Low Complexity I/Q Imbalance and Channel Estimation echniques for MIMO OFDM Systems Juinn-orng Deng, sin-shan sieh, and Kuo-ai Feng Department of Communications Engineering Yuan Ze University, 5 Yuan-ung oad, Chung-Li, aiwan E-mails: s980@mail.yzu.edu.tw Abstract In this paper, the joint estimation techniques of inphase and quadrature-phase (I/Q) imbalance and channel impulse response (CI) are proposed for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over ayleigh fading environments. A novel preamble-aided structure with orthogonal property is designed to cancel the image interference due to I/Q imbalance and channel effects. Simulation results confirm the proposed method with low computational complexity can accurately estimate the CI and I/Q imbalance parameters and achieve better root mean square error (MSE) performance over F impairment and multipath fading channel environments. Keywords SISO OFDM, MIMO OFDM, I/Q imbalance, channel estimation, preamble. I. IODUCIO Orthogonal frequency division multiplexing technique (OFDM) is applied widely to wireless communication systems. Besides, OFDM combines multiple-input and multiple-output (MIMO) can not only raise its data rate but also not occupy extra bandwidth. owever, MIMO systems means that the architecture of receiver involves more complexity than singleinput and single-output (SISO) systems. Figure shows the black diagram of OFDM systems. At the receiver side, directconversion receiver and superheterodyne receiver are widely used. Although the performance of superheterodyne is better than direct-conversion, the consumption and complexity are also higher. Due to the requirement of low computational complexity and low power consumption, the direct-conversion receivers have drawn a lot of attentions and exhibited great advantages in the next-generation wireless communication systems. On the other hand, some gain and phase mismatches in direct conversion receiver can seriously degrade the system performance. One of these mismatches is so-called the inphase and quadrature-phase (I/Q) imbalance which is induced by the mismatch of local oscillators. Especially, in the MIMO OFDM systems, I/Q imbalance leads to more obvious performance degradation. I/Q imbalance estimators and compensators have been studied by many researchers []-[8]. Among these works, the training sequences in []-[] and optimal sequence in [] are proposed to compensate the distortion of I/Q imbalance. hey are still provide high computational complexity operation to estimate the parameters. In this paper, we propose a preamble-aided method with low computational complexity advantage, which focuses on the estimation and compensation of the I/Q imbalance and multipath channel effects of MIMO OFDM system over the wireless ayleigh fading channels [], [5]. A novel preamble design, i.e., MIMO full-usage preamble sequence design, can jointly estimate the gain and phase parameters of I/Q imbalance and the channel impulse response (CI). On one hand, by using the proposed preamble sequence, the parameters of I/Q imbalance and CI can be accurately estimated and the image interference signal can be eliminated. On the other hand, it can equalize the received signal to detect the original transmitted data. Data bits Estimated data S/P P/S X 6QAM Modulator X 6QAM Demodulator IFF FF Add CP ayliegh Channel emove CP Figure. he black diagram of OFDM II. SYSEM AD SIGAL MODEL AWG A. MIMO OFDM Signal Model Figure shows an MIMO OFDM systems where the number of transmit and receive antennas are and, respectively. Assume there is no interference between each antenna and no inter symbol interference (ISI). We consider that channel effect which includes the wireless ayleigh fading channel and additive white Gaussian noise (AWG). he channel is given by ISB 978-89-968650-0- 8 January 7 ~ 0, 0 ICAC0
h h h,,, h h h,,, () h, h, h, Every element of is individually independent complex Gaussian random variable with a zero-mean and unit variance. he signal model for MIMO systems is given by F F F Where y x n () m m m m h, h, h, h, h, h, Figure. he channel of MIMO OFDM systems y F F F n and m is mth symbol of OFDM signal. y y y y is the received signal vector, x x x x is the transmitted signal vector, n n n n is AWG vector. ote that, for MIMO OFDM systems, the channel of every subcarrier from different antennas can be regard as flat fading channel. he received signal of kth subcarrier can be written as (). Where k 0,,, and is the length of subcarrier for OFDM. y x n () m m m m B. he eceived Signal Model with I/Q Imbalance he amplitude and phase mismatches of local oscillator are due to I/Q imbalance. his paper considers I/Q imbalance at receiver mainly. Figure illustrates I/Q imbalance at receiver, where g and ψ denote the gain and phase mismatch respectively andc ft c, where fc is the carrier frequency. In this paper, we will discuss effect of I/Q imbalance for SISO OFDM systems first, then extend it to MIMO OFDM systems. cos( t c ) gsin( t) c LPF LPF yi () t y () Q t ADC ADC Digital Baseband j yt () Figure. he black diagram of I/Q imbalance Baseband Processing When I/Q imbalance exists at receiver side, the received signal for SISO OFDM systems can be modelled as [] yˆ( t) yi( t) jyq( t) j y( t) ji ge y( t) () ky( t) ky ( t) where {.} and I{.} denote real part and image part of received signal respectively, and k ( ge j ), k ( ge j ) are the parameters of I/Q imbalance. In the case of perfect matching between the I and Q branch, it means that g= and ψ =0,and the parameters will be k, k 0. Assume there is perfectly synchronized for MIMO OFDM systems so that no interference between each signal. he received signal with I/Q imbalance can be extended from SISO OFDM systems to MIMO OFDM systems, then transfer it from time domain to frequency domain, the received signal can be modelled as yˆ m nt k m, nt nt, nt nt k k x k k k x k Where k and k the th received antenna and m (5) are the parameters of I/Q imbalance of m yˆ k represent the kth subcarrier of the mth OFDM symbol, where k { K,...,,,..., K}. We can observe the effect of I/Q imbalance of the received signal in Figures -6 []. he transmitted baseband signal is shown in Figure. he signal is up-converted to F and transmitted through the frequencyselective channel, resulting in the received F signal depicted in Figure 5. Subsequently, the received signal is downconverted, because there exhibits I/Q imbalance, the mirror signal is not fully rejected, and mixes down into the regarded baseband channel in Figure 6. In the presence of I/Q imbalance, the carrier of mirror signal will affect the carrier of signal. he more mismatches of gain and phase, the more serious performance degradation I/Q imbalance brings, and bit error rate (BE) will also raise. ISB 978-89-968650-0- 9 January 7 ~ 0, 0 ICAC0
Quadrature shown on Figure 8. he four parts includes preamble sequence, preamble sequence, preamble sequence, and preamble sequence. X Preamble Preamble Preamble Preamble Data X Preamble Preamble Preamble Preamble Data Figure 8. he structure of preamble design refered to IEEE 80.n -k k -k k Figure. X baseband -k Figure 6. X baseband k Figure 5. X F We also know the effect of I/Q imbalance on the received signal by the constellation for SISO OFDM systems. Using 6-quadrature amplitude modulation (6-QAM) with the mismatches parameters g=0% and ψ =5. he constellation with I/Q imbalance for SISO OFDM systems is shown in Figure 7. From Figure 7, it is shown that the 6 ideal red points become 6 dispersed points respectively. Assume 6 closed points are a group, and regard every group as a point, the 6 points are the result of the effect of the parameter k and channel. he mirror signal leads to the 6 closed points in a group, it means that the interference of I/Q imbalance may lead the point be removed from original decision region. hus, the wrong decision causes the wrong demodulation which will raise the BE..5 0.5 0-0.5-6QAM -.5 -.5 - -0.5 0 0.5.5 In-Phase Figure 7. he 6-QAM constellation with I/Q imbalance(g=0%,ψ=5 ) III. PEAMBLE DESIG AD ESIMAIO A. Preamble Design Structure for the ransmitter Consider the problem of jointly estimating the channel effect and I/Q imbalance, this paper proposes a preambleaided estimation method. eferring the standard of IEEE 80.n, there are four part in our novel preamble design In order to estimate channel effect and the parameters of I/Q imbalance, the preamble design needs to involve the orthogonal property between the real part preambles and image part preambles. herefore, the novel preamble design can assist the receiver to combat the image interference due to I/Q imbalance effect. Based on the requirement, the proposed novel preamble design structure, called full-usage preamble sequence design, is shown in Figure 9, which involves the conjugate symmetric preamble sequences and the different sign operation property to achieve the orthogonal feature. Besides, the Chu sequence [9] is utilized in the preamble sequence to assist the proposed estimator with more accuracy performance, i.e., X X j ( k ) q/ s, s e ( q, coprime) (6) s s s s s s Preamble Preamble Preamble Preamble s s s s s s s s s s Data Data Figure 9. he structure of full-usage preamble sequence design B. Joint Estimation of I/Q Imbalance and Channel Effect he overall schematic diagram of the proposed joint channel and I/Q imbalance parameter estimator is depicted in Figure 0 for MIMO OFDM systems. In the algorithm, we will first design the parameter estimator of SISO systems. hen, it can be extended to MIMO systems with more accuracy estimated performance. FF FF +k subcarriers Splitter -k subcarriers +k subcarriers Splitter -k subcarriers + Combine Combine + Combine Combine v v v () k v Combine Combine Combine Combine Preamble and z z () k Least Square Correlator and Preamble and z z Least Square Correlator and,, gˆ and ˆ,, gˆ and ˆ Figure 0. Black diagram of joint I/Q imbalance and channel effect estimation of full-usage preamble sequence disign ISB 978-89-968650-0- 0 January 7 ~ 0, 0 ICAC0
B.. s for SISO OFDM Systems Using (), the received signal in frequency domain without noise is where y ( ) ( ) s ( ) ( ) s ( ) (7) m k k k k k k k is given by 0 k 0 ( ) hen, using preamble shown in Figure 9, (7) can be rewritten as y ( k k ) s ( k k ) s ext, the upper half symbol of (9) is expressed by (8) (9) y { k k } s (0) For the bottom half symbol of (9), taking the complex conjugate at k frequency of it is given by y { k k } s () Similarly, by preamble, we have ()-() ( k k) s y () ( k k ) s y { k k } s () y { k k } s () eferring to the property of the imbalance parameters in (5)- (6) k k j k k ge (5) (6) ext, as shown in Figure 0, the first time-domain equal weight combiner technique of the two contiguous preambles in (0)-() and ()-() is utilized to cancel the image interference due to the orthogonal preamble structure design, i.e., v ( y y) k s (7) v ( y y) k s (8) Furthermore, in order to estimate the CI and imbalance parameters, the two parameters separation technique is proposed by the second frequency-domain equal weight combination and subtraction techniques of the two subcarriers symmetric preambles in (7) and (8), which is shown in Figure 0, i.e., z v v s (9) z v v z (0) ence, ˆ and ˆ can be acquired by the cross correlation and auto correlation schemes of (9) and (0), i.e., ˆ z z z (k) () ˆ ( k ) diag z ( k ) s ( k ) () ext, in order to enhance the estimation performance, the time-domain and frequency-domain weight combiner can be processed again for the image preambles, which is designed to cancel the real part preambles. ote that it is contrary to (7) and (8) algorithms. hat is, from (0)-() and ()-(), we can get the another parameter estimated result, i.e., v ( y y) k s () v ( y y) k s () z v v s (5) z v v s (6) ˆ z z z (7) ˆ ( k ) diag z ( k ) s ( k ) (8) In order to obtain more accurate estimations via the law of average, the imbalance and CI parameters are estimated as ˆ ( ˆ ˆ ) / (9) ˆ ( k ) diag ( k ), ( k ) (0) B.. s for MIMO OFDM Systems ext, the above proposed schemes can be extended to MIMO OFDM systems. Figure is shown the structure of channel between transmitter and receiver. X X (,) (,) (,) (,) X X Figure. he structure of channel for MIMO OFDM systems he channel can be written by where 0 0 (, ) (, ) (, ) () and are denoted by the th transmitted and th received antennas, respectively. As shown in Figure the 0, on the basis of the previous algorithms in (7)-() of SISO OFDM systems and preamble sequences - in Figure 9, ISB 978-89-968650-0- January 7 ~ 0, 0 ICAC0
MSE the time-frequency weight combined signal of the real part preambles of MIMO receiver can be derived by z s s () () (,) (,) z z () () () () z s s () () (,) (,) z z (5) () () () z ( s ) s (6) () (,) (,) z z (7) () () () z ( s ) s (8) () (,) (,) z z (9) () () () Moreover, as shown in Figure 0, the I/Q imbalance parameters can be estimated by the cross and auto correlation schemes, i.e., ˆ ˆ ( i) ( i) () i k z z () i z ( i) ( i) () i k z z () i z ( ), for i = and (0) ( ), for i = and () ext, in order to estimate CI, the combined signal in ()- (9) can be rewritten by matrix form, i.e., () (,) z s s () (,) z -s s () (,) z s s () (,) z -s s () () hus, the CI channel parameters can be estimated by preamble sequences via simple least square algorithm shown in Figure 0, which is only the scalar multiplication and division with low complexity benefit, i.e., s s (,) () ˆ -s s z (,) () ˆ () s s z s s (,) () ˆ -s s z (,) () ˆ (5) s s z Similarly, in order to enhance the estimation performance, referring the SISO algorithms in ()-(8), the another (,) imbalance and channel parameters, i.e., ˆ (,), ˆ, ˆ (,) (,), ˆ, ˆ, ˆ, ˆ and ˆ, can be () estimated by the image preambles of the time-frequency combiner scheme, which the derivations are omitted due to the same previous procedures. Moreover, by the law of average, () () () the MIMO imbalance parameters can be acquired with more accurate estimation result, i.e., ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ () () () () (6) () () () () (7) o sum of, based on the novel preamble structure design, a complete CI and I/Q imbalance parameters estimator is proposed for SISO and MIMO OFDM systems. In next section, its performance will be confirmed by computer simulations. IV. SIMULAIO ESULS In this section, simulation results are conducted to demonstrate the performance of the proposed estimation algorithms. For all simulations, there are 6 subcarriers for SISO OFDM and MIMO OFDM systems. here are preamble sequences and 6 OFDM symbols in a packet. he channel effect is ayleigh fading channel. he preamble sequences are the Chu sequence and the transmission data is 6-QAM symbols. Assume I/Q imbalance only happen at received side. We consider three different mismatch parameter pair of I/Q imbalance cases: () g= and ψ =0, () g=. and ψ =5, () g=. and ψ =0. When g= and ψ =0, there is no I/Q imbalance in the systems. 0 0 0-0 - 0-0 - 0-5 SISO, (g,)=(,0) SISO, (g,)=(.,5) SISO, (g,)=(.,0) MIMO, (g,)=(,0) MIMO, (g,)=(.,5) MIMO, (g,)=(.,0) 0-6 0 5 0 5 0 5 0 E b / 0 (db) Figure. MSE of I/Q imbalance parameters for SISO and MIMO OFDM systems In the first simulation, the MSE of I/Q imbalance parameters is evaluated as a function of E b / 0. Figure shows the MSE of I/Q imbalance parameters for both SISO OFDM and MIMO OFDM systems respectively. From Figure, it is shown that for all cases, the parameters of I/Q imbalance can be accurately estimated. It is noteworthy that the proposed MIMO estimation algorithm can provide better MSE performance than SISO estimator due to the more estimated parameters combination in (6)-(7). Besides, Figure performs MSE of the estimated channel for SISO OFDM and MIMO OFDM systems. Obviously, the ISB 978-89-968650-0- January 7 ~ 0, 0 ICAC0
MSE channel parameters can be accurately estimated as well. As expected, the proposed MIMO technique can achieve better performance than SISO systems. 0 0 0 SISO, (g,)=(,0) SISO, (g,)=(.,5) SISO, (g,)=(.,0) MIMO, (g,)=(,0) MIMO, (g,)=(.,5) MIMO, (g,)=(.,0) [8] Y.-. Chung and S.-M. Phoong, Joint estimation of I/Q imbalance andchannel response for MIMO OFDM system, in Proc. EUSIPCO, Sept.007. [9] D. C. Chu, Polyphase codes with good periodic correlation properties, IEEE rans. Inform. heory, vol. 8, no., pp. 5-5, July 97. 0-0 - 0-0 5 0 5 0 5 0 E / (db) b 0 Figure. MSE of estimated channel for SISO and MIMO OFDM systems V. COCLUSIOS In this paper, the estimation techniques of the I/Q imbalance and multipath channel effects of SISO and MIMO OFDM system are proposed over the wireless ayleigh fading channels. ote that a novel preamble structure design can provide the advantage of the low computational complexity to cancel the image interference and estimate the gain and phase parameters of I/Q imbalance and the channel impulse response (CI). Simulation results confirm the proposed MIMO method can accurately estimate the CI and I/Q imbalance parameters, and provide lower MSE performance than SISO methods over F impairment and channel effect environments. ACKOWLEDGME his work is sponsored by the ational Science Council,.O.C., under the Contract SC 0-0-E-55-006 and SC 0-85-C-55-00-E. EFEECES [] C.L. Liu, Impacts of I/Q imbalance on QPSK-OFDM-QAM detection, IEEE rans. Consumer Electron., vol., no., pp.98-989, Aug. 998. []. C. W. Schenk, F imperfections in high-rate wireless systems: impact and digital compensation, Springer Publisher, Feb. 008. [] Yuan-wui Chung and See-May Phoong, Joint estimation of I/Q imbalance, CFO andchannel response for MIMO OFDM systems, IEEE rans. Commun. Electron., vol. 58, no. 5, pp. 85-9, May00. [].C. W. Schenk, P.F.M. Smulders, and E.. Fledderus, Estimation and compensation of X and X IQ imbalance in OFDM base MIMO systems, in Proc. IEEE adio and Wireless Symposium, 006, pp. 5-8. [5] M. Windisch and G. Fettweis, Standard-independent I/Q imbalance compensation in OFDM direct-conversion receivers, in Proc. IEEE international OFDM Workshop, 00,pp. 57-6. [6] C. F. Chen, IQ Imbalance and Phase oise Compensation in MIMO- OFDM Systems, Univ of ational Chaio ung, MA, 0. [7] A. arighat,. Bagheri, and A.. Sayed, Compensation schemes and performance analysis of IQ imbalances in OFDM receivers, IEEE rans. SignalProcess., vol.5, no. 8, pp.57-68, Aug. 005. ISB 978-89-968650-0- January 7 ~ 0, 0 ICAC0