IN PHASE/ QUADRATURE IMBALANCE AND EFFECT OF TIMING JITTER ON ICI IN ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

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1 I PHASE/ QUADRAURE IMBALACE AD EFFEC OF IMIG JIER O ICI I ORHOGOAL FREQUECY DIVISIO MULIPLEXIG Gurram Swathi Madhuri 1 (PG Scholar) G.Swetha 2 (M.tech) Prakash J.Patil 3 ( M.tech ) 1 Department of ECE, Vijay Rural Engineering College, JU (H) 2 Associate Professor, Department of ECE, Vijay Rural Engineering College, JU (H) 3 Head of the Department, Department of ECE, Vijay Rural Engineering College, JU (H) ABSRAC In the high data rate orthogonal frequency division multiplexing (OFDM) systems has the problem of intercarrier interference (ICI) due to iming jitter and I/Q imbalance, this will lead the system performance as high bit error rate. We propose a new algorithm to analyze the interaction between timing jitter and I/Q balance which leads the extra ICI terms in their interaction. he analysis indicates that intercarrier interference (ICI) has equal real and imaginary components and is independent of received subcarrier index. Furthermore it is shown that the parameters values influence the intercarrier interference (ICI) from the relative contribution on timing jitter and I/Q imbalance, timing jitter taking over for larger jitter values and I/Q imbalance dominating when timing jitter is relatively small. he interaction is negligible for extra ICI in all cases. he experimental results best matches with the analytical value. Key words: - OFDM, ICI(Inter carrier interference), iming jitter, I/Q imbalance I. IRODUCIO A widely held technique for transmission of signals over wireless channels is Orthogonal Frequency Division Multiplexing (OFDM). In a several wireless standards such as digital video broadcasting (DVB-), digital audio broadcasting (DAB), the IEEE a [1] local area networks (LA) standard and the IEEE a [2] has been using OFDM scheme. In the optical fiber systems data rates are extremely high, for example the transmission of Gbits/s within an optical bandwidth of 22.8GHz has been shown up [3]. For the very high data rates, the OFDM systems demand high speed digital to analog converters (DACs) and analog to digital converters (ADCs) using precise sampling clocks. However the signal edges of the Practical sampling clocks deviate from the ideal position and these deviations are stated as timing jitter. he performance of the OFDM system is limited by timing jitter this has been analyzed in recent times [4-7]. he timing jitter causes noticeable performance degradation in high frequency band pass sampling receivers and mitigation techniques are proposed in [4]. In [5], an upper bound for the interference caused by timing jitter is derived and the effects of integer oversampling are studied. In [6], a more extensive analysis of timing jitter is presented including the effect of both white and colored timing jitter. In [6], we introduced a timing jitter matrix to describe the rotational and intercarrier interference (ICI) effect of timing jitter in OFDM systems and in [7] we applied this matrix to show that both fractional oversampling and integer oversampling can be used to reduce the ICI power due to timing jitter.

2 By using DACs, the real and imaginary parts of the digital baseband signal x are converted to analog baseband signals given by x (t) = Re X j2πtk exp (2) Fig 1. Simplified OFDM block diagram. x (t) = Im X j2πtk exp (3) I/Q imbalance occurs when a front-end component doesn t respect the power balance or the orthogonality between the I and Q branch [9]. While being able to easily cope with the frequency selective nature of a multi-path propagation channel, multi-carrier systems are very sensitive to I/Q imbalance [10]. In order to cope with these impairments, numerous approaches for a digital compensation of the I/Q imbalance have been proposed in the literature, see for example [11]. In this paper organized as section II describes the system model, Section III presents an analysis of the ICI power caused by the combined effect of timing jitter and I/Q imbalance. Simulations are presented in Section IV. Conclusions are drawn in Section V. I. SYSEM MODEL As shown in the figure.1,consider a OFDM system consist of subcarriers and the OFDM symbol period,not including cyclic prefix (CP), is. At the transmitter, in each symbol period complex values representing the constellation points are used to modulate subcarriers. he data to be transmitted in each OFDM symbol period is represented by complex vector X of length. In most OFDM systems the band-edge subcarriers are not used, so some of the elements of X are zero. he complex time domain samples at the output of the transmitter inverse fast Fourier transform (IFF) are given by / x = 1 X j2πnk exp. (1) where x (t) and x (t) denote the real and imaginary parts of analog baseband signal and Re { } and Im { } are the real and imaginary parts of the argument. x (t) and x (t)are subsequently combined by an I/Q mixer, which we assume to be ideal, to give the passband transmitted signal x (t) = x (t) cos(2πf t) x (t) sin(2πf t) = Re{x(t)exp (j2πf t)}, (4) Where f is the RF or optical carrier frequency, and x(t) = x (t) + j. x (t). At the receiver, the receiver signal is y (t) = x (t)h (t) + η (t), (5) where η (t) is bandpass AWG and h (t) is bandpass channel impulse response. ote that y (t), x (t), h (t), η (t) are all real, while all the baseband signals such as X, x, Y, y, x,, x,, y, and y,, baseband channel impulse response, h(t), and baseband AWG, η(t), are all complex. In the case of perfect matching between the I and Q branches, the quadrature demodulation and low-pass filtering of the received signal y (t) result in baseband I and Q components y (t) and y (t) given by y (t) = LPFcos(2πf t). y (t) (6)

3 y (t) = Re{x(t)h(t) + η(t) y (t) = LPF sin(2πf t). y (t) (7) y (t) = Im{x(t)h(t) + η(t) where LPF{ } represents the low-pass filtering. he quadrature down-converted signals are sampled by I and Q branch ADCs and these each introduce timing jitter [12]. We assume the timing jitter in the I branch is the same as timing jitter in the Q branch. he signal samples after the two ADCs are given by y, (t) = Re H j2πtk X exp + τ y (t) + η (8) 1 + ε 2 cos(2πf t + θ/2) -1 cos(2πf t + θ/2) Fig. 2. Block diagram of quadrature down-converter with I/Q amplitude and phase imbalance. y, (t) = Im H X + η (9) j2πtk exp + τ where τ is the discrete timing jitter and H is the discrete frequency domain channel response of the kth subcarrier. he resulting complex samples at the input to the FF are y = y, + j. y,. (10) In any practical system, perfect matching between I and Q branches is not possible due to limited accuracy in the implementation of the RF or optical front-end. In this paper, we consider only the I/Q imbalance at the receiver side. I/Q imbalance can be modeled as either symmetrical or asymmetrical. Both models are equivalent representations [15]. We will use the symmetrical model in this paper. In the symmetrical model [14], each arm experiences half of the phase and amplitude imbalance as shown in Fig. 2. Assume that there is a phase imbalance of θ degrees and an amplitude imbalance of δ db and that θ and δ are frequency independent. In this case, the FF output is given by [16] / Y = 1 y exp j2πnl / + β 1 y exp j2πnl (11) With α = cos(θ/2) + j(ε/2) sin(θ/2) (12) β = (ε/2)cos(θ/2) j sin(θ/2) (13) Where the superscript * denotes the complex conjugate and = 10 1 / III.IMIG JIER AALYICAL AD I/Q IMBALACE AALYSIS In this section, it is indicated that the noise as ICI components are added due to timing jitter in the received signal. We originate the ICI power caused by I/Q imbalance and timing jitter. Altering (11) into the compact matrix form Y = αwhx + βwh X m +, (14)

4 where W = X m Y = Y Y Y, = X X X w w,,, w, w, =, he elements of X m are the complex conjugate of the transmitted signal s mirror image. he elements of W are given by w, = 1 / exp 2πk n + τ exp j2πnl. (15) Both I/Q imbalance and timing jitter cause added noise like components in the received signal. From (14) Y = αhx + α(w I)HXβ + WH X m + (16) imbalance ICI due to both timing jitter and I/Q Substituting (12) into the first component of the right hand side of (16), we obtain Y = cos θ 2 HX + j ε 2 sin θ HX + α(w I)HX 2 + β(w I m )H X m + βh X + (17) Where I m is the mirror image of I. We are pondering a unity gain flat channel so H = 1. In order to recover the transmitted signal, both sides of (16) are scaled by cos to give Y cos θ = X + j ε 2 2 tan θ X + α 2 cos θ (W I)X 2 + β cos θ (W I m )X m + 2 cos θ, 2 (18) Where X is a wanted component From (15) and (17), we obtain Y cos (θ/2) = X jtan θ 2 X l + ε 2 X l + j ε 2 tan θ 2 X + w, I, X + j ε 2 tan θ 2 + ε 2 w, I, X l jtan θ 2 w, I, X l + l cos( θ 2 ) (19) In the right hand side of (19), all the components except the X component are noise and ICI components related to various impairments. here impairments come as timing jitter, I/Q imbalance and AWG. At the rear of, we look into the consequences of the both I/Q imbalance and timing jitter in a noiseless channel. Due to I/Q imbalance and timing jitter are independent of the subcarrier index, the average ICI power is the same as the average ICI power for each subcarrier. First, consider the contribution to ICI set off by the interaction between I/Q imbalance and jitter. his is given by the 6 th, 7 th and 8 th components of the right hand side of (19). he ICI power due to these is P = E j tan w, I, X + E w, I, X k + E jtan w, I, X k. (20) We take up the timing jitter is white, i.e, the correlation between different timing jitter samples is zero. By using the

5 method in [5], which applies a aylor series expansion, (20) can be simplified to give P = tan + + tan. (21) hus from (19) and (21) the ratio of the total ICI power (taking in all componets) to signal power ratio is given by γ = P σ 1 + ε 2 tan θ 2 + ε 2 + tan θ π σ + tan θ 2 + ε 2 + ε 2 tan θ, (22) 2 Where σ = σ / is the normalized standard deviation(sd) of the timing jitter. For σ < 0.01 the ICI depends strongly on th amplitude imbalance, but as timing jitter increases the effect o timing jitter dominates. he simulation results agree with analytical results given in (22). Fig. 5 shows the average ICI to signal power ratio against the timing jitter with both phase and amplitude imbalance. When θ = 1 and δ = 0.1 db, there is very little increase in ICI power compared with the plot without I/Q imbalance. However even when θ = 12 and δ = 1.5 db, and for σ > 0.15, the ICI power increase is not significant compared with the plot without I/Q imbalance. his indicates that timing jitter introduces more ICI power than I/Q imbalance. -15 performance Analysis at Del=0-20 IV. EXPERIMEAL RESULS In this section, the simulation results shows that the impairments caused by IQ imbalance and timing jitter are examination,to conform the derived analytical results. We employ a system with the subcarriers of =512, a flat channel and 2000 OFDM symbols. he ICI is camputed based on the extending of constallation points [17]. We observe the combined outcome of timing jitter an - - g a m m ( d b ) tet Fig..γ versus the phase imbalance with σ sig=0 sig=0.01 sig=0.03 sig=0.06 sig=0.1 IQ imbalance. he I/Q imbalance and timing jitter values a extremely system dependent [17]. Fig. 3 exposes the influenc -5 on the ICI to signal power ratio, γ, of varying phase imbalanc and timing jitter when there is no amplitude imbalance. Fig. shows the analytical and simulation results for changin amplitude imbalance and timing jitter when there is no phas imbalance,at the same time Fig. 5 gives results for a range o combinations of amplitude and timing jitter pha imbalance.fig. 3 (no amplitude imbalance) shows that fo σ < 0.01, the ICI hangs on strongly on te phase imbalance, b that as timing jitter levels increase,the effect of the timin jitter dominates and increasing the phase imbalance has only small effect. Fig. 4 (no phase imbalance) shows a similar effec - - g a m m ( d b ) del=0 theta=0 del=0.1 theta=1 del=0.3 theta=4 del=0.9 theta=8 del=1.5 theta= ormalized sigma Fig. γ. versus timing jitter with I/Q imbalance

6 121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz --g a m m (d b ) Delta (db) Fig. 4. γ versus the amplitude imbalance with σ sig=0 sig=0.01 sig=0.03 sig=0.06 sig=0.1 spectral efficiency over 1000 km of SSMF, J. Lightw. echnol., vol. 27, pp , [4] V. Syrjala and M. Valkama, Jitter mitigation in highfrequency bandpass-sampling OFDM radios, in Proc WCC, pp [5] K.. Manoj and G. hiagarajan, he effect of sampling jitter in OFDM systems, in Proc IEEE ICC, vol. 3, pp [6] U. Onunkwo, Y. Li, and A. Swami, Effect of timing jitter on OFDMbased UWB systems, IEEE J. Sel. Areas Commun., vol. 24, pp , [7] L. Yang, P. Fitzpatrick, and J. Armstrong, he effect of COCLUSIO In this paper, we showed that the impact and influence of the timing jitter and IQ imbalance in the high data rate OFDM systems. he results say that due to the IQ imbalance and the timing jitter introduces the presents the extra ICI at the receiver and this can produce a critical degradation ion the OFDM system. Due to the phase and amplitude imbalance in the OFDM system cause ICI besides timing jitter jointly produce the ICI in the system. he parameter values (θ, σ, δ) of system influence on the ICI from the relative contribution of the timing jitter and IQ imbalance, for the relative larger values of timing jitter domination and IQ imbalance dominating when timing jitter is relatively small. [REFERECES] [1] Part 11: Wireless LA Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5 GHz Band, IEEE Standard a [2] Local and Metropolitan Area etworks Part 16, Air Interface for Fixed Broadband Wireless Access Systems, IEEE Standard IEEE a. [3] S. L. Jansen, I. Morita,. C. W. Schenk, and H. anaka, timing jitter on high-speed OFDM systems, in Proc AusCW, pp [8] L. Yang and J. Armstrong, Oversampling to reduce the effect of timing jitter on high speed OFDM systems, IEEE Commun. Lett., vol. 14, pp , [9]. Jan ubbax, Boris Cˆome, Liesbet Van der Perre, Luc Deneire, St ephane Donnay, Marc Engels_IMEC - Kapeldreef 75, 3001 Heverlee, Belgium Compensation of IQ imbalance in OFDM systems /03/$ IEEE. [10]. Marcus Windisch, Gerhard Fettweis Dresden University of echnology, Vodafone Chair Mobile Communications Systems, D Dresden, Germany On the Impact of I/Q Imbalance in Multi-Carrier Systems for Different Channel Scenarios. [11]. M. Windisch and G. Fettweis, Standard-Independent I/Q Imbalance Compensation in OFDM Direct-Conversion Receivers, in Proc. 9th Intl. OFDM Workshop (InOWo 04), (Dresden, Germany), Sept [13] M. Shinagawa, Y. Akazawa, and. Wakimoto, Jitter analysis of highspeed sampling systems, IEEE J. Solid- State Circuits, vol. 25, pp , [14] J. ubbax, B. Come, L. Van der Perre, S. Donnay, M. Moonen, and H. De Man, Compensation of transmitter IQ

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