W2F.1

A Suppression Scheme of the ICI caused by PhaseNoise based on Partial Response Signaling in

OFDM SystemstKyung-Hwa Kim

Electrical EngineeringKorea Advanced Institute of Science and Technology

Daejeon, Korea 305-701Email: khwagcsplab.kaist.ac.krTelephone: +82-42-869-5440

Fax: +82-42-869-3410

Abstract- Phase noise destroys the orthogonality between sub-carriers in orthogonal frequency division multiplexing (OFDM)systems and creates intercarrier interference (ICI), which resultsin performance degradation. In this paper, partial responsesignaling (PRS) is used to reduce the effect of ICI caused byphase noise. The expression of ICI power with PRS is derivedand the optimum PRS coefficients that minimize the ICI powerare obtained. The simulation results show that the optimumPRS for OFDM systems obviously reduce the ICI power withoutdecreasing the bandwidth efficiency.

I. INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) is amulticarrier modulation technique that is widely used in manycommunication systems such as digital audio broadcasting(DAB) [1], digital video broadcasting (DVB) [2] and asym-metric digital subscriber line (ADSL) systems [3] as wellas IEEE 802.1 la [4], HIPERLAN/2 standards. In OFDMsystems, the entire bandwidth is divided into many orthogonalsubcarriers and information symbols are transmitted in parallelover these subcarriers by using computationally efficient FastFourier Transform (FFT) so that it can cope with the frequencyselective channels. One of the main drawbacks of OFDMsystems is its sensitivity to phase noise in the signal.

Phase noise destroys the orthogonality among subcarriersand introduces intercarrier interference (ICI), thereby its per-formance is considerably degraded. Phase noise effects inOFDM have been studied by several authors [5]-[1 1]. Thereare two effects of phase noise on OFDM systems: commonphase error (CPE) and intercarrier interference (ICI). SinceCPE causes subcarrier phase rotation, which is constant forall subcarriers, it can be corrected by pilot symbol estima-tion. On the contrary, ICI that introduces interferences to acertain symbol from all the other subcarriers of that symbolis impossible to reject completely in OFDM communication

t This research was supported in part by University IT Research Centerprogram of the government of Korea.

Hyung-Myung KimElectrical Engineering

Korea Advanced Institute of Science and TechnologyDaejeon, Korea 305-701

Email: hmkimgcsplab.kaist.ac.krTelephone: +82-42-869-3440

Fax: +82-42-869-3410

systems. To combat the ICI caused by phase noise, the ICI-self cancellation scheme was used [12]. Although this methodcan suppress the ICI significantly, it halves the bandwidthefficiency since it transmits each symbol over a pair ofadjacent subcarriers with a 1800 phase shift. Partial responsesignaling (PRS) used in conventional single carrier systemscan effectively reduces intersymbol interference caused bytiming errors in time domain without any sacrification of thebandwidth efficiency [13]. In the frequency domain, PRS withcorrelation polynomial F(D) = 1-D was used to mitigatethe ICI caused by carrier frequency offset in [14] and generalPRS was used to reduce the ICI caused by time variation ofwireless channel [15]. However, these previous scheme can'tbe directly used to suppress the ICI caused by phase noisesince the autocorrelation function of phase noise is needed tocompute the ICI power. In this paper, in order to suppress theICI caused by phase noise, the general PRS is considered andits optimual coefficients are obtained by solving the unit normconstrained optimization problem and it is shown that the ICIpower becomes less as the coefficient length increases.

The rest of the paper is organized as follows. In SectionII, two different types of phase noise model that are the basisfor the performance analysis and subsequent simulations aredescribed and PRS-OFDM system model with phase noiseis given in Section III. In Section IV, the ICI power withPRS is derived and the optimum weights of PRS are obtainedbased on the minimization of the ICI power and show theperformance improvement. In Section V, simulation resultsare presented and compared. Finally, the paper is concludedin Section VI.

II. PHASE NOISE MODEL

Phase noise 0(t) comes from the mismatch between thetransmitter and the receiver oscillators. There are two types ofphase noise model. The first type is obtained when the localoscillator (LO) is phase locked so that 0(t) is small. Phasenoise is modeled as a stationary Gaussian process with zero

0-7803-9282-5/05/$20.00 §2005 IEEE 253 ICICS 2005

mean and finite power. The power spectral density (PSD) ofphase noise is given in [11] as:

f 1-a, 0< fj < fL(f) = ls10 ( f) b fl< fj I < f2

l 1, f2 < j I < 2

(1)

where fi is the 3dB bandwidth of PSD and a gives aphase noise level near the center frequency up to +fi andc determines the noise floor. The power density decreases bylOb dB per decade of frequency for fi < fl < f2, f isthe sampling rate. Typical parameters are a 6.4, b = 4, c =10, fi 1kHz, f2 = 10kHz for European dTTb project [11]and a 8,b = 2, c = 12, fi = l0kHz, f2 = 100kHz fora real 5.2GHz frequency synthesizer [16]. The values of theparameters a and c and normalized bandwidth (3dB bandwidthof phase noise/subcarrier space) can be varied. When the PSDof phase noise is known, it's auto-correlation function (acf)can be easily obtained by Inverse Fourier Transform (IFFT)[12]. If 0(t) is sampled with period T5, its acf is

Ro(n, Tm) = E[O(nT,)O (mTsT)].Since 0(t) is so small, e(pT5) = eiO(PTO) can be approximatedas 1 + j(pT5) and the acf of e(pT5) is given through the acfof $(pT5) as follows

Re (p, q) = E[e(pTs)>* (qTs)= 1 + Ro(p, q). (2)

Because 0(pT5) is a stationary process, the acf of 0(pT5) is

Rqs(p,q) = R(p -q) J L(f)eJ2c7f(q-P)T8df= 2fl1O-a sinc(2irufl (q -p)Ts)

f2+1o-a ] -bcos2f(q-p)T5df

Da3ta ill . -|$-4 Mo0utatiron - SIP PRS IFFT P S. LPF

Channel

Data out -O Decoding P S. LPF

Fig. 1. PRS-OFDM Transmission.

J.(t1, t2) is a zero mean Gaussian randomvariance (x< for a given t1 and t2,

FC1C1( =E 1-j (T)I-(v)dTdvjt2 t2

2-iT7t1- t2.

For a zero-mean Gaussian random variable 1j2 tha the expectation of e is

E[e @]=-2

variable with

(6)

with variance

(7)Thus from (6) and (7), Re (p, q) can be represented as

Re(p, q) = exp(- r-yp -qT5). (8)

III. PRS-OFDM SYSTEMConsider a PRS-OFDM transmission over N subcarriers as

shown in Fig. 1. Let Xm be the transmitted symbol for themth subcarrier and c- for i = 0, , K-1 be the coefficientsof the PRS with unit norm (Z=01 c. = 1). Then the PRSOFDM-signal at the mth subcarrier is

K-1

Sm =ZCXm 0<m<N-1i=o

(9)

+ fst 10-C sinc(iruf5(q -p))-2f2 10-C sinc(2irf2(q- p)T). (3)

The other type of phase noise is obtained by assuming theLO is a frequency locked oscillator that is tuned to the carrierfrequency but is free running. In this case, phase noise ismodeled as a zero-mean, nonstationary, infinite-power Wienerprocess [5], [8], [17], i.e.,

t

¢)(t)= pj(T)dT

where ut(T) is a zero-mean white Gaussian frequency noisewith PSD 2rTy, where a is the 3 dB bandwidth of Lorentzianpower density spectrum of oscillator. The acf of samplede(pT5) is

Re(p, q) = E[e(pTs)e* (qTs)]where (1(tl, t2) is defined as

stl(1(tl t2) = 0(tl, (t2) = X H(T)dT.t2

(4)

(5)

where it is assumed that E( Xm 2) = 1 and E(XmX) = 0for m # 1. The transmitted OFDM signal in time domain is

N-1

s(t) = exp(j2-irft) E smp(t -mT5)m=o

(10)

where ft is the carrier frequency and p(t) is the impulseresponse of the low-pass filter (LPF) and s, is IFFT of SmWhen the received signal y(t) is assumed to be only affectedby phase noise 0(t), y(t) can be expressed as

N-1

y(t) = exp(j 4(t)) E skq(t- kT5) + n(t)k=O

(1 1)

where n(t) is AWGN and q(t) represents the combinedimpulse response of the channel, the transmitter and receiverfilter. When q(t) satisfies the Nyquist criterion for samplestaken at interval T5, y(t) can be sampled at the optimuminstant and its FFT is given by

Ym= N m<,Snexp(j(Ts))exp( (N e T+Wmk=O n=O

(12)

254

E[c-J'D(PT,,qT,)]

Let the ICI coefficient be

0p = {Z expC(kT)) exp ( -2ukP)k=O

and then the equation (12) can be represented as

Ym = SmOO+ Z Sn(9m-n + Wm,n74m

(13)

(14)

In (14), it is obvious that received signal is composed of adesired signal component and ICI term caused by phase noiseand the Fourier transform of AWGN.

IV. ICI SUPRESSIONIn the previous section, PRS-OFDM system with phase

noise was described. Here we derive the ICI power with PRSand find the optimum weights of PRS based on minimizingthe ICI power and analyze its performance.

A. The ICI Power with PRSThe total power of ICI is defined as

N-1 (5Pic,i EL Z SnOmn 2](15)

n=O,nyAm

If S0 is the desired signal, the ICI power can be rewritten as

Pici E Z SnOm j

F!N-1 K-1 2=E ( c-Xn-i)()-n]

Ln=1 i=ON-1

= E[|()-nl 2]n=lK-2 K-1-k N-1-k

+ 2,~3 ~ Cc1c1+kRe{E(08-n@)n+k)}i=0 k=i n=l

(16)From the equation (16), it can be observed that the ICI powercontains two parts: the first term is the inherent ICI power andthe second part is the ICI resulting from PRS. Therefore, theICI power can be reduced by minimizing the ICI term withPRS.

The second term in (16) is given byK-2 K-1-k N-1-k

PPRS= 2 X X c1c1+kRe{E(e8 -n* n+k)}i=0 k=l n=l

2K-2 K-1-k N-1-k 7-

N2 Z Z Z C1C1+k tal YN)i=0 k=l n=l

.Y,R (1)sin (N1=1

It can be represented in the matrix form as

PPRS = CTBKC

(17)

(18)

where

c = [CO :Cl, ,..~CK-1],T0 A1 A2A1 0 A1

BK= A2 A1 0

AK-1 AK-2 AK-3

Ak =I

tan 7rk) RTSkl1

R = [Re(0),Re(1),. .. , Re(N -

1=[1, 1, *,, 1].

AK-1AK-2AK-3

0-i

1)]T1

Sk is a diagonal matrix with its diagonal element as[N-1-k sil 27(n+k)(0) ,yN-1-k sn2k(n+k)(1) ...[/dnfl 1 i N'/- n=1 silln N

n= -k sil 2TF(n+$)(f)N ] and Re(l) is already obtained by(2) and (8).The minimum ICI power can be obtained by solving the

unit norm constrained optimization problem,

PPRS =miin cBKCc

s.t. IlCel2 = 1. (19)

It is easy to see that the eigenvector corresponding to theminimum eigenvalue A(K) of tha matrix BK beocmes theoptimal coefficient vector and the minimum value of the cost,PPRS, is A%$ . Therefore, the minimum ICI power becomes

N-1

Pmi = E E[l(- 12] +A>(K)in NAnn=l

(20)

B. Reduction of the ICI PowerTo show that the ICI power decreases as the K increases,

the symmetric toeplitz matrix BK is first partitioned as

BK bT

where Q is a (K -1) x (K -1) symmetric toeplitz matrixobtained from BK by deleting the last row and column witheigenvalues A(K-1) <ASK-1). <A%K-1) and b is a vec-tor given as [AK1, AK- 2, , Al]. Letx = [X1, X2,... , XKIis a eigenvector of BK associated with eigenvalues A(K) <

ASK) < < A%) and A(K) 7& A\ 1) for i- 1, K.Then

( Q-AV T

b) X = O (21)

By eliminating the variables x1, x2,... , XK-1 from (21), wehave

(A + bT(Q- Al)-b)XK = 0.Hence the eigenvalues of BK are roots of the followingequation

(22)A TQf(A)=A + bT(Q- Al)-b = 0

which is equivalent toK-1

f(A) A 1K EKlZ A(K-1)- A.

0. (23)

255

Cmparsion oftihe IC! por

+- OFDM withouPuSe OFDM with PFS K=3

* ... OFDM with PRS K-3o,,,,,, -,4, ,,,,,, O,,,,,,,,M,,,,w,,iat[h,,,P,,R,,S,,,,K,,-,,6,

-35

-38r

44

Comparsion f theiCpower

I+- OFDM withouPuSIIIOFDI IM witPFIS:

- OFDM with PRS K-3o'-- OFDM wit[hPRSK-6

-46

4

451

-54

555 5.5 6 a

Parametea10 10 5 11.5 12

Paamew125 13 I35 14

Fig. 2. ICI power versus parameter a of the acf, (eq.(2)) when the LO isphase locked.

Fig. 3. ICI power versus parameter c of the acf, (eq.(2)) when the LO isphase locked.

The ration function in (23) has K -1 poles that divide the realaxis into (_ 00, A(K-1)) (A(K-1) >(K-1)) (A(K- 1)Since f(A) is continuous and monotonically decreasing ineach interval, f (A) = 0 has unique solution in each Kinterval. Therefore, eigenvalues >(K 1) strictly interlace the

(K).eigenvalues A> , i.e.,

A(K) < A(K-1) < A(K) < A(K 1) < < A(K-1) < (K)

(24)This is known as the Cauchy's interlacing theorem [18]. Sincethe minimum eigenvalue, >(K) < A(2) A1, < 0, themiminum ICI power in (20) can be decrease as K increasesand the proposed scheme has better performance than that ofPRS-OFDM with K = 2 [14].

V. SIMULATION RESULTS

In this section, computer simulation results are presentedto illustrate the performance improvement of PRS-OFDMsystem. In order to compare the ICI power with and withoutPRS, it is assuemd that the total system bandwidth (5MHz) bedivided into 512 subcarriers. The acf of phase noise neededto compute the ICI power is given by (2) and (8). The valueof the parameter a, c and normalized 3dB bandwidth of theacf will be varied since they depend on the tuner technologyemployed.

Fig. 2 shows ICI power versus parameter a for the acf ofphase noise when the system is phase locked. Normalizedbandwidth is equal to 0.01 and c = 12 is chosen in (2).From the figure, the ICI power decreases as the value ofthe parameter a increases since the phase noise level of PSDdecreases. PRS has better performance as K increases and6-tap is enough to reduce the ICI power. There is about 5dB improvement for 3-tap PRS and about 7 dB or more

improvement for 6-tap PRS.

Coparision of the IC power

-34.

.36

1-

0 40-42

-44

-46

-48 *0G

-A=, .YeI*

OFDM wtho PRSOFDM wth PRS K 2OFDM wth PRS K-3OFDM wth PRS K-6

)02 0.03 O04 0.05N rmlze 3dBbandwidth

007

Fig. 4. ICI power versus normalized bandwidth of the acf, (eq. (2)) whenthe LO is phase locked.

Fig. 3 and Fig. 4 show the power of ICI for differentparameters c and normalized frequency offset, respectively. InFig. 3, although the OFDM with PRS has some performanceloss at the high noise floor, at least 3 dB gain is achieved byusing 6-tap PRS. According to [17], if the total degradation(at BER=10-4) <15 dB is accepted, the limit is normalizedbandwidth <0.01 for 16-QAM and normalized bandwidth<0.06 for QPSK. For 0.01 < normalized bandwidth < 0.07,the ICI power is reduced by about 5 dB for 3-tap PRS andabout 10 dB for 6-tap PRS, respectively, as shown in Fig. 4.

In the case of phase noise with Wiener distribution, theoptimum PRS also can reduce the ICI as shown in Fig. 5. Itcould be observed that the reduction of the ICI power is atleast 3 dB for 3-tap PRS.

256

040

Cmparsion oftihe IC! por

-13 -.a

C5 -1410 41

CL il SI~16OFDMwthout S

-117 e ,0. w 1tiF:tDMWthPRIMSK28 Mti = L OFOM wth PRS K

=190 01 O0 0.03 0,04 0 O 06 007

Normalize3 Bbandwidwth

Fig. 5. ICI power versus normalized bandwidth of acf, (eq. (8)) when theLO is frequency locked.

VI. CONCLUSIONSPhase noise introduces the ICI that is the main reason of

the performance degradation in the OFDM systems. In thispaper, partial response signaling is considered to suppress theICI caused by phase noise without decreasing the bandwidthefficiency. The general expression of the ICI power for PRS-OFDM was derived and optimum weights for PRS that min-imizes the power of ICI are obtained. The proposed schemeworks well for both stationary phase noise model and Wienerphase noise model. From the simulation results, it has beenfound that the ICI caused due to phase noise was suppressedby the partial response signaling and PRS-OFDM exhibits thebetter performance with the larger coefficient length.

REFERENCES

[1] ETSI, "Radio broadcasting system: Digital audio broadcasting DAB tomobile, portable and fied receduers," Tech. Rep. ETS 300 401, Aug.1997.

[2] , "Digital video broadcasing DVB: Farming structure, channelcoding and modulation for digital terrestrial television," Tech. Rep. EN300 744, Aug. 1997.

[3] K. Sistanizadeh, P. S. Chow, and J. M. Cioffi, "Multi-tone transmissionfor asymmetric digital sybscriber lines ADSL," in in Proc. IEEE ICC93.,1993, pp. 756-760.

[4] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY)Specifcation, IEEE Std. 802.1 la, 1997.

[5] T. Pollet, M. V. Bladel, and M. Moeneclaey, "BER sensity of OFDMsystems to carrier frequency offset and wiener phase noise," IEEE Trans.Commun., vol. 43, pp. 191-193, 1995.

[6] A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacingeffects on the performance of an OFDM communication system," IEEECommun. Lett., vol. 2, pp. 11-13, Jan. 1998.

[7] A. G. Armada, "Understanding the effects of phase noise in orthogo-nal frequency division multiplexing OFDM," IEEE Trans. Broadcast.,vol. 47, pp. 153-159, June 2001.

[8] L. Tomba, "On the effect of wiener phase noise in OFDM systems,"IEEE Trans. Commun., vol. 46, pp. 580-583, May 1989.

[9] M. S. El-Tanany, Y Wu, and L. Hazy, "Analytical modeling andsimulation of phase noise interference in OFDM-based digital televisionterrestrial broadcasting systems," IEEE Trans. Broadcast., vol. 47, pp.20-31, Mar. 2001.

S. Wu and Y Bar-Ness, "Performance analysis on the effect of phasenose in OFDM systems," in in Proc. Int. Symp. Spread-SpectrumTecjmoqies, Applications, Prague,Czech Repulbic, Sept. 2002, pp. 133-138.P. Robertson and S.Kaiser, "Analysis of the effects of phase noise inorthgonal frequency division multiplixing OFDM," in in Proc. Int. ConfCp,imocatopms, Seattle, WA, 1995, pp. 1652-1657.Z. Jianhua and H. Rohling, "Analysis of ICI cancellation scheme inOFDM systems with phase noise," IEEE Trans. Broadcast., vol. 50, pp.97-106, June 2004.J. G. Proakis, Digital communicatios, 3rd ed. New York, McGraw-Hill:Y Zhao, J. D. Leclereq and S. G., Eds., 1995.Y Zhao, J.-D. Leclercq, and S.-G. Haggman, "Intercarrier interferencecompression in OFDM communication systems by using correlatviecoding," IEEE Commun. Lett., vol. 2, pp. 214-216, Aug. 1998.H. Zhang and Y G. Li, "Optimum frequency-domain partial responseencoding in OFDM system," IEEE Trans. Commun., vol. 51, pp. 1064-1068, July 2004.A. Plattner, "Cellular atm network-transceiver specificaion," DASA, RS,0.3ed.,ser. internal document, Jan. 1998.E. Costa and S. Pupolin, "M-QAM-OFDM system performance inthe presence of a nonlinear amplifier and phase noise," IEEE Trans.Commun., vol. 50, pp. 462-472, Mar. 2002.

[18] B. N. Parllet, The Symmetric Eigenvalue Problem. Philadelphia: Societyfor Industrial and Applied Mathematics, 1993.

257