.
et equalizaal., 1996).
tion.
additional
IQ-regeneration
required stringently
But, An
since
we are aiming
at simple,islow-power,
high-speed
toand
recreate
the orthogonality
of the for
desired
and communicathe image
thus cost-effective
solutions
mobile
channel.
tions, such deconvolution algorithms turn out not to be suitMoreover,
we can
define a more
version for the
able
candidates
to compensate
thegeneral
frequency-selective
IQsignal-to-image-ratio
(SIR):
imbalances. The reason
for that are somewhat manifold, e.g.:
|G1 (ω)|2
algorithms usually require(16)
sevSI R– =adaptive deconvolution
.
2
|Ghundred
2 (ω)|
eral
up to thousands of symbols to reach their
Without
a mismatch
i.e.
respective
equilibrium,of the IQ-branches,
HI (ω) = HQ (ω), (16) turns into the relation for quasi– this
convergence
process
be been
went through
linear
imbalances
which
has must
already
depicted again
in
after
each
’environmental’
change
(significant
various articles, e.g. (Valkama et al., 2001; Windischtemperaet al.,
2004),ture
etc. change, reception-frequency changes, etc.), due to
the
consequent
changes
However,
in Eq. (13)
and within
Fig. 4,the
theanalog
term IQ-branches,
Z ∗ (−ω) is
caused by the imbalances and represents the image aliasing
– serious
mapping
thethe
frequency
response
the IQeffects.
Therefore,
we of
lose
separability
of theofrespecimbalances
requires
digital
filters
with
a
sufficient
taptive frequency signals. With practical analog implementalength,
whereas
the
update
of
each
tap
has
its
own
untions of receiver front-ends, the SI R is usually in the range
derlying
adaptive
algorithm
and
of (20 . . . 40) dB. For the most of currently utilized receiving methods (zero-IF, low-IF, wideband-IF) and usually pro– an additional digital memory will have to be implecessed modulation schemes/orders, this image attenuation is
mented just only to save all coefficients for a large variinsufficient. In principle, a compensation for IQ-imbalance
ety of reception situations.
is needed.
As already mentioned, there are several techniques to obtain the required separation matrix for quasi-linear mixtures.
Adaptive filters, blind algorithms as well as test-signal-based
calibration methods are state of the art (Valkama et al., 2001;
Windisch et al., 2004; Mailand et al., IST 2005).
For the task of retrieving the original signal out of the
convolved mixture as depicted in Eq. (13), different deconvolution algorithms were proposed, e.g. (Cardoso et al.,
1996). But, since we are aiming at simple, low-power, highspeed and thus cost effective solutions for mobile communications, such deconvolution algorithms turn out not to be
suitable candidates to compensate for the frequency-selective
www.adv-radio-sci.net/4/189/2006/
M. Mailand
et al.: IQ-imbalance
and its and
compensation
for non-ideal
analogAnalog
receivers
Marko Mailand
et al.: IQ-Imbalance
its Compensation
for Non-ideal
Receivers ...
whereas E{·} denotes the expectation or mean value. Standard
IQ-regeneration
compensate for a mixture of g,
4 Practically
requiredmethods
compensation
gQ , ϕ and α for considered quasi-linear amplitude and phase
impairments.
oneexpensive
sets the Ddeconvolution,
= 0 and
Q (ω) = 0 and Dwe
α (ω)
In order
to avoidIfthe
propose
thus
considers
not
to
have
frequency
dependencies
within
to compensate only for the mean values of the general,the
IQ-imbalance, one will obtain a relation for the quasi-linear
frequency-selective IQ-imbalance.
amplitude and phase impairments within G1 and G2 . Since
Let us consider to have only a relative IQ-branch
misthe respective algebraic expressions do not lead to further inmatch, i.e. HI (ω) = 1 and HQ (ω) = H̃Q (ω)/H̃I (ω). Hence,
sight, we leave it up to the recipient to recalculate the somewe obtain:
what long formulas if being interested.
front-end implementaNevertheless,
for typical, practical
1 ·
1
+
H
(ω)
g
exp(−j
ϕ)
(17)
G1 =
Q
tions
and amplitude impairments
2 the mean values for phase
◦
are1in the range of 1 . . . 2 and 1 . . . 2%, respectively. AlG2 =
· 1there
− Hare
g exp(j
.
(18)
Q (ω)
though
only
a fewϕ)
publications
about frequency2
dependent amplitude and phase impairments, we can as◦
Further,
(ω) is
divided deviations
into its mean
values
its
sume H
toQhave
maximum
of ±0.5
and and
±0.03dB
frequency-dependent
both, amplitude
per channel withinIQ-deviations
typical GSMfor
front-ends
or ±0.8◦and
and
±0.08dB per channel within IEEE 802.11a (WLAN) frontphase.
ends, amongst
others deduced
from (Sanderson
et al., 2003)
and =
(Nakagawa
al., ·2004).
the sparse citation
HQ (ω)
gQ + DQet(ω)
exp j Besides
α + Dα (ω)
(19)
about such measurements, it seems to be valid to assume valwith:ues within
n
this o
range, sincenalmost all commercially
available
o
gQ =
E |HQ (ω)|
, αwithout
= E arg
HQ (ω) compensation for
front-ends
operate
IQ-imbalance
frequency-selective influences, whereas there are definitely
whereas
E{·} denotes
the expectation
or variations.
mean value. Stanmismatches
due to fabrication
process
dard IQ-regeneration
methods
compensate
for acompensator
mixture of g,for
Hence, if we assume
to have
an arbitrary
mean
values
of the IQ-imbalances,
the influence
of amgQ , the
ϕ and
α for
considered
quasi-linear amplitude
and phase
plitude andIfphase
impairments
is comparably
and
impairments.
one sets
the DQ (ω)
= 0 and Dαmarginally
(ω) = 0 and
only for
limited
spectral part
of the signal.within
Therefore,
thusthis
considers
nota to
have frequency
dependencies
the
we concludeone
thatwill
expensive
IQ-regeneration
IQ-imbalance,
obtain deconvolutive
a relation for the
quasi-linear is
not a must
orderimpairments
to obtain sufficient
quality.
amplitude
and in
phase
within signal
G1 and
G2 . Since
the respective algebraic expressions do not lead to further insight,
leave it upResults
to the recipient to recalculate the some5 we
Simulation
what long formulas if being interested.
Nevertheless,
for typical,
practical
implementaComputer simulation
were
carried front-end
out to illustrate
the intertionsrelationships
the mean values
for
phase
and
amplitude
impairments
of the various IQ-imbalance sources
and their
www.adv-radio-sci.net/4/189/2006/
b)
0.0
~ 0.1 dB
|HQ| / |HI| [dB]
-0.3
-0.6
-0.9
-1.2
-1.5
-1.8
-0.9 -0.6 -0.3 0.0
0.3
0.6
Normalized Frequency
0.9
arg(HQ) - arg(HI) [deg]
a)
30
20
10
0
~ 2.9°
-10
-20
-30
-0.9 -0.6 -0.3 0.0
0.3
0.6
0.9
Normalized Frequency
Fig. 5. Relative frequency-dependent IQ-branch impairments of (a)
Fig. 5. Relative frequency-dependent IQ-branch impairments of (a)
amplitude
sigamplitudeand
and(b)
(b)phase;
phase;the
theeffective
effectiveregions
regions for
for the
the processed
processed signals
areareaccented.
nals
accented.
are in the1 range of 1 . . . 2◦ and 1 . . . 2%, respectively. Although there are only a few publications about frequencydependent amplitude and phase impairments, we can as0.1
sume to have maximum deviations of ±0.5◦ and ±0.03 dB
per channel within typical GSM front-ends or ±0.8◦ and
0.01per channel within IEEE 802.11a (WLAN) front±0.08 dB
ends, amongst others deduced from Nakagawa et al. (2004).
Besides1E-3
the sparseIdealcitation
16QAM about such measurements, it
g, ϕassume
, g and α compensated
seems to be valid to
values within this range, since
g, ϕ and g compensated
almost all commercially
available
front-ends operate withg, ϕ and α compensated
1E-4
Only g and ϕ compensated
out IQ-imbalance
compensation
for frequency-selective influences, whereas there are definitely mismatches due to fab0
2
4
6
8
10
12
14
rication process
variations.
SNR [dB]
Hence, if we assume to have an arbitrary compensator for
the mean values of the IQ-imbalances, the influence of amFig. 6.and
Symbol-Error-Rate
performances
for different
compensaplitude
phase impairments
is comparably
marginally
and
tion
scenarios
for
the
frequency-independent
portions
of
amplitude
this only for a limited spectral part of the signal. Therefore,
and phase; 16QAM, Low-IF reception, initial SIR = −20dB.
we conclude that expensive deconvolutive IQ-regeneration is
not a must in order to obtain sufficient signal quality.
SER
IQ-imbalances.
The
reasonsCompensation
for that are somewhat mani4 Practically
Required
fold, e.g.:
In order to avoid the expensive deconvolution, we propose
compensate
only for algorithms
the mean values
the general,
– toadaptive
deconvolution
usuallyofrequire
sevfrequency-selective
eral hundred up toIQ-imbalance.
thousands of symbols to reach their
Let us consider
to have only a relative IQ-branch misrespective
equilibrium,
match, i.e. HI (ω) = 1 and HQ (ω) = H̃Q (ω)/H̃I (ω).
we obtain: process must be went through again
– Hence,
this convergence
after each ’environmental’
change (significanttempera1 exp(−j ϕ)
G1 reception-frequency
= · 1 + HQ (ω) g changes,
ture change,
etc.), due (17)
to
2
the consequent changes
within
the
analog
IQ-branches,
1
(18)
G2 = · 1 − HQ (ω) g exp(j ϕ) .
2
– serious mapping of the frequency response of the IQFurther,
HQ (ω)
is divided
mean
values and
imbalances
requires
digital into
filtersitswith
a sufficient
tap-its
frequency-dependent
both,
and
length, whereas the IQ-deviations
update of eachfortap
has amplitude
its own unphase.
derlying adaptive algorithm and
α+D
(ω)imple– an Hadditional
digital
will jhave
toαbe
Q (ω) = g
Q + Dmemory
Q (ω) · exp
n to save all
o coefficients
n for a largeovari(19)
mented just only
with:
g
=
E
|H
(ω)|
,
α
=
E
arg
H
(ω)
Q
Q
Q
ety of reception situations.
1935
Q
Q
compensation with the overall transmission performance of
the imbalanced front-end.
5 Simulation results
Within the simulation, a 16QAM-modulated signal was
transmitted
over an additive
white
gaussian
noise
(AWGN)
Computer simulation
have been
carried
out to
illustrate
the
channel
under
the
assumption
to
have
an
optimal
transmitter.
interrelationships of the various IQ-imbalance sources and
The compensation
receiver front-end
multiplicative
mixing perforlike in
their
withutilizes
the overall
transmission
Fig. 1a) and thus Fig. 3 with a low-IF frequency conversion.
mance of the imbalanced front-end.
The channel bandwidth was set to 20MHz with a bandgap of
Within the simulation, a 16 QAM-modulated signal was
12MHz, whereas the carrier frequency was fRF = 500MHz
transmitted over an additive white gaussian noise
(AWGN)
and the IF was selected at 32MHz. The transmission was
channel under the assumption to have an optimal transmitsplit into blocks of 1024 symbols with each block comprister.
front-endforutilizes
multiplicative
like
ingThe
64 receiver
training symbols
synchronization,
etc. mixing
The system
inused
Fig.a 1a
and
thus
Fig.
3
with
a
low-IF
frequency
consplit raised cosine pulse forming with a rolloff factor
version.
channel
bandwidth
20 MHz
with
of 0.35. The
Within
the IQ-paths
fromwas
the set
LO,torelative
impaira ments
bandgap
of
12
MHz,
whereas
the
carrier
frequency
was
for amplitude and phase were included with g = 0.98
◦was selected at 32 MHz. The
fRF
=
500
MHz
and
the
IF
(−0.175dB) and ϕ = −2 , respectively. The frequencytransmission
wasinsplit
blocks of was
1024modelled
symbols by
with
each
selective error
theinto
IQ-branches
imbalblock
comprising
64
training
symbols
for
synchronization,
anced LPF.
etc. In
TheFig.
system
used
a splitIQ-branch
raised cosine
pulse forming
with
5, the
relative
impairments
are illusa trated
rollofffor
factor
of
0.35.
Within
the
IQ-paths
from
the
LO,
a worst case scenario. As it can be seen, there
relative
impairments
for
amplitude
and
phase
were
included
are additional mean values, i.e. frequency-independent im-
Adv. Radio Sci., 4, 189–195, 2006
(18)
Fig. 5. Relative frequency-dependent IQ-branch impairments of (a)
amplitude and (b) phase; the effective regions for the processed signals are accented.
194
M. Mailand et al.: IQ-imbalance
and its compensation for
non-ideal
analog
receivers
6
Marko
Mailand
et al.:
IQ-Imbalance and
1
SIR = -40dB
for
amand
ore,
on is
nterheir
Q-channel
Ideal 16QAM
g, ϕ, gQ and α compensated
g, ϕ and gQ compensated
g, ϕ and α compensated
Only g and ϕ compensated
1E-3
1E-4
0
2
4
6
8
10
12
14
and phase; 16QAM, Low-IF reception, initial SIR = −20dB.
respectively. The
compensation
with the
overall
frequency-selective
error
in thetransmission
IQ-branches performance
was modelled of
thebyimbalanced
front-end.
imbalanced LPF.
Within
a 16QAM-modulated
was
In Fig.the
5, simulation,
the relative IQ-branch
impairments signal
are illustransmitted
an case
additive
white As
gaussian
noise
(AWGN)
trated for over
a worst
scenario.
it can be
seen,
there
channel
under the
assumption
to have
an optimal transmitter.
are additional
mean
values, i.e.
frequency-independent
impairments,
the amplitude
the phase with
gQ ∼ like
0.99 in
The
receiver for
front-end
utilizesand
multiplicative
mixing
(−0.087
dB)
andFig.
α ∼3−with
1.4◦ .aThe
amplitude
alternates
with
Fig.
1a) and
thus
low-IF
frequency
conversion.
variations
of
±0.05
dB,
which
is
approximately
within
the of
The channel bandwidth was set to 20MHz with a bandgap
variation
range
of
technical
implementations.
In
order
to
12MHz, whereas the carrier frequency was fRF = 500MHz
obtain
results
at
a
low-level
limit
of
implementations
with
and the IF was selected at 32MHz. The transmission was
almost insufficient matching, we selected the phase to vary
split into blocks
of 1024 symbols with each block compriswith ±1.5◦ , what is more than twice the variation within a
ing 64 training symbols for synchronization, etc. The system
typical IQ-processing front-end.
usedNevertheless,
a split raiseditcosine
pulse forming
a rolloff factor
can be observed
that thewith
symbol-error-rate
of (SER)
0.35. performance
Within the IQ-paths
from
the
LO,
relative
impairof the whole system reaches acceptable
ments
for ifamplitude
phase
includedand
with
g =im0.98
values,
the mean and
values
for were
all amplitude
phase
(−0.175dB)
and compensated
ϕ = −2◦ , for
respectively.
ThedB),
frequencypairments were
(at SI R = −20
Fig. 6.
selective
error
the IQ-branches
modelled
imbalObviously,
theinoverall
performance was
increases
as theby
respecanced
LPF.
tive frequency
independent impairments are removed. Since
the
result5,forthe
the relative
compensation
of all mean
values ofare
ampliIn Fig.
IQ-branch
impairments
illustude
and
phase
errors
(concerning
IQ-imbalance)
is
near
to
trated for a worst case scenario. As it can be seen, there
the
ideal,
theoretical
SER-performance
for
a
16
QAM
sigare additional mean values, i.e. frequency-independent imnal, we can state that no further, expensive deconvolution of
the IQ-signals is required. However, if one would do so, the
performance would improve further.
The demodulations’ dependence on the initial signal-tointerference ratio (SI R) is indicated in Fig. 7. For the given
simulation setup, an SI R of −40 dB or less frustrates the
demodulation almost completely, even for high SN R. Starting at SI R ≥ −35 dB, the receiver was able to detect the IQsignals properly resulting in acceptable SER-values.
Based on the presented results, we can conclude that the
demodulation of digitally modulated signals reaches a suffiAdv. Radio Sci., 4, 189–195, 2006
3
2
2
1
1
0
-1
-2
-2
-3
-3
-4
-4
0
1
2
3
4
-5
-5 -4 -3 -2 -1
5
4
4
3
3
2
2
1
1
0
-1
-2
3
4
5
-2
-3
-4
2
3
4
5
Con
Based o
front-en
nals, a
technolo
down-co
compon
compen
ments o
Acknowl
Munich,
thors wo
Design G
0
-4
1
2
-1
-3
0
1
SIR = -25dB
5
I-channel
0
I-channel
5
-5
-5 -4 -3 -2 -1
6
0
-1
SIR = -35dB
Fig.
Symbol-Error-Rate performances
performances for
Fig.
6. 6.Symbol-Error-Rate
fordifferent
differentcompensacompensation scenarios for the frequency-independent portions of amplitude
tion scenarios for the frequency-independent portions of amplitude
and phase; 16 QAM, Low-IF reception, initial SI R = −20 dB.
with g = 0.98 (−0.175 dB) and
4
3
I-channel
SNR [dB]
ϕ = −2◦ ,
4
-5
-5 -4 -3 -2 -1
Q-channel
ntaents
Alncyas3dB
and
ont003)
tion
valable
for
tely
0.01
SER
tanof g,
hase
and
the
near
ince
r inme-
0.1
5
Q-channel
(19)
cient lev
front-en
plitude
SIR = -30dB
5
Q-channel
its
and
-5
-5 -4 -3 -2 -1
0
1
2
3
4
5
Referen
I-channel
Fig.7.7.IQ-constellations
IQ-constellationsfor
fordifferent
differentinitial
initialsignal-to-interferencesignal-to-interferenceFig.
ratios(SIR);
(SI R);16QAM,
16 QAM,Low-IF
Low-IFreception,
reception,SN
SNR
= 20dB
20 dBcompencompenratios
R=
sation ofof all
all frequency-independent
frequency-independent amplitude
amplitude and
and phase
phase impairimpairsation
ments,
i.e.
g,
ϕ,
g
,
α.
ments, i.e. g, ϕ, gQQ, α.
cient level for
for the
a reasonably
imbalanced
IQ-processing
pairments,
amplitudebadly
and the
phase with
gQ ∼ 0.99
front-end,
if
the
quasi-linear
(mean)
values
of
phase
andwith
am(−0.087dB) and α ∼ −1.4◦ . The amplitude alternates
plitude
impairments
have
been
compensated
for.
variations of ±0.05dB, which is approximately within the
variation range of technical implementations. In order to
obtain
results at a low-level limit of implementations with
6 Conclusions
almost insufficient matching, we selected the phase to vary
with
±1.5
, what
is more
than twice
variation
within a
Based
on ◦the
general
transmission
of the
direct
dow-conversion
typical
IQ-processing
front-end.
front-ends
with respect
to in-phase and quadrature-phase sigNevertheless,
observed that
the was
symbol-error-rate
nals,
a generallyit can
validbeimbalance
model
explained for
(SER)
performance of thefront-ends
whole system
reaches acceptable
technology-independent
and arbitrary
frequency
values,
if the meanThe
values
for all amplitude
and phase imdown conversion.
investigations
on frequency-selective
pairments
were
compensated
for (at SIR
−20dB),
Fig. the
6.
components
within
the IQ-branches
led to=the
result, that
Obviously,
the overall
performance
increases
as the respeccompensation
of the mean
values of
the respective
impairtive
frequency
removed. Since
ments
ought toindependent
be sufficientimpairments
for mobile are
communications
rethe
result
for
the
compensation
of
all
mean
values
of ampliceiver.
tude and phase errors (concerning IQ-imbalance) is near to
Acknowledgements.
research was supported
SiemenssigAG
the
ideal, theoreticalThis
SER-performance
for aby
16QAM
Munich, Communications, Mobile Devices. Additionally the aunal,
we can state that no further, expensive deconvolution of
thors would like to thank the staff of the Chair Information Techthe IQ-signals is required. However, if one would do so, the
nology for Traffic Systems for inspiring discussions.
performance would improve further.
The demodulations’ dependence on the initial signal-tointerference
References ratio (SIR) is indicated in Fig. 7. For the given
simulation setup, an SIR of −40dB or less frustrates the deCardoso, J.-F.;
Hvancompletely,
Laheld, B.: even
Equivariant
adaptive
sepmodulation
almost
for high
SN R.source
Starting
aration,
Trans.
Signal Processing,
12, 3017–3030,
at SIR
≥ IEEE
−35dB,
theonreceiver
was able 44,
to detect
the IQ1996.
signals
properly resulting in acceptable SER-values.
Based on the presented results, we can conclude that the
demodulation of digitally www.adv-radio-sci.net/4/189/2006/
modulated signals reaches a suffi-
Valkama
for I/Q
IEEE
pp. 23
Cardoso
aratio
1996,
Ratni, M
band D
ware D
sonal,
bon, P
Hentsche
Comm
trol, C
mame
Mailand
Port
Wirel
(WCN
Valkama
Frequ
Metho
cessin
Taiwa
Windisch
Estim
tional
cessin
Mailand
Comp
Conve
nicati
Nakagaw
Comp
Vehic
les, U
M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers
Hentschel, T.: A Simple IQ-Regeneration Technique for Six-Port
Communication Receivers, 1st International Symposium on Control, Communications and Signal Processing (ISCCSP), Hammamet, Tunesia, 311–314, 2004.
Mailand, M. and Jentschel, H.-J.: An Effort Reduced SixPort Direct Conversion Receiver and Its Calibration, IEEE
Wireless Communications and Networking Conference 2005
(WCNC’2005), New Orleans, USA, 568–572, 2005.
Mailand, M.; Jentschel, H.-J. and Richter, R.: Blind IQ-Imbalance
Compensation Using Iterative Inversion for Arbitrary Direct
Conversion Receivers, 14th IST Mobile and Wireless Communications Summit, Dresden, Germany, 2005.
Nakagawa, T.; Matsui, M. and Araki, K.: Gain/Phase Imbalance
Compensation for Multi-Band Quadrature Receivers, IEEE 60th
Vehicular Technology Conference (VTC2004-Fall), Los Angeles, USA, 2004.
Ratni, M.; Krupezevic, D.; Wang, Z. and Jürgensen, J.-U.: Broad-
www.adv-radio-sci.net/4/189/2006/
195
band Digital Direct Down Conversion Receiver Suitable for Software Defined Radio, 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC, Lisbon, Portugal, 93–99, 2002.
Valkama, M.; Renfors, M. and Koivunen, V.: Compensation of
Frequency-Selective I/Q Imbalances in Wideband Receivers:
Methods and Algorithms, 3rd IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC ’01),
Taiwan, 42–45, 2001.
Valkama, M.; Renfors, M. and Koivunen, V.: Advanced Methods
for I/Q Imbalance Compensation in Communication Receivers,
IEEE Trans. on Signal Processing, 49, 10, 2335–2344, 2001.
Windisch, M. and Fettweis, G.: Blind I/Q Imbalance Parameter
Estimation and Compensation in Low-IF Receivers, 1st International Symposium on Control, Communications and Signal Processing (ISCCSP’04), Hammamet, Tunisia, 75–78, 2004.
Adv. Radio Sci., 4, 189–195, 2006