Suppression of Interference due to IQ Modulators in OFDM(A)Based Communication Systems

Huseyin ArslanElectrical Engineering Department University of South Florida, Tampa, FL

e-mail:arslan@eng.usf.edu

Abstract— Multi-carrier modulation techniques, like OFDM,has been gaining significant interest for future wireless com-munication systems. In spite of all the advantages of OFDM,it has its own challenges. There are several impairments thatcan degrade the performance of the OFDM systems if thesystem and transceivers are not designed properly. IQ modulatorimpairements are among those that can limit the performancesignificantly. One of the major impacts of the IQ modulator inmultiuser OFDM(A) systems (like in WiMAX) is that it introducesinterference between the modulated symbols on the image carri-ers. In this paper, the interference effect caused by IQ modulatorswill be discussed. Self and multi-access interference caused by theIQ modulators will be explained for multiuser OFDM(A) systems.A joint demodulation based approach to suppress IQ modulatorinterference will be developed. The performance of the proposedalgorithm will be obtained and the performance gains with respectto the conventional receiver will be demonstrated.

I. INTRODUCTION

Wireless communication systems have evolved substantiallyover the last two decades. The explosive growth of the wirelesscommunication market is expected to continue in the future,as the demand for all types of wireless services is increasing.Due to their ability to provide high data rates for multimediaapplications, multi-carrier modulation techniques are gaining astrong interest for wide area, local area, and personal area net-works. A special case of multi-carrier modulation is orthogonalfrequency division multiplexing (OFDM) that can overcomemany problems that arise with high data rate communication,the biggest of which is time dispersion [1]-[4]. OFDM hasfound applications in many wireless technologies and recentlyit has been applied to Wireless Metropolitan Area Networks(WMAN) for fixed and mobile wireless access [5], [6].

Although OFDM has proven to be a powerful modulationtechnique, it has its own challenges. There are several impair-ments that can degrade the performance of the OFDM systemsif the system and the transceivers are not properly designed.For example, the transmitted signal, which goes through the IQvector modulator, experiences several levels of signal distortiondue to imperfection in the modulator [7], [8]. These distortionscan greatly affect the performance of the received signal andthe overall system performance. The major IQ impairmentscan be classified as IQ offset, IQ gain imbalance, and IQquadrature-error. Note that the IQ impairments in the receivedsignal will have quite different impact on OFDM based systemscompared to the conventional single carrier systems.

One of the major impacts of the IQ modulator in multi-user OFDMA systems (like in WiMAX) is that it introducesinterference between the modulated symbols on the imagecarriers. In other words, the received signal at every carrier ofinterest (let’s say kth carrier) will be dependent on the symboltransmitted on that carrier as well as the symbol transmittedon the opposite “image” carrier (i.e. -kth carrier). As a result,the image carrier will cause interference on the carrier ofinterest. Depending on the transmission on the image carrier,this causes self or multi-access interference. If the transmissionon the image carrier belongs to the same user, this will causeself interference. For example, in a TDMA (time divisionmultiple access) based OFDM system (like the OFDM-256mode of IEEE 802.16 standard), the type of intererence isthe self interference. On the other hand, if the image carriertransmission belongs to another user, it will cause multi-accessinterference. For example, in OFDMA mode of the IEEE802.16 standard, the interference can be both self or multi-access interference.

In this paper, first, the interference effect caused by IQmodulators will be discussed. Then, an algorithm to cancel theeffect of self and multi-access interference will be proposed.The proposed algorithm can be applied to both single userOFDM and multiuser OFDMA systems in the same way.The performance of the proposed algorithm will be obtainedthrough computer simulations, and the performance gains withrespect to the conventional receiver will be demonstrated.

II. SYSTEM MODEL

Let’s assume a baseband equivalent transceiver systemmodel. The information bits from the upper layers of theprotocol stacks are first passed through a channel coding. Thebits after the channel coding are mapped to symbols dependingon the type of modulation used. Different mapping optionsare available like BPSK, QPSK, 16-QAM, or 64-QAM. Theconstellation-mapped data symbols are then mapped onto allallocated data subcarriers. Once all the subcarriers that willform a full OFDM symbol have been populated, the serial datasymbols are then converted to parallel blocks, and an InverseFast Fourier Transform (IFFT) is applied to these parallelblocks to obtain the time domain OFDM symbols. The timedomain samples of an OFDM symbol can be obtained from

1-4244-0063-5/06/$20.00 ©2006 IEEE

frequency domain symbols as

xm(n) =N−1∑k=0

Xm(k)ej2πnk/N 0 ≤ n ≤ N − 1 (1)

where Xm(k) is the modulated data on the k-th subcarrier ofthe m-th OFDM symbol, and N is the number of subcarriers.The guard interval (Tg), also commonly referred to as the cyclicprefix, is a copy of the end of the symbol that is prepended tothe beginning of the symbol. Cyclic prefix is used to mitigatethe effect of time dispersion and its duration has to exceed themaximum excess delay of the channel in order to avoid ISI[9]. As long as maximum excess delay (τmax) is smaller thanthe length of the cyclic extension (Tg), the distorted part of thesignal from the previous OFDM symbol will stay within theguard interval which will be removed later. Therefore ISI willbe prevented.

The time domain complex samples x(n) are passed throughthe analog front-end of the transmitter, which includes DAC(digital-to-analog-converter), IQ modulator, mixers, analog fil-ters, power amplifier, and antenna.

The transmitted signal that goes through the actual wirelessmedium will be received by the receiver antenna. The wirelessmedium introduces many effects, corrupting the signal andoften placing limitations on the performance of the system.The received signal passes through the receiver analog front-end to give baseband IQ samples for further processing usingdigital signal processing techniques.

III. IQ IMPAIRMENT EFFECTS

IQ modulator modulates the in-phase “I” and quadrature-phase “Q” components with high frequency carriers. Thetransmitted signal that goes through IQ vector modulator ex-periences several level of signal distortion due to imperfectionin the IQ modulator [7], [8]. The major IQ impairments can beclassified as IQ offset, IQ gain imbalance, and IQ quadrature-error. IQ Offset, also called IQ origin offset or carrier leakage,indicates the magnitude of the carrier feedthrough. IQ Offsetcan be observed as an offset in the constellation. Gain mis-match or gain imbalance will result in the amplitude of onechannel being smaller that the other (please see Figure 1. Thebaseband model of IQ origin offset and IQ gain imbalancethat are introduced into time-domain transmitted signal can berepresented as

ym(n) = Is�{xm(n)} + jQs�{xm(n)} + Iof + jQof (2)

where �{x} represents the real part of x and �{x} representsthe imaginary part of x. When Is = Qs, the IQ imbalance willbe zero, and when both Iof and Qof are zero, there will notbe any IQ offset.

Quadrature Skew Error indicates the orthogonal error be-tween the I and Q signals. Ideally, I and Q channels should beexactly orthogonal (90 degrees apart). When the orthogonalityis not ideal (less or more than 90 degrees apart, 90 ± α),then a quadrature error is observed (please see Figure 2). For

example, the following model shows the quadrature offset thatis introduced into the time-domain signal

ym(n) = �{xm(n)} + �{xm(n)}sin(α)+ j�(xm(n))cos(α) (3)

where α is the quadrature error. When α is equal 0 degreeym(n) will be equal to xm(n) (no quadrature error).

If we ignore the DC carrier (which is often not usedin OFDM based standards), the transmitter IQ impairements(excluding the origin offset) can be represented in a unifiedform in frequency domain transmitted samples as

Xm(k) =Xm(k)

2{Is + Qse

−jα}

+Xm(−k)

2{Is − Qse

−jα} (4)

As can be seen from the above equation, the transmitted signal(after the IQ modulator) at the kth carrier depends not onlyon the symbol that is allocated to the kth carrier, but also tothe symbol that is allocated to the −kth carrier. Note that inmulti-user OFDMA system, the kth carrier and the image −kthcarrier can be assigned to different users. Therefore, dependingon whether the image carriers are assigned to the same user orto different users, the IQ impairements cause self or multiuserinterference, respectively. If these interferences are not handledproperly at the receiver, they will cause performance degrada-tion. The IQ modulator impairements cause also distortion inthe signal amplitude and phase. However, this can be handledby a proper channel estimator, as the distortion effect can befolded into the effective channel frequency response.

Note that, in this paper, it is assumed that the IQ im-pairements are due to the transmitter IQ modulator. Since thereceiver IQ modulator effects are known at the receiver, thesecan always be precomputed and precompansated at the receiver.The challenge is to be able to identify the effect of the IQimpairements caused by any type of receiver in real-time andcompensate its effects.

By incorporating the radio channel effects, the receivedsignal can then be modeled as

Y (k) = H(k)X(k) + Z(k) (5)

where H(k) is the channel frequency response on the kthcarrier, and Z(k) is the additive white Gaussian noise term.

Y (k) = X(k)︸ ︷︷ ︸TX symbol

H(k)Is + Qse

−jα

2︸ ︷︷ ︸Effective channel

+ X(−k)H(k)Is − Qse

−jα

2︸ ︷︷ ︸Interference due to IQ modulator

+ Z(k)︸ ︷︷ ︸Noise

(6)

IV. CANCELLATION OF INTERFERENCE DUE TO IQIMPAIREMENTS

The conventional frequency domain equalization (channelinversion), which is very popularly used in OFDM systems,

does not compensate the IQ errors. As a matter of fact, theIQ impairements cause equalization errors. As a result, newapproaches need to be developed that can compensate the effectof IQ interference before or during the equalization process.In this paper, it is assumed that the channel and IQ effectscorresponding to multiple users are estimated and known tothe receiver. The practical estimation of these quantities willbe discussed in a follow up paper. The focus of this paper ison how to suppress the interference caused by the IQ errors.

In this paper, we adopt the popular multiuser detectionapproaches applied in code division multiple access (CDMA)systems to IQ impairment suppression. In order to suppressself and multi-access interference caused by IQ impairements,a joint demodulator that demodulates the signal on both thecarrier of interest and the image carrier simultaneously isproposed. Unlike the conventional detectors where the signalin each carrier is demodulated separately by interpreting theinterference from the image carrier as noise, the joint demodu-lator hypothesizes the interference terms and interprets the in-terference as part of the signal dimension. In essence, the jointdemodulator interprets the signal as a multi-dimensional signaland tries to demodulate the signals in both carriers jointly.The complexity of joint demodulator is in the exponentialincrease in number of hypothesis compared to the conventionaldemodulator where the complexity is linear. However, sinceonly two carriers are demodulated simultaneously, the approachis still feasible compared to other joint demodulators in theliterature. Even if the number of users are more than two,still, only the images carriers (i.e. the kth and −kth carriers)are demodulated jointly. This will completely suppress theinterference caused by IQ impairements. Therefore, there isno need to demodulate all the carriers jointly. This is quitedifferent than the joint demodulation approaches applied inCDMA literature, and makes the detection complexity man-ageable. Let’s go through a simple example to demonstrate thecomplexity. Let’s assume that QPSK modulated symbols areused; the total number of carriers within an OFDM symbolis 128, and let’s assume that only 100 of those carriers arecarrying data symbols (the rest of the carriers are used forguard band and the DC carrier which is not used for symboltransmission). In a conventional demodulator, the signal ineach carrier is detected individually. If each carrier symboldetection complexity is quantified as X , the total complexitywill be 100X . In joint demodulation, we will first pair thesamples in the data carrying 100 carriers into 50 pairs (wherethe image carriers are making each pair). In each pair, thesymbols transmitted in both image carriers will be demodulatedjointly with an approximate complexity of X2. Therefore, thetotal complexity will be 50X2. Here, what is meant by Xis the number of possible hypothesis. For QPSK modulationwith a conventional detector, the number of hypothesis is 4(corresponding to each possible transmitted QPSK symbol). Injoint demodulator, the number of hypothesis that need to becalculated will be 16. Of course, the complexities calculatedabove are overly simplified to explain the idea clearly. In

practice, the actual complexity of the joint demodulator willbe more (since the calculation of each hypothesis in jointdemodulator requires more calculation, and the selection ofthe best hypothesis is also more complex).

The joint metric for the proposed detector can be written as

ejoint(k,−k) = |Y (k) − Yhyp(k)|2+ |Y (−k) − Yhyp(−k)|2 (7)

where the Y (k) and Y (−k) are the received signal pairs onthe image carriers, the signal hypothesis at a carrier (let’s saykth carrier) can be obtained as

Yhyp(k) = Xhyp(k)H(k)Is + Qse

−jα

2

+ Xhyp(−k)H(k)Is − Qse

−jα

2(8)

where Xhyp(k) is the transmitted symbol hypothesis at thekth carrier, and V represents the estimate of a parameter V . Ina conventional detector, the metric that is used is the simplesingle dimensional Euclidean which can be written as

econventional(k) = |Y (k) − Xhyp(k)H(k)|2 (9)

V. PERFORMANCE RESULTS

Figures 3 through 8 show the performances of the proposeddetector and the conventional detector (without IQ interferencecancellation) in various scenarios. The performance resultsare obtained in frequency selective fading channel under theeffect of several degrees IQ impairements and with differentlevels of background noise (i.e various SNR). Two differentmodulations, 64-QAM and 16-QAM, are tested. Notice thatjoint demodulator completely suppresses the effect of IQ inter-ference at the expense of some extra computational complexity.The performance gains are very significant when the receivedsignal is dominated by the IQ impairements (i.e. for high SNRvalues). The gains are especially more important when higherorder modulations are used.

VI. CONCLUSION

IQ modulator impairements impact the performance ofthe OFDM based multicarrier system performance. The selfand multiuser interference caused by these impairements onOFDMA based systems is discussed in this paper. A solutionthat can handle these interferences is also provided. Theproposed solution offers improved receiver performance atthe expense of some computational complexity. The proposedsolution assumes that the values of the IQ impairements (likethe IQ imbalance and quadrature offset) are calculated beforethe detection process. The practical estimation of these valuesare currently being studied by the author and are planned tobe published in a follow up paper.

The proposed solution can be applied to single user OFDMand multiuser OFDMA systems. In the multiuser OFDMAcase, in this paper, it has been assumed that a single transmitter(with the same IQ modulator) is used to transmit the OFDMA

waveform (as in downlink transmission). This simplifies theproblem when the image carriers are belong to different users,as the IQ impairements will be the same for multiple users.However, in the uplink OFDMA, the IQ impairements will bedifferent for different users. Therefore, in the future work, theproposed study needs to be extended to cover these cases aswell.

REFERENCES

[1] A. R. S. Bahai, B. R. Saltzberg, and M. Ergen, Multi-Carrier DigitalCommunication: Theory and Applications of OFDM. New York, NY:Kluwer Academic/Plenum, 1999.

[2] R. Prasad and R. V. Nee, OFDM for Wireless Multimedia Communica-tions. Boston, London: Artech House Publishers, 2000.

[3] M. Engels, Wireless OFDM systems: How to make them work? KluwerAcademic Publishers, 2002.

[4] J. Heiskala and J. Terry, OFDM Wireless LANs: A Theoretical andPractical Guide. 201 West 103rd St., Indianapolis, IN: Sams Publishing,2002.

[5] IEEE Standard for Local and Metropolitan area networks, Part 16: AirInterface for Fixed Broadband Wireless Access Systems, The Institute ofElectrical and Electronics Engineering, Inc. Std. IEEE 802.16-2004, 2004.

[6] “IEEE 802.16e, mobile WirelessMAN.” [Online]. Available:http://www.ieee802.org/16/tge/index.html

[7] P. Rykaczewski, D. Pienkowski, R. Circa, and B. Steinke, “Signal path op-timization in software defined radio systems,” IEEE Trans. on MicrowaveTheory and Techniques, vol. 53, no. 3, pp. 1056–1064, 2005.

[8] A. Tarighat, R. Bagheri, and A. H. Sayed, “Compensation schemes andperformance analysis of IQ imbalances in OFDM receivers,” IEEE Trans.on Sig. Processing, vol. 53, no. 8, pp. 3257–3268, 2005.

[9] F. Tufvesson, “Design of wireless communication systems – issues onsynchronization, channel estimation and multi-carrier systems,” Ph.D.dissertation, Lund University, Aug. 2000.

In-Phase (I)

cos(w t)c

Quadrature-Phase (Q)

Qs

Is

csin(w t)

Fig. 1. Block diagram of IQ modulator with IQ gain imbalance

In-Phase (I)

cos(w t)c

90 + QEo

Quadrature-Phase (Q)

0o

Fig. 2. Block diagram of IQ modulator with Quadrature error

0 1 2 3 4 5 6 7 8 9 10

10−2

10−1

Quadrature Skew (degree)

Sym

bol E

rror

Rat

e

Conv. det. (SNR=20dB)

Joint det. (SNR=20dB)

Conv. det. (SNR=21.5dB)

Joint det. (SNR=21.5dB)

Conv. det. (SNR=23dB)

Joint det. (SNR=23dB)

Fig. 3. Performance of the proposed joint detector and the conventionaldetector. SER versus quadrature skew angle for various SNR values are shownwithout IQ imbalance. A 64-QAM modulation is used.

14 16 18 20 22 24

10−2

10−1

SNR (dB)

Sym

bol E

rror

Rat

e

Conv. det. (QE=10 degree)

Joint det. (QE=10 degree)

Conv. det. (QE=6 degree)

Joint det. (QE=6 degree)

Fig. 4. Performance of the proposed joint detector and the conventionaldetector. SER versus SNR for various quadrature skew values are shownwithout IQ imbalance. A 64-QAM modulation is used.

14 16 18 20 22 24 26 28 30

10−2

10−1

SNR (dB)

Sym

bol E

rror

Rat

e

Conv. det. (QE=10 degree)

Joint det. (QE=10 degree)

Conv. det. (QE=6 degree)

Joint det. (QE=6 degree)

Fig. 5. Performance of the proposed joint detector and the conventionaldetector. SER versus SNR for various quadrature skew values are shown withan IQ imbalance of 16 percent. A 64-QAM modulation is used.

0 1 2 3 4 5 6 7 8 9 1010

−5

10−4

10−3

10−2

Quadrature Skew (degree)

Sym

bol E

rror

Rat

e

Conv. det. (SNR=21.5dB)

Joint det. (SNR=21.5dB)

Conv. det. (SNR=23dB)

Joint det. (SNR=23dB)

Fig. 6. Performance of the proposed joint detector and the conventionaldetector. SER versus quadrature skew angle for various SNR values are shownwithout IQ imbalance. A 16-QAM modulation is used.

11 12 13 14 15 16 17 18 19 20

10−3

10−2

10−1

SNR (dB)

Sym

bol E

rror

Rat

e

Conv. det. (QE=10 degree)Joint det. (QE=10 degree)Conv. det. (QE=6 degree)Joint det. (QE=6 degree)

Fig. 7. Performance of the proposed joint detector and the conventionaldetector. SER versus SNR for various quadrature skew values are shownwithout IQ imbalance. A 16-QAM modulation is used.

9 10 11 12 13 14 15 16 17 18 19 20

10−3

10−2

10−1

SNR (dB)

Sym

bol E

rror

Rat

e

Conv. det. (QE=10 degree)Joint det. (QE=10 degree)Conv. det. (QE=6 degree)Joint det. (QE=6 degree)

Fig. 8. Performance of the proposed joint detector and the conventionaldetector. SER versus SNR for various quadrature skew values are shown withan IQ imbalance of 16 percent. A 16-QAM modulation is used.