Estimation and Compensation of IQ Imbalance in Millimeter-Wave OFDM UWB System

Transcription

1 Journal of Computers Vol. 8, No. 4, 07, pp doi:0.3966/ Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System Zhan Xu *, Ya-Bing Cheng, and Shi-Jie Ren 3,4 Shool of Information and Communiation Engineering, Beijing Information Siene & Tehnology University, Beijing 009 xuzhan@bistu.edu.n NVIDIA Semiondutor Tehnial Servies (Shanghai) Co., Ltd. (Beijing Branh), Beijing 0000 hybhao666@6.om 3 Shool of Information and Eletronis, Beijing Institute of Tehnology, Beijing Shandong Provinial Key Laboratory of Optial Communiation Siene and Tehnology, Liaoheng University, Shandong Provine, 5000 renshj@tom.om Reeived 8 Otober 06; Revised 3 June 07; Aepted 6 June 07 Abstrat. A new estimation and ompensation method for I/ imbalane based on joint time and frequeny domain is proposed in this paper, whih is well appliable to orthogonal frequeny division multiplexing (OFDM) ultra-wideband (UWB) millimeter-wave (mm-wave) ommuniations. Firstly, the method maes full use of the harateristis of I and signals in time domain, whih have idential power and are unorrelated. Amplitude imbalane fator and phase imbalane fator are estimated using preamble symbols. Seondly, a set of speial pilots are designed in the frequeny domain, and LS algorithm is utilized to estimate the residual imbalane fators to further redue I imbalane. Simulation results show that I imbalane an be well estimated and ompensated with low omplexity. Keywords: frequeny domain, I imbalane, mm-wave, OFDM-UWB, time domain Introdution Millimeter-wave ommuniation system whih operates at frequenies between 30GHz to 300GHz [], is reognized as a ey tehnology in 5G due to several hundred MHz bandwidth. Compared with traditional mirowave ommuniation with relatively narrow bandwidth, hardware impairments in mm-wave ommuniation reates more negative impat on system performane []. I imbalane in mm-wave OFDM-UWB system is disussed in this paper. Radio Frequeny (RF) plays an important role in wireless ommuniations system. There are two types of Traditional RF reeiver, one is super heterodyne reeiver and the other is zero-intermediate frequeny (zero-if) reeiver. Compared with super heterodyne reeiver, the zero-if reeiver has been widely used in wireless ommuniations [3] with the advantage of small in size, simple in arhiteture, easy to integrate, energy onservation and low-ost. However, the advantage of simple implementation also brings serious I imbalane in Zero-IF reeiver [4]. The overall performane will rapidly deteriorate without I imbalane estimation and ompensation [5]. The effet of I imbalanes on OFDM systems and the performane degradation have been investigated [6]. The existene of I imbalane in OFDM system is dedued [7]. A time domain estimation and ompensation method without feedba mehanism is proposed [8]. A new I imbalane ompensation method for OFDM systems using pilot signals inserted in frequeny domain is proposed * Corresponding Author 79

2 Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System [9]. Some researhers have studied I imbalane estimation and ompensation in OFDM system with arrier-frequeny offset (CFO). Barhumi and Moonen proposed a frequeny-domain equalization tehnique for OFDM transmission over frequeny-seletive hannels [0]. They onsider the ase where the reeiver analog front-end suffers from I-imbalane and the loal osillator suffers from CFO. Oa, Ahn, Omori and Hashimoto proposed novel I imbalane and CFO estimation shemes []. Wu, Li, Zhao proposed two novel preamble strutures and the orresponding estimation algorithms that an treat the CFO and TX/RX I imbalane together in mm-wave ommuniation system []. For mm-wave OFDM-UWB system, sine the signal bandwidth is muh larger ompared with the narrowband system, the nonlinearity of RF transeiver is the main bottlene limiting the performane of the ommuniations. A new estimation and ompensation method based on joint time and frequeny domain is proposed to ombat I imbalane problem. This paper is organized as follows. The I imbalane theoretial analysis are disussed in setion, inluding mathematial models and performane analysis in the zero-if reeiver. The priniple of estimation and ompensation method is disussed in setion 3. Simulation results are shown in setion 4. Finally, the summaries of the paper are given in setion 5. Theoretial Analysis of I Imbalane. System Model The baseband signal in OFDM system an be expressed as: N / jπ fst xt () = Re () N = N/ In the above formula, R is the modulation signal on the th subarrier, f s is the adjaent subarrier frequeny interval. The signal bandwidth of UWB system disussed in this paper is 58 MHz, where fs = 4.5MHz, N is the sub-arrier numbers of IFFT/FFT. RF reeiving signal an be defined as: r t = r t e = r t f t r t f t () jπ ft RF () Re{ () I ()os( π ) ( )sin( π ) where f is the frequeny of Loal Osillator (LO), wt () is the additive white Gaussian noise (AWGN). Zero-IF reeiver arhiteture in UWB system is shown in Fig.. Where, LNA is Low-Noise Amplifier, VGA is Variable-Gain Amplifier, and LPF is Low-Pass Filter. Loal Osillator produes the in-phase omponent and quadrature omponent. Fig.. Shemati of zero-if reeiver with I imbalane Amplitude imbalane and phase imbalane are represented by g and θ in the Fig.. I Loal Osillator signals are expressed as: xlo, I () t = os( π ft) (3) xlo, () t = gsin( π ft+ θ) (4) 80

3 Journal of Computers Vol. 8, No. 4, 07 Taing into aount of the influene of I imbalane, the in-phase omponent of baseband signal yi () t is expressed as: yi() t = rrf()os( t π ft) = [ ri( t)os( π ft) r( t) sin( π ft)]os( π ft) (5) = ri()[ t + os(4 π ft)] r ()sin(4 t π f t). A low pass filter (LPF) is designed to eliminate the high frequeny omponent in the in-phase omponent, then in-phase omponent an be expressed as: y () t = r () t (6) I Similarly, taing into aount of the influene of I imbalane, the quadrature omponent of the baseband signal an be expressed as: y() t = rrf() t gsin( π ft+ θ) = [ r I( t)os( π ft) + r( t) sin( π ft )] gsin( π ft + θ) (7) = gri( t)[sin(4 π ft + θ) + sin θ] + gr ( t)[os(4 π f t θ) os θ]. A same LPF is designed to eliminate the high frequeny omponent in the quadrature omponent, and then quadrature omponent an be expressed as: I y ( t) = gr (t)sin( θ) gr (t)os( θ) (8) I After proessing by the orthogonal mixer and LPF, the signal an be expressed as: yt () = yi() t jy() t = y () t jg{ r ()sin( t θ) r ()os( t θ) I I = [ + g os( θ ) jg sin( θ )]( ri () t jr ()) t + [ g os( θ ) jg sin( θ )]( ri ( t ) + jr ( t )) jθ jθ + ge ge * = rt () + r() t = αrt + βr t * () (). ()(9) where, α and β are defined as: jθ jθ + ge -ge α =, β= (0) The disrete signal an be expressed as: y n = r n + r n () * i ( ) α ( ) β ( ). Performane Analysis of I Imbalane Effets After onverting time domain signals to frequeny domain signals using Fast Fourier Transform (FFT), the signal on the -th subarrier an be represented as: 8

4 Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System R = R + R () * α β As an be seen from the above formula, the existene of I imbalane brings Signal of Image Interferene (SOII) on reeived signals. The impat of I imbalane on reeived signals is mainly embodied in two aspets: one is a omplex fator α whih brings multipliative distortion, the other is a omplex fator β whih generates SOII. For the zero-if reeiver, the SOII is the signal itself, namely I ross modulation signal, as shown in Fig., where Δ represents the enter frequeny differene of adjaent hannel and Signal of Interest (SOI). Fig.. SOII in Zero-IF reeiver As an be seen from equation (), the power gain of SOI and its SOII are α and β respetively aused by amplitude imbalane and phase imbalane. Image rejetion ratio (IRR) an be defined as: L UAD ( g ) ( g ) α + + gosθ + β + βosθ = = = (3) β + gosθ + β βosθ + α where β α IRR is a two-dimensional funtion with respet to amplitude error and phase error, the relationship between them is shown in Fig. 3. Fig. 3. The relationship between image rejetion ratio and amplitude/phase fator in orthogonal mixer Restrited to non-ideal fators of analog omponents, the analog orthogonal mixer annot eliminate I imbalane fundamentally. Although with deades of development, analog orthogonal mixer still introdues non-ideal I imbalane fator. When amplitude imbalane fator is equal to.5 and phase imbalane fator is equal to 0 degrees, analog orthogonal mixer an only provide 4dB IRR aording to equation (3). SOII result in a sharp deline in the performane of the wireless system without effiient I ompensation [3]. Meanwhile, the spetrum density of reeived signal is usually very low for UWB reeiver, and therefore if there is a strong SOII in the system, it is neessary to estimate and 8

5 Journal of Computers Vol. 8, No. 4, 07 ompensate I imbalane aused by analog orthogonal mixer. In UWB system, the IRR of RF reeiver is required to ahieve 40dB or more, and therefore, the reeiver needs to have the ability of no more than % of amplitude imbalane fator and no more than degree of phase imbalane fator aording to equation (). However, limited by the level of integrated iruit tehnology, RF reeiver annot ahieve this performane urrently. 3 I Imbalane Compensation Algorithm in OFDM-UWB System 3. Compensation in Time Domain The time-domain signals ti ( n ) and t ( n ) with PSK ode modulation has the following harateristis: { I ( ) { ( ) E t n = E t n (4) { I E t ( n) t ( n ) = 0 (5) whih means ti ( n ) and t ( n ) are a pair of I signals with idential power, zero mean, and orthogonality. ti ( n) and t ( n ) are sent to IFFT module to generate OFDM symbols. Sine the influene of I imbalane on signals is linear, the existene of I imbalane does not hange idential power and orthogonality of I signals [4-5]. Amplitude/phase imbalane fators an be estimated by using the harateristis, the speifi algorithm is as follows: I/ signals have idential power and are unorrelated aording to equation (4) and (5), it an be onluded that: { {( osθ I sin θ) { I E y = E gr gr = g E y (6) The estimation value of amplitude imbalane fator g an be represented as: Aording to orthogonality of I signals: E { y ( n) g E{ yi ( n) = (7) { I( ) ( ) { I( ) [ ( )os θ I( )sin θ] sin θ { I ( ) E y n y n = E r n gr n gr n = g E y n (8) Hene, θ an be expressed as follows: E { yi( n) y( n) arsin E{ y ( ) { I n E y( n) θ = (9) In pratial appliation, the mathematial expetation in the above formula an be replaed by mean value of the finite samples: g = M { y ( n) n= M { yi ( n) n= (0) 83

6 Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System = arsin n= θ M { yi( n) y( n) M M { yi ( n) { y( n) n= n= () where M represents samples. In this paper, two OFDM preamble symbols are used as the training sequene in time domain. FFT/IFFT length is 8, CP length is 36. Therefore, M = *(8+36) = 38. Finally, signals in time domain an be ompensated as follows utilizing estimation values ĝ and θ ˆ : y ( ) ˆ sin ˆ ( ) n + g θ yi n yi( n) = yi( n), y( n) = () gˆ osθˆ 3. Compensation in Frequeny Domain However, for one thing, under the frame struture in OFDM-UWB system where only a few preamble symbols exist, there is a lot of residual I imbalane in UWB system after time-domain ompensation. For another, sine there is a time seletive fading harateristis in the wireless hannel, the performane of OFDM-UWB reeiver will deteriorate if only using few preamble symbols to estimate and ompensate I imbalane, espeially for those OFDM symbols loated in the behind portion of radio frame struture. The pilots in frequeny domain within eah OFDM symbol is used to further eliminate the residual I imbalane. In AWGN hannel, equation () an be rewritten as: The pilot deployment in this paper is as follows: R = R + R + N (3) * α β A ( ) > 0 P = 0 0 where is the number of subarrier, P is the -th pilot subarrier, A( ) is a onstant. We an get: * (4) P = αp + N, P = βp + N (5) where P is the measured value of P at reeiver, P * is the onjugate of P. Aording to the priniple of least squares (LS), the objetive funtion is defined as follows: J = P P P P (6) * ( ) ( ) In order to get α (LS estimation value of α ), the objetive funtion J needs to be minimized. Let J = 0, aordingly, α an be expressed as: α P N α = = α + (7) P P The above formula shows that the estimation variane is inversely proportional to signal-to-noise ratio(snr). The larger the SNR, the better the estimation performane. Estimation variane is defined as: δ = (8) SNR Suppose there are K forward pilots in eah OFDM symbol, the number of α K estimation values are further proessed by Maximum Lielihood (ML) estimation: are also K. The 84

7 Journal of Computers Vol. 8, No. 4, 07 α = α (9) K K S P where SP is the set of forward pilots in OFDM symbols. α is the mean value of α. Estimation variane proessed by ML estimation an be expressed as: δ = δ (30) K Estimation variane is further redued by K via ML estimation. In this paper, there are pilots in eah OFDM symbol, where the number of forward pilots is 6. Similarly, β (estimation value of β ) an be expressed as: β = β (3) K K S P α and β are taen to the formula, R (the orretion value of R ( α ) R β ( R ) = α β * * R ) an be obtained as follows: (3) 4 Simulation For the performane evaluation of the method proposed in this paper, a system simulation platform has been established. The simulation onditions are as follows: SNR = 30dB, I amplitude imbalane fator is.5, phase imbalane fator is 0 degrees, and we adopt the frequeny-dependent I imbalane model in wideband senarios [6]. The influene of I imbalane on OFDM symbols onstellation is shown in Fig. 4. I imbalane has not only led to the rotation of the onstellation, but also auses inter-symbol interferene (ISI). After estimation and ompensation in time domain, the improved onstellation is shown in Fig. 5. In the proposed method for OFDM-UWB system, OFDM preamble symbols are used as the training sequene in time domain followed by estimation and ompensation in frequeny domain to eliminate residual I imbalane. The post-proessed onstellation using estimation and ompensation method both in time domain and frequeny domain is shown in Fig. 6. The bit error rate (BER) performanes of the proposed method and traditional time-domain method are shown in Fig. 7. We an see a signifiant improvement using our proposed method. Fig. 4. Constellation without ompensation 85

8 Estimation and Compensation of I Imbalane in Millimeter-Wave OFDM UWB System Fig. 5. Constellation after ompensation in time domain Fig. 6. Constellation after ompensation in time domain and frequeny domain 5 Conlusion 86 Fig. 7. BER of the proposed method and traditional time-domain method A new method for estimation of I imbalane based on time domain and frequeny domain is proposed in this paper, whih well appliable for mm-wave OFDM-UWB ommuniation system. The system model and performane analysis of I imbalane effets on the wireless ommuniations system are disussed in this paper firstly, followed by the estimation and ompensation method. Compensation in time

9 Journal of Computers Vol. 8, No. 4, 07 domain maes full use of the properties of I and signals. As for frequeny domain method, a set of speial pilots are designed, and LS algorithm is utilized to estimate the residual imbalane fators to further redue I imbalane. Simulation results prove the effetiveness of the proposed method. Anowledgment This wor was supported in part by the National Natural Siene Foundation of China (No ), by China s 863 plan program (No. 05AA0A706), by Beijing Exellent Talent Support Program (No ZK08) Beijing Nova Program (Z ) and Siene Foundation of Beijing Information Siene & Tehnology University (No ). Referenes [] M. Tesanovi, M. Neovee, mmwave-based mobile aess for 5G: ey hallenges and projeted standards and regulatory roadmap, in: Pro. 05 IEEE Global Communiation Conferene (GLOBECOM), 05. [] M. Wu, D. Wuebben, A. Deorsy, P. Baraa, V. Braun, H. Halbauer, Hardware impairments in millimeter mave ommuniations using OFDM and SC-FDE, in: Pro. 0th International ITG Worshop on Smart Antennas, 06. [3] B. Abil, B. Nsiri, G. Ferree, D. Aboutajdine, Carrier frequeny offset estimation in MC-DS-CDMA systems with zero-if reeivers, in: Pro. 5th International Symposium on I/V Communiations and Mobile Networ, Rabat, 00. [4] H.T. Huang, C.T. Lin, S.C. Chiang, B.J. Lin, Volterra nonlinearity ompensator for I/ imbalaned mm-wave OFDM RoF systems, in: Pro. International Topial Meeting on Mirowave Photonis, Paphos, Cyprus, 05. [5] N.T. Hieu, H.G. Ryu, C.X. Wang, H.H. Chen, The impat of the I/ mismathing errors on the BER performane of OFDM ommuniation systems, in: Pro. IEEE International Conferene Communiation, 007. [6] J. Lin, E. Tsui, Joint adaptive transmitter/reeiver I imbalane orretion for OFDM systems, IEEE International Symposium on Personal (004) [7] A. Tarighat, R. Bagheri, A.H. Sayed, Compensation shemes and performane analysis of I imbalanes in OFDM reeivers, IEEE Transations on Signal Proessing 53(8) (005) [8] Y. Liang, F. Shu, Y.J. Zhang, Joint I imbalane and hannel estimation for MIMO-OFDM systems with sparse multipath hannles, Journal of Eletronis & Information Tehnology 35()(03) [9] Y. Egashira, Y. Tanabe, K. Sato, A novel I imbalane ompensation method with pilot-signals for OFDM system, in: Pro. IEEE Vehiular Tehnology Conferene, 006. [0] I. Barhumi, M. Moonen, I-imbalane ompensation for OFDM in the Presene of IBI and Carrier-Frequeny Offset, IEEE Transations on Signal Proessing, 55()(007) [] H. Oa, C.J. Ahn, T. Omori, K.Y. Hashimoto, I imbalane and arrier frequeny offset ompensation shemes for TFI- OFDM, in: Pro. IEEE International Symposium on Intelligent Signal Proessing and Communiation Systems, 04. [] F. Wu, Y. Li, M.J. Zhao, Estimation of TX I/ imbalane at the RX side with RX I/ imbalane and arrier frequeny offset for OFDM systems, in: Pro. 04 IEEE Globeom Worshops (GC Wshps), 04. [3] Y.B. Shen, Key tehnology researh on missile borne/airborne spread spetrum transeiver, [dissertation] Beijing: Beijing Institute of Tehnology, 007. [4] Y. Liu, D. Peng, C.C. Yin, A new I imbalane ompensation algorithm with high performane in MIMO-OFDM reeiver, Journal of Ciruits and Systems 4()(009) [5] B. Razavi, Design onsiderations for diret-onversion reeivers, IEEE Transations on Ciruits and Systems II: Analog 87

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