iq-imbalance and its compensation for non-ideal analog receivers

Adv. Radio Sci., 4, 189–195, 2006www.adv-radio-sci.net/4/189/2006/© Author(s) 2006. This work is licensedunder a Creative Commons License.

Advances inRadio Science

IQ-imbalance and its compensation for non-ideal analog receiverscomprising 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 ter-minals, more and more analog components are replaced byappropriate digital processing. On the one hand, the ana-log front-ends become less complex. On the other hand,more digital signal processing is required to compensatefor the spurious effects of the front-end. In this arti-cle, the frequency-selective imbalance of the in-phase andquadrature-phase signals is addressed. A closed representa-tion of arbitrary signals being processed by an arbitrary im-balanced analog front-end is provided. The analysis is validfor both, direct conversion and intermediate frequency (IF)reception. With the consideration of practical variations ofamplitude and phase impairments, the influence of only thefrequency-dependent portions of the impairments is inves-tigated. It is shown, that the compensation of the quasi-linear impairments is sufficient and complex deconvolutiveIQ-regeneration procedures are not stringently required toobtain sufficient signal qualities.

1 Introduction

In modern mobile communication receivers, more and moreanalog components are replaced by digital building blocks.One the one hand, this leads to less circuitry effort (chipsize, power consumption, etc.) in the analog domain. On theother hand, additional digital signal processing is required inorder to remove spurious effect of the sub-optimum analogfront-end.

In this article, we investigate a certain type of ana-log signal distortions, i.e. the in-phase (I) and quadrature-phase (Q) imbalance. For heterodyne or intermediate fre-quency (IF) reception, IQ-imbalance causes the well-knownimage problem. There, the respective image channel mixes

Correspondence to:M. Mailand([email protected])

partially onto the wanted signal during the IF-down con-version, (Valkama et al., 2001). Within an homodyne, di-rect conversion or zero-IF reception, IQ-imbalance leads toa distortion of the IQ-signals themselves within the respec-tive wanted channel. For both frequency down conversionconcepts, the IQ-imbalance is a serious issue degrading thereception performance. This spurious effect occurs mainlydue to amplitude- and phase-impairments between the localoscillator paths as well as due to mismatches between therespective IQ-branches after the analog down conversion.

For the case of wideband transmission, the anyway distort-ing IQ-imbalance mixing becomes an IQ-imbalance convo-lution, due to the frequency selectivity of the analog front-end components after the down conversion. Thereby, es-pecially different impulse responses of filters and IF- orbaseband-amplifiers have significant influence.

For direct conversion and IF-conversion, we will showfor transmissions utilizing wideband signals, that the impactof the IQ-imbalance convolution or the frequency selectiv-ity of the components, respectively, has not to be consideredstringently. Mainly, the mean values of the phase- and am-plitude impairments of the IQ-imbalance convolution causemost of the signal distortions. Therefore, it will be sufficientto compensate for the frequency-selective IQ-imbalance con-volution with methods primarily developed for ‘simple’ IQ-imbalance compensation, e.g. by utilizing blind source sepa-ration (BSS) algorithms, (Cardoso et al., 1996).

2 Receiver front-ends

The technique of direct down conversion (DDC) transformsthe RF-signal directly down to baseband. For that purpose,the LO is set to the carrier frequencyωLO = ωRF of thewanted channel. Due to temperature dependencies, produc-tion imperfections etc., the analog components in the I- andQ-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 M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers2 Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ...

90°

LNA

BPF/LPF

BPF/LPF

ADC

ADC

cos(ωRF t)

analog digital

sRF (t)DSP

LO

Frequency Down-

Conversion(Mixing incl.

Amplitude & Phase Errors of the LO-

Paths)

z’I(t)

z’Q(t)

ŝI(k)

ŝQ(k)

a) b)

(·)²

(·)²

(·)²M1

M3

φ3

g3

φ1

g1

M2

φ2

g2

φ2

g2

φ1

g1

M1

Fig. 1. General DDC front-end utilizing a) multiplicative mixingor b) additive mixing; with imbalance of the LO-signal and pathmismatches.

ideal LO-signal changes into

sLO(t) = g1 · cos(ωLO t+ϕ1)− j g2 · sin(ωLO t+ϕ2) (1)

for the distorted paths (see Fig. 1).Independent of the respective front-end architecture, there

will be different signal paths for the I-signal and the Q-signal.These signal paths are also expected to be unmatched in therealistic case. Hence, they influence the IQ-components byan additional scaling, i.e. path mismatchMi for thei th path.

For further investigations, we assume that any type of re-ceiver being regarded comprises some direct current (DC)offset cancellation.

The influence of flicker noise or1/f -noise which is anadditional serious problem especially for CMOS implemen-tations of DDC receivers is not addressed in this paper.

2.1 Multiplicative Mixing

Multiplicative mixing is the conventional implementation ofdirect down conversion. Here, the RF-signal is multiplied bythe original LO-signal within one path (in-phase signal, I)and by a90◦ rotated LO-signal in a second path (quadrature-phase signal, Q), i.e. in principlex(t) = LPF{sRF (t) ·sLO(t)}. The upper signal branch is assumed not to bematched to the second path. This leads to a relative pathmismatchM1. In Fig. 1a), the receiver front-end with therespective impairments is shown. After mixing, the low passfilter (LPF) suppresses the unwanted higher frequency terms.Thus, almost only the IQ-signals of interest will be digitized.According to Fig. 1a) and considering all the impairments,we get:

z′I(k) =12

g1 M1 ·(sI(k) cos(ϕ1) + sQ(k) sin(ϕ1)

)(2)

z′Q(k) =12

g2 ·(−sI(k) sin(ϕ2) + sQ(k) cos(ϕ2)

). (3)

In general, the equations (2) and (3) can be rewritten in amatrix form to consider all possible, linear imbalances (ex-cept DC-offsets):

z′ = As =[z′I(k)z′Q(k)

]=

[A1 B1

A2 B2

] [sI(k)sQ(k)

]. (4)

We consider to have arbitrary gain and phase impairmentswithin each of the IQ-paths, although a relative IQ-imbalancewas sufficient, (Valkama et al., 2001). Hereupon, we definethe signal-to-interference ratio (SIR) for the IQ-branches:

SIRI = 20 · log10

| A1 || B1 |

, SIRQ = 20 · log10

| B2 || A2 |

. (5)

2.2 Additive Mixing

Direct down conversion by additive mixing gained a lot ofattention in the recent years. Usually, the six-port technol-ogy is applied. In the use as communication receiver the for-mer six-port was reduced to a five-port structure. Fig. 1b)shows the general architecture for additive DDC utilizinga five-port. Clearly, the mixers (multiplicative elements inFig. 1a) ) are replaced by appropriate summing elements fol-lowed by a square-law device (in general, a simple nonlinearcomponent, e.g. a diode). The advantages compared to themixer-based concept are e.g., better robustness for RF-signalpower level fluctuations, DC-offsets can be cancelled moreeasily and it is possible to implement broadband receivers ina comparably simple manner, (Ratni et al., 2002).

The down-converted signal before analog-to-digital con-version (A/D) of the front-end can generally be denoted with

z′i(t) = g2i Mi + Mi · (s2

I(t) + s2Q(t))︸︷︷︸

rectified wave including DC-offsets

(6)

+ 2 Mi ·(sI(t) gi cos(ϕi) + sQ(t) gi sin(ϕi)

)︸︷︷︸wanted signal components

The phase shift elementsϕi and the attenua-tion/amplification componentsgi within the five-portcomprise known, wanted values as well as impairments.Hence, they contribute to the indeterminacy of the front-endtransmission due to spurious effects.

The rectified wave which comprises the DC-offsets can beeasily removed by a simple front-end calibration (Hentschel, 2004) or by the implementation of an appropriate front-endarchitecture (Mailand et al., WCNC 2005).

Therefore, we obtain measurements which consist onlyof linear mixtures of the IQ-signals, i.e.z′i(k) = 2 Mi ·(sI(k) gi cos(ϕi) + sQ(k) gi sin(ϕi)

)in (6). In conse-

quence, the transmission of the DDC front-end with additivemixing is determined by

z′ = As =[z′I(k)z′Q(k)

]=

[A1 B1

A2 B2

] [sI(k)sQ(k)

]. (7)

The phase parametersϕi ∈ [0, 2π) have to be different ofeach other, to assure a possible separation ofsI(t) andsQ(t),i.e. to guarantee a nonsingular mixing matrixA.

Fig. 1. General DDC front-end utilizing(a) multiplicative mixingor (b) additive mixing; with imbalance of the LO-signal and pathmismatches.

as the actual phase of the respective LO-signal to the I- orQ-path will differ from the respective optimal values result-ing in phaseϕi and amplitudegi imbalances. Therefore, theideal LO-signal changes into

sLO(t) = g1 · cos(ωLO t + ϕ1)

−j g2 · sin(ωLO t + ϕ2) (1)

for the distorted paths (see Fig.1).Independent of the respective front-end architecture, there

will be different signal paths for the I-signal and the Q-signal.These signal paths are also expected to be unmatched in therealistic case. Hence, they influence the IQ-components byan additional scaling, i.e. path mismatchMi for thei th path.

For further investigations, we assume that any type of re-ceiver being regarded comprises some direct current (DC)offset cancellation.

The influence of flicker noise or 1/f -noise which is anadditional serious problem especially for CMOS implemen-tations of DDC receivers is not addressed in this paper.

2.1 Multiplicative mixing

Multiplicative mixing is the conventional implementationof direct down conversion. Here, the RF-signal is mul-tiplied by the original LO-signal within one path (in-phase signal, I) and by a 90◦ rotated LO-signal in a sec-ond path (quadrature-phase signal, Q), i.e. in principlex(t) = LPF{sRF (t) · sLO(t)}. The upper signal branch is as-sumed not to be matched to the second path. This leads toa relative path mismatchM1. In Fig. 1a, the receiver front-end with the respective impairments is shown. After mixing,the low pass filter (LPF) suppresses the unwanted higher fre-quency terms. Thus, almost only the IQ-signals of interestwill be digitized. According to Fig.1a and considering all

the impairments, we get:

z′

I (k) =1

2g1 M1 ·

(sI (k) cos(ϕ1) + sQ(k) sin(ϕ1)

)(2)

z′

Q(k) =1

2g2 ·

(−sI (k) sin(ϕ2) + sQ(k) cos(ϕ2)

). (3)

In general, the Eqs. (2) and (3) can be rewritten in a ma-trix form to consider all possible, linear imbalances (exceptDC-offsets):

z′= A s =

[z′

I (k)

z′

Q(k)

]=

[A1 B1A2 B2

] [sI (k)

sQ(k)

]. (4)

We consider to have arbitrary gain and phase impairmentswithin each of the IQ-paths, although a relative IQ-imbalancewas sufficient, (Valkama et al., 2001). Hereupon, we definethe signal-to-interference ratio (SIR) for the IQ-branches:

SIRI = 20 · log10| A1 |

| B1 |, SIRQ = 20 · log10

| B2 |

| A2 |. (5)

2.2 Additive mixing

Direct down conversion by additive mixing gained a lot of at-tention in the recent years. Usually, the six-port technologyis applied. In the use as communications receiver the for-mer six-port was reduced to a five-port structure. Figure1bshows the general architecture for additive DDC utilizinga five-port. Clearly, the mixers (multiplicative elements inFig. 1a are replaced by appropriate summing elements fol-lowed by a square-law device (in general, a simple nonlinearcomponent, e.g. a diode). The advantages compared to themixer-based concept are e.g., better robustness for RF-signalpower level fluctuations, DC-offsets can be cancelled moreeasily and it is possible to implement broadband receivers ina comparably simple manner, (Ratni et al., 2002).

The down converted signal before analog-to-digital con-version (A/D) of the front-end can generally be denoted with

z′

i(t) = g2i Mi + Mi · (s2

I (t) + s2Q(t))︸︷︷︸

rectified wave including DC-offsets

+ 2Mi ·(sI (t) gi cos(ϕi) + sQ(t) gi sin(ϕi)

)︸︷︷︸wanted signal components

(6)

The phase shift elementsϕi and the attenua-tion/amplification componentsgi within the five-portcomprise known, wanted values as well as impairments.Hence, they contribute to the indeterminacy of the front-endtransmission due to spurious effects.

The rectified wave which comprises the DC-offsets can beeasily removed by a simple front-end calibration (Hentschel,2004) or by the implementation of an appropriate front-endarchitecture (Mailand et al., WCNC 2005).

Therefore, we obtain measurements which con-sist only of linear mixtures of the IQ-signals, i.e.z′

i(k) = 2Mi ·(sI (k) gi cos(ϕi) + sQ(k) gi sin(ϕi)

)in

Adv. Radio Sci., 4, 189–195, 2006 www.adv-radio-sci.net/4/189/2006/

M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers 191Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ... 3

SRF (ω)

ω

B

ωRF ωRF+ωIFωRF -ωIF

SIFSIM S0SIMS0

SIF*

* *

-ωRF -(ωRF-ωIF)-(ωRF +ωIF)

Fig. 2. Schematic frequency domain illustration of the RF-signalcomprising three channels centered atωRF .

The composition of the base-band signals or front-endmeasurementsxi(k) is systematically a mixture of I-signalsand Q-signals for additive mixing. Utilizing multiplicativemixing, the IQ-mixture within one measurementz′i(k) is dueto front-end impairments.

Nevertheless, although the analog processing is signifi-cantly different, the general description of direct down con-version transmission, considering spurious effects, is thesame for both, multiplicative and additive mixing. Further-more, an analysis of the interrelationships for IF-receptionleads to comparable conclusions. With respect to IQ-imbalance, the analog front-end can be modelled indepen-dently from the utilized technology.

The problem to be solved is how to regenerate the originalIQ-signals without knowledge of the front-end transmission,i.e. the mixing matrixA. For that purpose, adaptive filter-ing and blind source separation algorithms can be applied(Valkama et al., 2001) as well as several calibration proce-dures (Hentschel , 2004) for both of the front-end architec-tures.

3 IQ-Imbalance - Effects of Amplitude/Phase Impair-ments and Path Mismatches

In the previous sections, we assumed to have only quasi-linear impairments. In reality, the amplitude and phase im-pairments have a frequency dependent characteristic. Hence,different parts (at different frequencies) of a single chan-nel will be affected differently. Usually, this effect be-comes more serious with wider bandwidths. In such cases,the known techniques of IQ-regeneration will have to betranslated into a deconvolution methods which consider thefrequency-selectivity of the imbalance.

Therefore, we need a general description of the widebandsignal being affected by amplitude/phase impairments andpath mismatches. Following the explanations in (Valkamaet al., 2001), we consider a multichannel received signal

sRF (t) = 2 · <{

z(t) exp(jωRF t)}

= z(t) exp(jωRF t) + z∗(t) exp(−jωRF t) (8)

which is centered atωRF and covers a bandwidthB (Fig. 2).The operation(·)∗ denotes complex conjugation of its argu-ment. In (8)

z(t) = s0(t) + sIF (t) exp(jωIF t) + sIM (t) exp(−jωIF t)= zI(t) + j · zQ(t) (9)

is the general multichannel baseband signal.Without the loss of general validity, the analog com-

ponents: LO-paths within the frequency down-conversionstage, branch filters and amplifiers, analog-to-digital con-verters (ADC) contribute to the respective frequency-independent or frequency-selective IQ-imbalances. Hence,we can combine the several components what leads to a moregeneral front-end model. In Fig. 3, the amplitude and phaseimpairments are modelled by the relative errorsg andϕ, re-spectively, within the mixing stage.HNOM (ω) representsthe nominal low-pass-filter (LPF) functionality which rejectsthe high frequency components after the down-conversion.Therefore, the complex signal after the nominal LPF of thebranches is:

x(t) = LPFNOM

{sRF (t) · sLO(t)

}= zI(t) + j ·

(g cos(ϕ) zQ(t)− g sin(ϕ) zI(t)

)= xI(t) + j · xQ(t) .

(10)

The transfer functionsHI(ω) andHQ(ω) stand for the actualmismatch due to the frequency-selective differences of theanalog components of the in-phase and the quadrature-phasebranch, respectively. With the use of (10), we obtain the finalIQ-imbalanced signal mixture as:

Z ′(ω) = HI(ω) XI(ω) + j ·HQ(ω) XQ(ω)= Z ′

I(ω) + j · Z ′Q(ω) (11)

= HI(ω)ZI(ω)

+ j ·HQ(ω) ·(g cos(ϕ)ZQ(ω)− g sin(ϕ) ZI(ω)

)=

(HI(ω)− j HQ(ω) g sin(ϕ)

)· ZI(ω)

+ j ·(HQ(ω) g cos(ϕ)

)ZQ(ω)

= AI(ω) · ZI(ω) + j ·AQ(ω) · ZQ(ω) (12)

Thus, equation (12) is the generalized version of (4) and (7)and can be used for the description of any type of imbalancedIQ-processing front-end.

With the simplifications in (Valkama et al., 2001), thedown-converted and generally imbalanced signal can be de-noted as

Z ′(ω) = G1(ω) · Z(ω) + G2(ω) · Z∗(−ω) (13)

with

G1(ω) =12·(AI(ω) + AQ(ω)

)=

12·(HI(ω) + HQ(ω) g exp(−j ϕ)

) (14)

Fig. 2. Schematic frequency domain illustration of the RF-signalcomprising three channels centered atωRF .

Eq. (6). In consequence, the transmission of the DDCfront-end with additive mixing is determined by

z′= A s =

[z′

I (k)

z′

Q(k)

]=

[A1 B1A2 B2

] [sI (k)

sQ(k)

]. (7)

The phase parametersϕi ∈ [0, 2π) have to be different ofeach other, to assure a possible separation ofsI (t) andsQ(t),i.e. to guarantee a nonsingular mixing matrixA.

The composition of the baseband signals or front-end mea-surementsxi(k) is systematically a mixture of I-signals andQ-signals for additive mixing. Utilizing multiplicative mix-ing, the IQ-mixture within one measurementz′

i(k) is due tofront-end impairments.

Nevertheless, although the analog processing is signifi-cantly different, the general description of direct down con-version transmission, considering spurious effects, is thesame for both, multiplicative and additive mixing. Further-more, an analysis of the interrelationships for IF-receptionleads to comparable conclusions. With respect to IQ-imbalance, the analog front-end can be modelled indepen-dently from the utilized technology.

The problem to be solved is how to regenerate the originalIQ-signals without knowledge of the front-end transmission,i.e. the mixing matrixA. For that purpose, adaptive filter-ing and blind source separation algorithms can be applied(Valkama et al., 2001) as well as several calibration proce-dures (Hentschel, 2004) for both of the front-end architec-tures.

3 IQ-imbalance - effects of amplitude/phase impair-ments and path mismatches

In the previous sections, we assumed to have only quasi-linear impairments. In reality, the amplitude and phase im-pairments have a frequency dependent characteristic. Hence,different parts (at different frequencies) of a single chan-nel will be affected differently. Usually, this effect be-comes more serious with wider bandwidths. In such cases,the known techniques of IQ-regeneration will have to be

4 Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ...

90°

ADC

ADC

ŝI(k)

ŝQ(k)

z’I(t)

cos(ωRF t)

analog digital

DSP

LO

sRF(t)HNOM(f )

HNOM(f ) HQ(f )

HI(f )

φ

g

Frequency Down-Conversion

z’Q(t)

xI(t)

xQ(t)

Fig. 3. Imbalanced front-end model; considering frequency-independent and frequency-selective IQ-imbalance; multiplicativefrequency-conversion utlized.

Z*(-ω)

ω

SIM(-ω)S0(-ω)SIF(-ω)* *

*

ωIF-ωIF

SIM(ω)S0(ω) SIF(ω)

Z(ω)

ωωIF-ωIF

a)

Z’(ω)

ωωIF-ωIF

b)

Fig. 4. Schematic description of (a) a general multichannel signaland (b) the respective resulting IQ-imbalanced mixture.

and

G2(ω) =12·(AI(ω)−AQ(ω)

)=

12·(HI(ω)−HQ(ω) g exp(j ϕ)

).

(15)

In Fig. 4, the overlapping is shown ofZ(ω) andZ∗(−ω)due to the IQ-imbalance as given in (13). This results inthe imbalanced multichannel baseband observationZ ′(ω)shown in Fig. 4(b). In general, there are two possible imbal-ance scenarios: for IF-reception, the image and the desiredsignal mix onto each other (SIF and SIM ) or, within di-rect conversion, the desired signal is distorted by a complexscaled and complex conjugated version of itself (S0). Fur-thermore, it should be mentioned that IQ-imbalance does notequal the distortions of the channel affecting the respectiveIQ-signals in general. On the one hand, for zero-IF recep-tion (z(t) = s0(t)), the general imbalance description (13)shows comparable transmission behavior as the RF-channel.Hence, in this case, one could include the IQ-regenerationwithin the channel equalization, at least partly. But, on

the other hand, an IF-reception with state-of the art analogIQ-front-ends, can not guarantee a sufficient image-channel-rejection before the first frequency conversion. As result, theimage channel will overlap onto the desired channel, whichcan not be compensated for by channel equalization. Anadditional IQ-regeneration is required stringently to recreatethe orthogonality of the desired and the image channel.

Moreover, we can define a more general version for thesignal-to-image-ratio (SIR):

SIR =|G1(ω)|2

|G2(ω)|2. (16)

Without a mismatch of the IQ-branches, i.e.HI(ω) =HQ(ω), (16) turns into the relation for quasi-linear imbal-ances which has already been depicted in various articles,e.g. (Valkama et al., 2001), (Windisch et al., 2004), etc.

However, in (13) and Fig. 4, the termZ∗(−ω) is causedby the imbalances and represents the image aliasing ef-fects. Therefore, we lose the separability of the respec-tive frequency-signals. With practical analog implementa-tions of receiver front-ends, theSIR is usually in the rangeof (20 . . . 40)dB. For the most of currently utilized receiv-ing methods (zero-IF, low-IF, wideband-IF) and usually pro-cessed modulation schemes/orders, this image attenuation isinsufficient. In principle, a compensation for IQ-imbalanceis needed.

As already mentioned, there are several techniques to ob-tain the required separation matrix for quasi-linear mixtures.Adaptive filters, blind algorithms as well as test-signal-basedcalibration 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 theconvolved mixture as depicted in (13), different deconvolu-tion algorithms were proposed, e.g. (Cardoso et al., 1996).But, since we are aiming at simple, low-power, high-speedand thus cost-effective solutions for mobile communica-tions, such deconvolution algorithms turn out not to be suit-able candidates to compensate the frequency-selective IQ-imbalances. The reason for that are somewhat manifold, e.g.:

– adaptive deconvolution algorithms usually require sev-eral hundred up to thousands of symbols to reach theirrespective equilibrium,

– this convergence process must be went through againafter each ’environmental’ change (significant tempera-ture change, reception-frequency changes, etc.), due tothe consequent changes within the analog IQ-branches,

– serious mapping of the frequency response of the IQ-imbalances requires digital filters with a sufficient tap-length, whereas the update of each tap has its own un-derlying adaptive algorithm and

– an additional digital memory will have to be imple-mented just only to save all coefficients for a large vari-ety of reception situations.

Fig. 3. Imbalanced front-end model; considering frequency-independent and frequency-selective IQ-imbalance; multiplicativefrequency conversion utilized.

translated into deconvolution methods which consider thefrequency-selectivity of the imbalance.

Therefore, we need a general description of the widebandsignal being affected by amplitude/phase impairments andpath mismatches. Following the explanations in (Valkamaet al., 2001), we consider a multichannel received signal

sRF (t) = 2 · <

{z(t) exp(jωRF t)

}= z(t) exp(jωRF t) + z∗(t) exp(−jωRF t) (8)

which is centered atωRF and covers a bandwidthB (Fig. 2).The operation(·)∗ denotes complex conjugation of its argu-ment. In Eq. (8)

z(t) = s0(t) + sIF (t) exp(jωIF t) + sIM(t) exp(−jωIF t)

= zI (t) + j · zQ(t) (9)

is the general multichannel baseband signal.Without the loss of general validity, the analog compo-

nents: LO-paths within the frequency down conversion stage,branch filters and amplifiers, analog-to-digital converters(ADC) contribute to the respective frequency-independent orfrequency-selective IQ-imbalances. Hence, we can combinethe several components what leads to a more general front-end model. In Fig.3, the amplitude and phase impairmentsare modelled by the relative errorsg and ϕ, respectively,within the mixing stage.HNOM(ω) represents the nominallow-pass-filter (LPF) functionality which rejects the high fre-quency components after the down conversion. Therefore,the complex signal after the nominal LPF of the branches is:

x(t) = LPFNOM

{sRF (t) · sLO(t)

}= zI (t) + j ·

(g cos(ϕ) zQ(t) − g sin(ϕ) zI (t)

)= xI (t) + j · xQ(t) . (10)

The transfer functionsHI (ω) andHQ(ω) stand for the actualmismatch due to the frequency-selective differences of theanalog components of the in-phase and the quadrature-phase

www.adv-radio-sci.net/4/189/2006/ Adv. Radio Sci., 4, 189–195, 2006

192 M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers


90°

ADC

ADC

ŝI(k)

ŝQ(k)

z’I(t)

cos(ωRF t)

analog digital

DSP

LO

sRF(t)HNOM(f )

HNOM(f ) HQ(f )

HI(f )

φ

g

Frequency Down-Conversion

z’Q(t)

xI(t)

xQ(t)

Fig. 3. Imbalanced front-end model; considering frequency-independent and frequency-selective IQ-imbalance; multiplicativefrequency-conversion utlized.

Z*(-ω)

ω

SIM(-ω)S0(-ω)SIF(-ω)* *

*

ωIF-ωIF

SIM(ω)S0(ω) SIF(ω)

Z(ω)

ωωIF-ωIF

a)

Z’(ω)

ωωIF-ωIF

b)

Fig. 4. Schematic description of (a) a general multichannel signaland (b) the respective resulting IQ-imbalanced mixture.

and

G2(ω) =12·(AI(ω)−AQ(ω)

)=

12·(HI(ω)−HQ(ω) g exp(j ϕ)

).

(15)

In Fig. 4, the overlapping is shown ofZ(ω) andZ∗(−ω)due to the IQ-imbalance as given in (13). This results inthe imbalanced multichannel baseband observationZ ′(ω)shown in Fig. 4(b). In general, there are two possible imbal-ance scenarios: for IF-reception, the image and the desiredsignal mix onto each other (SIF and SIM ) or, within di-rect conversion, the desired signal is distorted by a complexscaled and complex conjugated version of itself (S0). Fur-thermore, it should be mentioned that IQ-imbalance does notequal the distortions of the channel affecting the respectiveIQ-signals in general. On the one hand, for zero-IF recep-tion (z(t) = s0(t)), the general imbalance description (13)shows comparable transmission behavior as the RF-channel.Hence, in this case, one could include the IQ-regenerationwithin the channel equalization, at least partly. But, on

the other hand, an IF-reception with state-of the art analogIQ-front-ends, can not guarantee a sufficient image-channel-rejection before the first frequency conversion. As result, theimage channel will overlap onto the desired channel, whichcan not be compensated for by channel equalization. Anadditional IQ-regeneration is required stringently to recreatethe orthogonality of the desired and the image channel.


SIR =|G1(ω)|2

|G2(ω)|2. (16)

Without a mismatch of the IQ-branches, i.e.HI(ω) =HQ(ω), (16) turns into the relation for quasi-linear imbal-ances which has already been depicted in various articles,e.g. (Valkama et al., 2001), (Windisch et al., 2004), etc.

However, in (13) and Fig. 4, the termZ∗(−ω) is causedby the imbalances and represents the image aliasing ef-fects. Therefore, we lose the separability of the respec-tive frequency-signals. With practical analog implementa-tions of receiver front-ends, theSIR is usually in the rangeof (20 . . . 40)dB. For the most of currently utilized receiv-ing methods (zero-IF, low-IF, wideband-IF) and usually pro-cessed modulation schemes/orders, this image attenuation isinsufficient. In principle, a compensation for IQ-imbalanceis needed.

As already mentioned, there are several techniques to ob-tain the required separation matrix for quasi-linear mixtures.Adaptive filters, blind algorithms as well as test-signal-basedcalibration 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 theconvolved mixture as depicted in (13), different deconvolu-tion algorithms were proposed, e.g. (Cardoso et al., 1996).But, since we are aiming at simple, low-power, high-speedand thus cost-effective solutions for mobile communica-tions, such deconvolution algorithms turn out not to be suit-able candidates to compensate the frequency-selective IQ-imbalances. The reason for that are somewhat manifold, e.g.:





Fig. 4. Schematic description of(a) a general multichannel signaland(b) the respective resulting IQ-imbalanced mixture.

branch, respectively. With the use of Eq. (10), we obtain thefinal IQ-imbalanced signal mixture as:

Z′(ω) = HI (ω) XI (ω) + j · HQ(ω) XQ(ω)

= Z′

I (ω) + j · Z′

Q(ω) (11)

= HI (ω) ZI (ω)

+ j · HQ(ω) ·

(g cos(ϕ) ZQ(ω) − g sin(ϕ)ZI (ω)

)=

(HI (ω) − j HQ(ω) g sin(ϕ)

)· ZI (ω)

+ j ·

(HQ(ω) g cos(ϕ)

)ZQ(ω)

= AI (ω) · ZI (ω) + j · AQ(ω) · ZQ(ω) (12)

Thus, Eq. (12) is the generalized version of Eqs. (4) and (7)and can be used for the description of any type of imbalancedIQ-processing front-end.

With the simplifications in (Valkama et al., 2001), thedown converted and generally imbalanced signal can be de-noted as

Z′(ω) = G1(ω) · Z(ω) + G2(ω) · Z∗(−ω) (13)

with

G1(ω) =1

2·

(AI (ω) + AQ(ω)

)=

1

2·

(HI (ω) + HQ(ω) g exp(−j ϕ)

)(14)

and

G2(ω) =1

2·

(AI (ω) − AQ(ω)

)=

1

2·

(HI (ω) − HQ(ω) g exp(j ϕ)

). (15)

In Fig. 4, the overlapping is shown ofZ(ω) andZ∗(−ω)

due to the IQ-imbalance as given in Eq. (13). This resultsin the imbalanced multichannel baseband observationZ′(ω)

shown in Fig.4b. In general, there are two possible im-balance scenarios: for IF-reception, the image and the de-sired signal mix onto each other (SIF andSIM ) or, withindirect conversion, the desired signal is distorted by a com-plex scaled and complex conjugated version of itself (S0).Furthermore, it should be mentioned that IQ-imbalance doesnot equal the distortions of the channel affecting the re-spective IQ-signals in general. On the one hand, for zero-IF reception (z(t) = s0(t)), the general imbalance descrip-tion (13) shows comparable transmission behavior like theRF-channel. Hence, in this case, one could include the IQ-regeneration within the channel equalization, at least partly.But, on the other hand, an IF-reception with state-of the artanalog IQ-front-ends, can not guarantee a sufficient image-channel-rejection before the first frequency conversion. Asresult, the image channel will overlap onto the desired chan-nel, which can not be compensated for by channel equaliza-tion. An additional IQ-regeneration is required stringentlyto recreate the orthogonality of the desired and the imagechannel.


SIR =|G1(ω)|2

|G2(ω)|2. (16)

Without a mismatch of the IQ-branches, i.e.HI (ω)= HQ(ω), (16) turns into the relation for quasi-linear imbalances which has already been depicted invarious articles, e.g. (Valkama et al., 2001; Windisch et al.,2004), etc.

However, in Eq. (13) and Fig. 4, the termZ∗(−ω) iscaused by the imbalances and represents the image aliasingeffects. Therefore, we lose the separability of the respec-tive frequency signals. With practical analog implementa-tions of receiver front-ends, theSIR is usually in the rangeof (20. . . 40) dB. For the most of currently utilized receiv-ing methods (zero-IF, low-IF, wideband-IF) and usually pro-cessed modulation schemes/orders, this image attenuation isinsufficient. In principle, a compensation for IQ-imbalanceis needed.

As already mentioned, there are several techniques to ob-tain the required separation matrix for quasi-linear mixtures.Adaptive filters, blind algorithms as well as test-signal-basedcalibration 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 theconvolved mixture as depicted in Eq. (13), different de-convolution algorithms were proposed, e.g. (Cardoso et al.,1996). But, since we are aiming at simple, low-power, high-speed and thus cost effective solutions for mobile commu-nications, such deconvolution algorithms turn out not to besuitable candidates to compensate for the frequency-selective


M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers 193

IQ-imbalances. The reasons for that are somewhat mani-fold, e.g.:





4 Practically required compensation

In order to avoid the expensive deconvolution, we proposeto compensate only for the mean values of the general,frequency-selective IQ-imbalance.

Let us consider to have only a relative IQ-branch mis-match, i.e.HI (ω) = 1 andHQ(ω)= HQ(ω)/HI (ω). Hence,we obtain:

G1 =1

2·

(1 + HQ(ω) g exp(−j ϕ)

)(17)

G2 =1

2·

(1 − HQ(ω) g exp(j ϕ)

). (18)

Further, HQ(ω) is divided into its mean values and itsfrequency-dependent IQ-deviations for both, amplitude andphase.

HQ(ω) =

(gQ + DQ(ω)

)· exp

(j(α + Dα(ω)

))(19)

with:

gQ = E{|HQ(ω)|

}, α = E

{arg

(HQ(ω)

)}whereasE{·} denotes the expectation or mean value. Stan-dard IQ-regeneration methods compensate for a mixture ofg,gQ, ϕ andα for considered quasi-linear amplitude and phaseimpairments. If one sets theDQ(ω)= 0 andDα(ω) = 0 andthus considers not to have frequency dependencies within theIQ-imbalance, one will obtain a relation for the quasi-linearamplitude and phase impairments withinG1 andG2. Sincethe respective algebraic expressions do not lead to further in-sight, we leave it up to the recipient to recalculate the some-what long formulas if being interested.

Nevertheless, for typical, practical front-end implementa-tions the mean values for phase and amplitude impairments

Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ... 5

4 Practically Required Compensation


Let us consider to have only a relative IQ-branch mis-match, i.e. HI(ω) = 1 and HQ(ω) = HQ(ω)/HI(ω).Hence, we obtain:

G1 =12·(1 + HQ(ω) g exp(−j ϕ)

)(17)

G2 =12·(1−HQ(ω) g exp(j ϕ)

). (18)


HQ(ω) =(gQ + DQ(ω)

)· exp

(j(α + Dα(ω)

))with: gQ = E

{|HQ(ω)|

}, α = E

{arg

(HQ(ω)

)} (19)

whereasE{·} denotes the expectation or mean value. Stan-dard IQ-regeneration methods compensate for a mixture ofg,gQ, ϕ andα for considered quasi-linear amplitude and phaseimpairments. If one sets theDQ(ω) = 0 andDα(ω) = 0 andthus considers not to have frequency dependencies within theIQ-imbalance, one will obtain a relation for the quasi-linearamplitude and phase impairments withinG1 andG2. Sincethe respective algebraic expressions do not lead to further in-sight, we leave it up to the recipient to recalculate the some-what long formulas if being interested.

Nevertheless, for typical, practical front-end implementa-tions the mean values for phase and amplitude impairmentsare in the range of1 . . . 2◦ and1 . . . 2%, respectively. Al-though there are only a few publications about frequency-dependent amplitude and phase impairments, we can as-sume to have maximum deviations of±0.5◦ and±0.03dBper channel within typical GSM front-ends or±0.8◦ and±0.08dB per channel within IEEE 802.11a (WLAN) front-ends, amongst others deduced from (Sanderson et al., 2003)and (Nakagawa et al., 2004). Besides the sparse citationabout such measurements, it seems to be valid to assume val-ues within this range, since almost all commercially availablefront-ends operate without IQ-imbalance compensation forfrequency-selective influences, whereas there are definitelymismatches due to fabrication process variations.

Hence, if we assume to have an arbitrary compensator forthe mean values of the IQ-imbalances, the influence of am-plitude and phase impairments is comparably marginally andthis only for a limited spectral part of the signal. Therefore,we conclude that expensive deconvolutive IQ-regeneration isnot a must in order to obtain sufficient signal quality.

5 Simulation Results

Computer simulation were carried out to illustrate the inter-relationships of the various IQ-imbalance sources and their

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9-1.8

-1.5

-1.2

-0.9

-0.6

-0.3

0.0

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9-30

-20

-10

0

10

20

30

~ 0.1 dB

a)

|HQ| /

|HI|

[dB

]

Normalized Frequency

~ 2.9°

b)

arg(HQ) -

arg

(HI)

[deg

]


Fig. 5. Relative frequency-dependent IQ-branch impairments of (a)amplitude and (b) phase; the effective regions for the processed sig-nals are accented.

0 2 4 6 8 10 12 14

1E-4

1E-3

0.01

0.1

1

SER

SNR [dB]

Ideal 16QAM g, ϕ, gQ and α compensated g, ϕ and gQ compensated g, ϕ and α compensated Only g and ϕ compensated

Fig. 6. Symbol-Error-Rate performances for different compensa-tion scenarios for the frequency-independent portions of amplitudeand phase; 16QAM, Low-IF reception, initialSIR = −20dB.

compensation with the overall transmission performance ofthe imbalanced front-end.

Within the simulation, a 16QAM-modulated signal wastransmitted over an additive white gaussian noise (AWGN)channel under the assumption to have an optimal transmitter.The receiver front-end utilizes multiplicative mixing like inFig. 1a) and thus Fig. 3 with a low-IF frequency conversion.The channel bandwidth was set to 20MHz with a bandgap of12MHz, whereas the carrier frequency wasfRF = 500MHzand the IF was selected at 32MHz. The transmission wassplit into blocks of 1024 symbols with each block compris-ing 64 training symbols for synchronization, etc. The systemused a split raised cosine pulse forming with a rolloff factorof 0.35. Within the IQ-paths from the LO, relative impair-ments for amplitude and phase were included withg = 0.98(−0.175dB) andϕ = −2◦, respectively. The frequency-selective error in the IQ-branches was modelled by imbal-anced LPF.

In Fig. 5, the relative IQ-branch impairments are illus-trated for a worst case scenario. As it can be seen, thereare additional mean values, i.e. frequency-independent im-

Fig. 5. Relative frequency-dependent IQ-branch impairments of(a)amplitude and(b) phase; the effective regions for the processed sig-nals are accented.

are in the range of 1. . . 2◦ and 1. . . 2%, respectively. Al-though there are only a few publications about frequency-dependent amplitude and phase impairments, we can as-sume to have maximum deviations of±0.5◦ and±0.03 dBper channel within typical GSM front-ends or±0.8◦ and±0.08 dB per channel within IEEE 802.11a (WLAN) front-ends, amongst others deduced fromNakagawa et al.(2004).Besides the sparse citation about such measurements, itseems to be valid to assume values within this range, sincealmost all commercially available front-ends operate with-out IQ-imbalance compensation for frequency-selective in-fluences, whereas there are definitely mismatches due to fab-rication process variations.


5 Simulation results

Computer simulation have been carried out to illustrate theinterrelationships of the various IQ-imbalance sources andtheir compensation with the overall transmission perfor-mance of the imbalanced front-end.

Within the simulation, a 16 QAM-modulated signal wastransmitted over an additive white gaussian noise (AWGN)channel under the assumption to have an optimal transmit-ter. The receiver front-end utilizes multiplicative mixing likein Fig. 1a and thus Fig.3 with a low-IF frequency con-version. The channel bandwidth was set to 20 MHz witha bandgap of 12 MHz, whereas the carrier frequency wasfRF = 500 MHz and the IF was selected at 32 MHz. Thetransmission was split into blocks of 1024 symbols with eachblock comprising 64 training symbols for synchronization,etc. The system used a split raised cosine pulse forming witha rolloff factor of 0.35. Within the IQ-paths from the LO,relative impairments for amplitude and phase were included


194 M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers

Marko Mailand et al.: IQ-Imbalance and its Compensation for Non-ideal Analog Receivers ... 5

4 Practically Required Compensation


Let us consider to have only a relative IQ-branch mis-match, i.e. HI(ω) = 1 and HQ(ω) = HQ(ω)/HI(ω).Hence, we obtain:

G1 =12·(1 + HQ(ω) g exp(−j ϕ)

)(17)

G2 =12·(1−HQ(ω) g exp(j ϕ)

). (18)


HQ(ω) =(gQ + DQ(ω)

)· exp

(j(α + Dα(ω)

))with: gQ = E

{|HQ(ω)|

}, α = E

{arg

(HQ(ω)

)} (19)

whereasE{·} denotes the expectation or mean value. Stan-dard IQ-regeneration methods compensate for a mixture ofg,gQ, ϕ andα for considered quasi-linear amplitude and phaseimpairments. If one sets theDQ(ω) = 0 andDα(ω) = 0 andthus considers not to have frequency dependencies within theIQ-imbalance, one will obtain a relation for the quasi-linearamplitude and phase impairments withinG1 andG2. Sincethe respective algebraic expressions do not lead to further in-sight, we leave it up to the recipient to recalculate the some-what long formulas if being interested.

Nevertheless, for typical, practical front-end implementa-tions the mean values for phase and amplitude impairmentsare in the range of1 . . . 2◦ and1 . . . 2%, respectively. Al-though there are only a few publications about frequency-dependent amplitude and phase impairments, we can as-sume to have maximum deviations of±0.5◦ and±0.03dBper channel within typical GSM front-ends or±0.8◦ and±0.08dB per channel within IEEE 802.11a (WLAN) front-ends, amongst others deduced from (Sanderson et al., 2003)and (Nakagawa et al., 2004). Besides the sparse citationabout such measurements, it seems to be valid to assume val-ues within this range, since almost all commercially availablefront-ends operate without IQ-imbalance compensation forfrequency-selective influences, whereas there are definitelymismatches due to fabrication process variations.


5 Simulation Results

Computer simulation were carried out to illustrate the inter-relationships of the various IQ-imbalance sources and their

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9-1.8

-1.5

-1.2

-0.9

-0.6

-0.3

0.0

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9-30

-20

-10

0

10

20

30

~ 0.1 dB

a)

|HQ| /

|HI|

[dB

]


~ 2.9°

b)

arg(HQ) -

arg

(HI)

[deg

]


Fig. 5. Relative frequency-dependent IQ-branch impairments of (a)amplitude and (b) phase; the effective regions for the processed sig-nals are accented.

0 2 4 6 8 10 12 14

1E-4

1E-3

0.01

0.1

1

SE

R

SNR [dB]

Ideal 16QAM g, ϕ, gQ and α compensated g, ϕ and gQ compensated g, ϕ and α compensated Only g and ϕ compensated

Fig. 6. Symbol-Error-Rate performances for different compensa-tion scenarios for the frequency-independent portions of amplitudeand phase; 16QAM, Low-IF reception, initialSIR = −20dB.

compensation with the overall transmission performance ofthe imbalanced front-end.

Within the simulation, a 16QAM-modulated signal wastransmitted over an additive white gaussian noise (AWGN)channel under the assumption to have an optimal transmitter.The receiver front-end utilizes multiplicative mixing like inFig. 1a) and thus Fig. 3 with a low-IF frequency conversion.The channel bandwidth was set to 20MHz with a bandgap of12MHz, whereas the carrier frequency wasfRF = 500MHzand the IF was selected at 32MHz. The transmission wassplit into blocks of 1024 symbols with each block compris-ing 64 training symbols for synchronization, etc. The systemused a split raised cosine pulse forming with a rolloff factorof 0.35. Within the IQ-paths from the LO, relative impair-ments for amplitude and phase were included withg = 0.98(−0.175dB) andϕ = −2◦, respectively. The frequency-selective error in the IQ-branches was modelled by imbal-anced LPF.

In Fig. 5, the relative IQ-branch impairments are illus-trated for a worst case scenario. As it can be seen, thereare additional mean values, i.e. frequency-independent im-

Fig. 6. Symbol-Error-Rate performances for different compensa-tion scenarios for the frequency-independent portions of amplitudeand phase; 16 QAM, Low-IF reception, initialSIR = −20 dB.

with g = 0.98 (−0.175 dB) andϕ = −2◦, respectively. Thefrequency-selective error in the IQ-branches was modelledby imbalanced LPF.

In Fig. 5, the relative IQ-branch impairments are illus-trated for a worst case scenario. As it can be seen, thereare additional mean values, i.e. frequency-independent im-pairments, for the amplitude and the phase withgQ ∼ 0.99(−0.087 dB) andα ∼ − 1.4◦. The amplitude alternates withvariations of±0.05 dB, which is approximately within thevariation range of technical implementations. In order toobtain results at a low-level limit of implementations withalmost insufficient matching, we selected the phase to varywith ±1.5◦, what is more than twice the variation within atypical IQ-processing front-end.

Nevertheless, it can be observed that the symbol-error-rate(SER) performance of the whole system reaches acceptablevalues, if the mean values for all amplitude and phase im-pairments were compensated for (atSIR = −20 dB), Fig.6.Obviously, the overall performance increases as the respec-tive frequency independent impairments are removed. Sincethe result for the compensation of all mean values of ampli-tude and phase errors (concerning IQ-imbalance) is near tothe ideal, theoreticalSER-performance for a 16 QAM sig-nal, we can state that no further, expensive deconvolution ofthe IQ-signals is required. However, if one would do so, theperformance would improve further.

The demodulations’ dependence on the initial signal-to-interference ratio (SIR) is indicated in Fig.7. For the givensimulation setup, anSIR of −40 dB or less frustrates thedemodulation almost completely, even for highSNR. Start-ing atSIR ≥ −35 dB, the receiver was able to detect the IQ-signals properly resulting in acceptableSER-values.

Based on the presented results, we can conclude that thedemodulation of digitally modulated signals reaches a suffi-


-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Q-c

hann

el

I-channel

SIR = -40dB SIR = -30dB

Q-c

hann

el

I-channel

SIR = -35dB

Q-c

hann

elI-channel

SIR = -25dB

Q-c

hann

el

I-channel

Fig. 7. IQ-constellations for different initial signal-to-interference-ratios (SIR); 16QAM, Low-IF reception,SNR = 20dB compen-sation of all frequency-independent amplitude and phase impair-ments, i.e.g, ϕ, gQ, α.

pairments, for the amplitude and the phase withgQ ∼ 0.99(−0.087dB) andα ∼ −1.4◦. The amplitude alternates withvariations of±0.05dB, which is approximately within thevariation range of technical implementations. In order toobtain results at a low-level limit of implementations withalmost insufficient matching, we selected the phase to varywith ±1.5◦, what is more than twice the variation within atypical IQ-processing front-end.

Nevertheless, it can be observed that the symbol-error-rate(SER) performance of the whole system reaches acceptablevalues, if the mean values for all amplitude and phase im-pairments were compensated for (atSIR = −20dB), Fig. 6.Obviously, the overall performance increases as the respec-tive frequency independent impairments are removed. Sincethe result for the compensation of all mean values of ampli-tude and phase errors (concerning IQ-imbalance) is near tothe ideal, theoreticalSER-performance for a 16QAM sig-nal, we can state that no further, expensive deconvolution ofthe IQ-signals is required. However, if one would do so, theperformance would improve further.

The demodulations’ dependence on the initial signal-to-interference ratio (SIR) is indicated in Fig. 7. For the givensimulation setup, anSIR of −40dB or less frustrates the de-modulation almost completely, even for highSNR. Startingat SIR ≥ −35dB, the receiver was able to detect the IQ-signals properly resulting in acceptableSER-values.

Based on the presented results, we can conclude that thedemodulation of digitally modulated signals reaches a suffi-

cient level for a reasonably badly imbalanced IQ-processingfront-end, if the quasi-linear (mean values) of phase and am-plitude impairments have been compensated for.

6 Conclusion

Based on the general transmission of direct dow-conversionfront-ends with respect to in-phase and quadrature-phase sig-nals, a generally valid imbalance model was explained fortechnology-independent front-ends and arbitrary frequencydown-conversion. The investigations on frequency-selectivecomponents within the IQ-branches led to the result, that thecompensation of the mean values of the respective impair-ments ought to be sufficient mobile communications receiver.

Acknowledgements.This research was supported by Siemens AGMunich, Communications, Mobile Devices. Additionally the au-thors would like to thank the staff of the Communication SystemsDesign Group for inspiring discussions.

References

Valkama, M.; Renfors, M. and Koivunen, V.: Advanced Methodsfor I/Q Imbalance Compensation in Communication Receivers,IEEE Trans. on Signal Processing, vol. 49, no. 10, Oct. 2001,pp. 2335-2344.

Cardoso, J.-F.; Hvan Laheld, B.: Equivariant adaptive source sep-aration, IEEE Trans. on Signal Processing, vol. 44, no. 12, Dec.1996, pp. 3017-3030.

Ratni, M.; Krupezevic, D.; Wang, Z. and Jurgensen, J.-U.: Broad-band Digital Direct Down Conversion Receiver Suitable for Soft-ware Defined Radio, 13th IEEE International Symposium on Per-sonal, Indoor and Mobile Radio Communications PIMRC, Lis-bon, Portugal, Sept. 2002, pp. 93-99.

Hentschel, T.: A Simple IQ-Regeneration Technique for Six-PortCommunication Receivers,1st International Symposium on Con-trol, Communications and Signal Processing (ISCCSP), Ham-mamet, Tunesia, Mar. 2004.

Mailand, M. and Jentschel, H.-J.: An Effort Reduced Six-Port Direct Conversion Receiver and Its Calibration, IEEEWireless Communications and Networking Conference 2005(WCNC’2005), New Orleans, USA, Mar. 2005.

Valkama, M.; Renfors, M. and Koivunen, V.: Compensation ofFrequency-Selective I/Q Imbalances in Wideband Receivers:Methods and Algorithms,3rd IEEE Workshop on Signal Pro-cessing Advances in Wireless Communications (SPAWC ’01),Taiwan, Mar. 2001.

Windisch, M. and Fettweis, G.: Blind I/Q Imbalance ParameterEstimation and Compensation in Low-IF Receivers,1st Interna-tional Symposium on Control, Communications and Signal Pro-cessing (ISCCSP’04), Hammamet, Tunisia, Mar. 2004.

Mailand, M.; Jentschel, H.-J. and Richter, R.: Blind IQ-ImbalanceCompensation Using Iterative Inversion for Arbitrary DirectConversion Receivers,14th IST Mobile and Wireless Commu-nications Summit, Dresden, Germany, June 2005.

Nakagawa, T.; Matsui, M. and Araki, K.: Gain/Phase ImbalanceCompensation for Multi-Band Quadrature Receivers, IEEE60th

Vehicular Technology Conference (VTC2004-Fall), Los Ange-les, USA, 2004.

Fig. 7. IQ-constellations for different initial signal-to-interference-ratios (SIR); 16 QAM, Low-IF reception,SNR = 20 dB compen-sation of all frequency-independent amplitude and phase impair-ments, i.e.g, ϕ, gQ, α.

cient level for a reasonably badly imbalanced IQ-processingfront-end, if the quasi-linear (mean) values of phase and am-plitude impairments have been compensated for.

6 Conclusions

Based on the general transmission of direct dow-conversionfront-ends with respect to in-phase and quadrature-phase sig-nals, a generally valid imbalance model was explained fortechnology-independent front-ends and arbitrary frequencydown conversion. The investigations on frequency-selectivecomponents within the IQ-branches led to the result, that thecompensation of the mean values of the respective impair-ments ought to be sufficient for mobile communications re-ceiver.

Acknowledgements.This research was supported by Siemens AGMunich, Communications, Mobile Devices. Additionally the au-thors would like to thank the staff of the Chair Information Tech-nology for Traffic Systems for inspiring discussions.

References

Cardoso, J.-F.; Hvan Laheld, B.: Equivariant adaptive source sep-aration, IEEE Trans. on Signal Processing, 44, 12, 3017–3030,1996.


M. Mailand et al.: IQ-imbalance and its compensation for non-ideal analog receivers 195

Hentschel, T.: A Simple IQ-Regeneration Technique for Six-PortCommunication Receivers, 1st International Symposium on Con-trol, Communications and Signal Processing (ISCCSP), Ham-mamet, Tunesia, 311–314, 2004.

Mailand, M. and Jentschel, H.-J.: An Effort Reduced Six-Port Direct Conversion Receiver and Its Calibration, IEEEWireless Communications and Networking Conference 2005(WCNC’2005), New Orleans, USA, 568–572, 2005.

Mailand, M.; Jentschel, H.-J. and Richter, R.: Blind IQ-ImbalanceCompensation Using Iterative Inversion for Arbitrary DirectConversion Receivers, 14th IST Mobile and Wireless Commu-nications Summit, Dresden, Germany, 2005.

Nakagawa, T.; Matsui, M. and Araki, K.: Gain/Phase ImbalanceCompensation for Multi-Band Quadrature Receivers, IEEE 60th

Vehicular Technology Conference (VTC2004-Fall), Los Ange-les, USA, 2004.

Ratni, M.; Krupezevic, D.; Wang, Z. and Jurgensen, J.-U.: Broad-

band Digital Direct Down Conversion Receiver Suitable for Soft-ware Defined Radio, 13th IEEE International Symposium on Per-sonal, Indoor and Mobile Radio Communications PIMRC, Lis-bon, Portugal, 93–99, 2002.

Valkama, M.; Renfors, M. and Koivunen, V.: Compensation ofFrequency-Selective I/Q Imbalances in Wideband Receivers:Methods and Algorithms, 3rd IEEE Workshop on Signal Pro-cessing Advances in Wireless Communications (SPAWC ’01),Taiwan, 42–45, 2001.

Valkama, M.; Renfors, M. and Koivunen, V.: Advanced Methodsfor 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 ParameterEstimation and Compensation in Low-IF Receivers, 1st Interna-tional Symposium on Control, Communications and Signal Pro-cessing (ISCCSP’04), Hammamet, Tunisia, 75–78, 2004.


iq-imbalance and its compensation for non-ideal analog receivers

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