JOINT COMPENSATION OF OFDM TRANSMITTER AND RECEIVER IQ IMBALANCE IN THE PRESENCE OF CARRIER FREQUENCY OFFSET

JOINT COMPENSATION OF OFDM TRANSMITTER AND RECEIVER IQ IMBALANCE IN THE PRESENCE OF CARRIER FREQUENCY OFFSET Deeaknath Tandur, and Marc Moonen ESAT/SCD-SISTA, KULeuven Kasteelark Arenberg 10, B-3001, Leuven-Heverlee, Belgium hone: + (32) 1632 1841, fax: + (32) 1632 1970, email:{deeaknathtandur, marcmoonen}@esatkuleuvenbe ABSTRACT Zero-IF based OFDM transmitters and receivers are gaining a lot of interest because of their otential to enable low-cost, low-ower and less bulky terminals However these systems suffer from In-hase/Quadrature-hase (IQ) imbalances in the front-end analog rocessing which may have a huge imact on the erformance We also consider the case where the local oscillator suffers from carrier frequency offset As OFDM is very sensitive to the carrier frequency offset, this distortion needs to be taken into account in the derivation and analysis of any IQ imbalance estimation/comensation scheme In this aer the effect of both transmitter and receiver IQ imbalance under carrier frequency offset in an OFDM system is studied and algorithms are develoed to comensate for such distortions in the digital domain 1 INTRODUCTION Orthogonal Frequency Division Multilexing (OFDM) is a oular, standardized technique for broadband wireless systems: it is used for Wireless LAN 1], Fixed Broadband Wireless Access 2], Digital Video & Audio Broadcasting 3], etc Recently, a lot of effort is sent in develoing integrated, cost and ower efficient OFDM receivers The Zero-IF architecture (or Direct-Conversion architecture) is an attractive candidate As the name suggests, the Zero-IF architecture converts the RF signal directly to baseband or vice-versa without any Intermediate Frequencies (IF) The Zero-IF architecture erforms In-hase/Quadrature-hase (IQ) modulation and demodulation in the analog domain As a result the matching between the analog I and Q aths and their comonents are imerfect This leads to IQ imbalance distortion which significantly degrades the signal quality Rather than decreasing IQ imbalance by increasing the design time and the comonent cost, IQ imbalance can also be tolerated and then comensated digitally Along with IQ imbalance, OFDM systems are also very sensitive to Carrier Frequency Offset (CFO) The erformance degradation due to receiver IQ imbalance and CFO on OFDM systems have been investigated in 4] and 5] Several comensation algorithms considering either only receiver IQ imbalance or transmitter IQ imbalance individually have been develoed in 6],7] and 8] Recently, joint transmitter and receiver IQ imbalance comensation algorithms have been roosed in 9] and 10] However, all the above mentioned algorithms ignore the roblem of joint IQ imbalance at both transmitter and receiver along with CFO estimation and comensation While the combination of CFO with receiver IQ imbalance has been studied in 11], to the best of our knowledge, no general solution has been roosed so far for the comlete roblem combining CFO with both transmitter and receiver IQ imbalance This reort is organized as follows In section II, we describe the imact of IQ imbalance and CFO in OFDM systems In section III, the basics of a suitable transmitter and receiver IQ imbalance and CFO comensation scheme are exlained Section IV resents the various comensation algorithms Our simulation results are shown in section V and finally the conclusion is given in section VI 2 IQ IMBALANCE AND CFO MODEL We analyze the effect of IQ imbalance in time and frequency domain Frequency domain signals are underscored, while time domain signals are not Signals are indicated in bold and scalar arameters in normal font Suerscrits, T, H reresent conjugate,transose and Hermitian resectively In general, IQ imbalance (both transmitter and receiver imbalance) can be characterized by 2 arameters: an amlitude mismatch ε between the I and Q branch and a hase orthogonality mismatch φ The comlex baseband equation for IQ imbalance effect on an ideal time domain signal vector r is given by 12]: r iq = (cos φ + jεsin φ)r+(εcos φ jsin φ)r (1) r iq = αr+βr (2) with () the comlex conjugate and α = cos φ + jεsin φ (3) β = εcos φ jsin φ (4) If no IQ imbalance is resent, then ε = φ = 0 and thus α = 1 and β = 0 and then (2) reduces to r iq = r Parameters (α, β) are used for analytical derivations, as they form a more tractable mathematical descrition of the IQ imbalance For simulations, the more hysically relevant arameters (ε, φ) will be used The IQ imbalance imact on the frequency domain signal vector r = DFT {r} is: r = DFT {r iq } iq = DFT {αidft(r )+βidft(r )] } r = αr + βr m iq (5)

Here () m denotes the mirroring oeration in which the vector indices are reversed, such that r m l] = r l m ] { lm = 2+N l f or l = 2N where l m = l f or l = 1 ie, l m is the mirror carrier of l and N is the number of carriers in an OFDM symbol When the imact of both transmitter and receiver IQ imbalance is considered, equations (2) and (5) change as follows: r Tiq-Riq = (α t r+ β t r )+ (α t r+ β t r ) = ( α t + β t )r+( β t + α t )r r = ( α t + β t )r +( β t + α t )r m Tiq-Riq where (α t,β t ),(, ) reresent the transmitter and receiver IQ imbalance resectively If the transmission channel is frequency selective, it introduces a filtering that should be included in formulas (6) If the channel imulse resonse is shorter than the OFDM cyclic refix, which is a standard assumtion, formula (6) is changed to: r Tiq-c-Riq = IDFT(c DFT(α t r+ β t r )) + (IDFT(c DFT(α t r+ β t r ))) r Tiq-c-Riq =( α t c + β t c m ) r +( β t c + α t c m ) r m where denotes comonent-wise vector multilication and reresents the channel s frequency resonse c Equation (7) shows that due to transmitter and receiver IQ imbalance ower leaks from the signal on the mirror carrier (r m ) to the carrier under consideration (r ) and thus causes Inter-Carrier-Interference (ICI) As OFDM is very sensitive to ICI, IQ imbalance causes severe erformance degradation Since OFDM is very sensitive to CFO, this distortion also needs to be taken into account CFO occurs when there is a frequency deviation between the sine wave roduced by the receiver local oscillator and the transmitter local oscillator In 11], it was shown that when CFO is resent together with receiver IQ imbalance, the resulting baseband signal can be written as: (6) (7) r cfo-riq = r e j2π ft + r j2π ft (8) where f is CFO in the system and t is the time vector For the case involving CFO as well as transmitter and receiver IQ imbalance, the above equation changes to: r Tiq-cfo-Riq = (α t r+ β t r j2π ft + (α t r+β t r ) j2π ft =( α t r+ β t r j2π ft +( αt r + βt j2π ft r (9) Finally, if the channel is frequency selective, with frequency resonse c, formula (9) can be generalized to: r Tiq-c-cfo-Riq = (IDFT(c DFT(α t r+β t r j2π ft )) + (IDFT(c DFT(α t r+ β t r ))) j2π ft (10) The joint effect of both transmitter and receiver IQ imbalance along with CFO results in a severe ICI Thus a digital comensation is required which limits the achievable oerating SNR at the receiver and the achievable data rates 3 IQ IMBALANCE AND CFO COMPENSATION Following the joint model from the revious section, formula (10), we know that the received OFDM symbol in time domain is given as: r Tiq-c-cfo-Riq = e j2π ft + j2π ft (11) where = IDFT(c DFT(α t r+β t r )) Equation (11) exlicitly shows only the CFO and the receiver IQ imbalance The channel filtering and the distortion due to transmitter IQ imbalance are hidden in the definition of and so not considered for the time being We now assume that the CFO can be estimated accurately in the OFDM system In ractice, several CFO estimation schemes indeed exist that are found to be sufficiently robust against the IQ imbalance 11] and 13] Thus, given a good estimate of f, we first erform an element wise multilication of the received distorted symbol in equation (11) with the estimated negative frequency offset e j2π ft This results in a vector r 1 as follows: j2π ft r 1 = r Tiq-c-cfo-Riq = + 2 j2π ft = + q (12) Similarly, we also erform an element wise multilication of the comlex conjugate of the received signal with the negative frequency offset e j2π ft resulting in a vector r 2 as follows: r 2 = (r Tiq-c-cfo-Riq ) j2π ft = (αr j2π ft + βr e j2π ft j2π ft = βr + 2 j2π ft = β r + q (13) Both the signals r 1 and r 2 consist of two contributions and q scaled by different weighing factors is called the desired signal and q the undesired signal This is because in frequency domain, the former gives rise to the desired signal, while the latter yields a mirror image and causes ICI (because of the comlex conjugate), subject to leakage caused by the exonential term (e 2 j2π ft ) Transforming equations (12) and (13) to the frequency domain, we obtain:

] r 2 = ] ] q αr β r (14) Equation (14) can be written more exlicitly for each comonent (frequency bin) l of the OFDM symbol: l] r 2 l] ] = l] ql] ] ] αr β r (15) From this it follows that the desired signal l] can be obtained by taking an aroriate linear combination of r 1 l] and r 2 l], ie l] r 2 l] ] ] l] r 2 l] ] ] = l] = l] l] = ql] ] ql] ] αr 1 0] l] r 2 l] ] ] ] ] From the definition of it follows that DFT(α t r+β t r ), hence l] = cl](α t rl]+β t r m l]) l] = cl] l] where l] = (α t rl]+β t r m l]) By combining equations (16) and (17) we obtain: l] = l] r 2 l] ] ] l] l] (16) = c (17) (18) which means that by taking an aroriate (now frequency bin deendent) linear combination of r 1 l] and r 2 l], signal l] is obtained which is only distorted by transmitter IQ imbalance, ie l] = α t rl]+β t r m l] = α t rl]+β t r l m ] (19) where l m is the mirror index of l In a similar fashion, an aroriate linear combination of r 1 l m ] and r 2 l m ] can then be found, ie l m ] = l m ] r 2 l m ] ] leading to a signal l m ] equal to ] τlm ] υl m ] l m ] = α t rl m ]+β t r m l m ] = α t rl m ]+β t r l] lm ] = β t r l]+α t r l m ] (20) (21) Formula (19) and (21) can be combined into l] ] lm ] = r l] r l m ] ] ] αt β t β t α t (22) From this it follows that the transmitted signal r l] can be obtained by taking an aroriate linear combination of l] and lm ] By substituting the formula for l] and lm ] in the formulas (18) and (20), rl] can be obtained directly as: r l] = l] r 2 l] r 1 l m ] r 2 l m ] ] χl] ψl] γl] (23) ρl] where the weights χl],ψl],γl],ρl] are derived from all the reviously used weights This formula demonstrates that a receiver structure can be designed that exactly comensates for the transmitter and the receiver IQ imbalances, the CFO and the channel effect The coefficients χl], ψl], γl], ρl] can be comuted from the α t,β t,,, f and c, if these are available In the next section various algorithms are exlained which comensate the joint transmitter and receiver IQ imbalance along with CFO by the initialization of χl],ψl],γl],ρl] 4 COMPENSATION ALGORITHMS 41 Least-Square Comensation The Least Square (LS) estimate of the coefficient vector χl], ψl], γl], ρl] can be comuted as 14]: χl] ψl] γl] = (Al] H Al]) 1 Al] H dl] (24) ρl] where Al] is the data matrix given for i = K training symbols r 1 l] (1) r 2 l] (1) r 1 l m ] (1) r 2 l m ] (1) r 1 l] (2) r 2 l] (2) r 1 l m ] (2) r 2 l m ] (2) Al] = r 1 l] (K) r 2 l] (K) r 1 l m ] (K) r 2 l m ] (K) and dl] is the desired data vector containing K transmitted training symbols dl] = d l] (1) dl] (2) dl] (K)] T Regularization can be used when it is required to combat ill-conditioning in the data Al] Thus deending on the number of training symbols, K realizations of the above equation can be collected to erform the LS estimation of the coefficient matrix The resulting coefficient vector can then be substituted in formula (23) to obtain the transmitted OFDM symbol r

r 1] r 2] r N] Serial to Parallel OFDM mod IFFT Add cyclic refix Parallel to Serial Transmitter IQ distortion r Tiq Multiath Channel Rayleigh fading channel Noise CFO & Receiver IQ distortion r Tiq-c-CFO-Riq Serial to Parallel Remove Cyclic Prefix -CFO () r 1 -CFO r 2 FFT FFT r 1 1] r 1 1] () r 1 N] r 1 N] r 2 1] () r 2 N] r 2 1] r 2 N] Equalizer -LS/RLS (4 ta) r l] = χl] r 1 l] + ψl] r 2 l])+ γl] r 1 l m ] + ρl] r 2 l m ]) OFDM Demod Parallel to Serial r 1] r 2] r N] Figure 1: OFDM system with ost-fft comensation of transmitter and receiver IQ imbalance with CFO 42 Adative Equalization We roose a training based system with 4 ta adative equalizer to comensate transmitter and receiver IQ imbalance with CFO The equalizer tas wl] can be udated adatively to the coefficient vector χl], ψl], γl], ρl] by any of the standard adative algorithms For our simulations we have used the RLS scheme for its suerior convergence roerties The RLS algorithm to comute the coefficient vector is listed in Algorithm 1 14] To better illustrate the udate equations, we use the time (or iteration) index i As a result let wl] (i) reresent the equalization vectors at time instant i δ is the regularization factor which is a small ositive constant Algorithm 1 RLS direct equalization with CFO For all the carriers in OFDM symbol l=1n comute Initialize the algorithm by setting wl] (i=0) = 0 4 1 P (i=0) = δ 1 I 4 4 For each iteration i = 1K comute ul] (i) = l] (i) r 2 l] (i) r 1 l m ] (i) r 2 l m ] (i)] T ξ (i) = dl] (i) wl] H(i1) ul] (i) wl] (i) = wl] (i1) P (i1) ul] (i) (i) + 1+ul] H(i) P (i1) ξ ul] (i) P (i) = P (i1) P (i1) ul] (i) 1+ul] H(i) P (i1) ul] (i) uh(i) P (i1) At the end of the training the weights wl] corresond to the coefficient vector χl], ψl], γl], ρl] The weights wl] are then substituted in formula (23) to obtain the transmitted symbol r l] 5 SIMULATION RESULTS A tyical OFDM system (similar to IEEE 80211a) is simulated to evaluate the erformance of the comensation scheme for transmitter and receiver IQ imbalance under CFO The erformance comarison is made with an ideal system with no front-end distortion and with a system with no comensation algorithm included An end-to-end OFDM system with the comensation scheme is shown in Figure 1 The equalizer has four tas and the ta values are calculated using one of the algorithms roosed in the revious section It is noted that the receiver structure shown in Figure 1 generalizes earlier structures for secific subroblems Reference 8] and 11] for instance aly to the comensation of CFO with either transmitter or with receiver IQ imbalance but not both In this case the outut of any one FFT branch can be taken (instead of both oututs) as the comensation can then be obtained with a two ta adative equalizer The arameters used in the simulation are: OFDM symbol length of N = 64, cyclic refix of CP = 16 There are two different channel rofiles: 1) an additive white Gaussian noise (AWGN) channel with a single ta unity gain and 2) a multiath channel with 4 tas where the tas are chosen indeendently with comlex Gaussian distribution Every channel realization is indeendent of the revious one and the BER results deicted are from averaging the BER curves over several indeendent channels We consider IQ amlitude imbalance ε = 5% and hase imbalance φ = 5 at both transmitter and receiver The CFO (ζ = f NT ) is assumed to be 032 where T is the samling eriod The IQ imbalance distortion taken are tyical values achievable in ractical integrated circuit imlementations Figure 2 shows the erformance curves (BER vs SNR) for uncoded 64QAM OFDM system With no comensation scheme in lace, the OFDM system is comletely unusable Even for the case when there is only transmitter and receiver IQ imbalance and no CFO, the BER is very high For the case with the comensation scheme emloyed, the curves are very close to the ideal situation with no front-end distortion

10 0 10 0 Uncoded BER 10 1 10 2 10 3 Ideal case no IQ & CFO imbalance IQ imbalance & CFO No Comensation Only IQ imbalance No Comensation IQ imbalance & CFO LS comensation IQ imbalance & CFO RLS comensation Uncoded BER 10 1 10 2 10 4 10 5 10 6 10 15 20 25 30 35 40 SNR in db 10 3 Ideal case no IQ & CFO imbalance IQ imbalance & CFO No Comensation Only IQ imbalance No Comensation IQ imbalance & CFO LS comensation IQ imbalance & CFO RLS comensation 10 4 10 15 20 25 30 35 40 SNR in db (a) AWGN flat channel (non-fading) (b) 4-ta comlex Gaussian channel (fading) Figure 2: BER vs SNR simulated for 64QAM constellation with training length of 15 OFDM symbols in LS and RLS solutions, transmitter hase imbalance of φ t = 5, transmitter amlitude imbalance of ε t = 5%, receiver hase imbalance of φ r = 5, receiver amlitude imbalance of ε t = 5% and CFO of ζ = 032 (ζ = f NT) The design of Zero-IF receivers tyically yields an IQ imbalance on the order of (ε, φ) = (2 3%,2 3 ) 15] When CFO is also resent, the system certainly cannot work without a suitable comensation technique Moreover, very large IQ imbalance values can be corrected just as easily with this comensation scheme Thus the resented IQ-CFO mitigation allows to greatly relax the Zero-IF design secifications 6 CONCLUSION In this reort the joint effect of OFDM transmitter and receiver IQ imbalance under CFO is studied and algorithms are develoed to comensate for such distortions in the digital domain The algorithms rovide a very efficient ost-fft equalization which leads to near ideal comensation REFERENCES 1] IEEE standard 80211a-1999: wireless LAN medium access control (MAC) & hysical layer (PHY) secifications, high-seed hysical layer in 5 GHz band, 1999 2] IKoffman and VRoman, Broadband wireless access solutions based on OFDM access in IEEE 80216, IEEE Comm Magazine, vol 40, no 4, 96-103, Aril 2002 3] ETSI Digital Video Broadcasting; Framing structure, Channel Coding & Modulation for Digital TV, 2004 4] TPollet, M Van Bladel and M Moeneclaey, BER sensitivity of OFDM systems to carrier frequency offset and wiener hase noise, IEEE Trans on Communications, vol 43, no 2/3/4, 191-193, 1995 5] CLLiu, Imact of I/Q imbalance on QPSK-OFDM- QAM detection, IEEE Trans on Consumer Electronics, vol 44, 984-989, Aug 1998 6] ATarighat, RBagheri and AHSayed, Comensation schemes and erformance analysis of IQ imbalances in OFDM receivers, IEEE Trans on Signal Processing, vol 22, no 4, 24-40, July 2005 7] ASchuchert, RHasholzner and P Antoine, A novel IQ imbalance comensation scheme for the recetion of OFDM signals, IEEE Trans on Consumer Electronics, vol 47, no 48, 313-318, Aug 2001 8] JTubbax, BCome, LVan der Perre, MMoonen and HDe Man, Comensation of transmitter IQ imbalance for OFDM systems, Proc Int Conference on Acoustics, Seech and Signal Processing, Montreal, Canada, May 2004, 325-328 9] J Lin and E Tsui, Joint adative transmitter/recevier IQ imbalance correction for OFDM systems, IEEE Int Symosium on Personal, Indoor and Mobile Radio Comm, Barcelona, Sain, Set 2004, 1511-1516 10] A Tarighat and A H Sayed, OFDM systems with both transmitter & receiver IQ imbalances, Proc IEEE Int Worksho on Signal Processing Advances in Wireless Comm, New York, NY, June 2005, 735-739 11] JTubbax, BCome, LVan der Perre, MEngels,MMoonen and HDe Man, Joint comensation of IQ imbalance and CFO in OFDM systems, Proc Radio and Wireless Conf, Boston, MA, Aug 2003, 39-42 12] BRazavi RF Microelectronics, Prentice Hall, 1998 13] SFouladifard and HShafiee, Frequency offset estimation in OFDM systems in resence of IQ imbalance, Proc Int Conference on Communications, Anchorage, AK, May 2003, 2071-2075 14] SHaykin, Adative Filter Theory, Prentice Hall, 2002 15] BCome, DHausie, et al, Single-ackage directconversion receiver for 80211a enhanced with fast converging digital com techniques, IEEE Int Microwave Symosium, Fort Worth, TX, June 2004, 555-558