Hindawi Publishing CorporationJournal of Computer Systems, Networks, and CommunicationsVolume 2008, Article ID 895158, 7 pagesdoi:10.1155/2008/895158
Research ArticleOFDM Synchronization Errors and Effects ofPhase Noise on WLAN Transceivers
Mourad Melliti, Salem Hasnaoui, and Ridha Bouallegue
Systeme de Communications Sys’Com Laboratoire, Ecole Nationale d’Ingenieurs de Tunis, 1002 Tunis, Tunisia
Correspondence should be addressed to Mourad Melliti, [email protected]
Received 29 January 2008; Revised 22 May 2008; Accepted 28 December 2008
Recommended by Jie Li
This work aims at frequency synchronization in OFDM IEEE 802.11g Transceivers. The degradation of performance results fromthe detrimental effects introduced by frequency offset and phase noise. First, we present a robust method to detect and synchronizethe OFDM signal with severe noise and interference corruption based on calculating the accumulated phase difference for eachsubcarrier. Then, we present a simple architecture to implement the proposed methods. These methods are simulated and analyzedby computer. Finally, we propose many algorithms to correct the common phase error (CPE) of the phase noise and track well itsvariation.
Orthogonal frequency division multiplexing (OFDM) hasbeen gaining popularity in a variety of digital communi-cation systems, such as wireless LAN 802.11a and 802.11g.The imperfect synchronization between the tuner’s localoscillation in transmitter and in receiver brings not onlyfrequency offset but also phase noise. Many algorithms havebeen put forward for estimating and correcting commonphase error (CPE). This paper proposes a novel adaptivealgorithm for correcting CPE. The simulation results showthat the algorithm is of good performance in CPE estimation.
After a brief introduction to OFDM systems in Section 2,this paper will be concerned in defining the general problemof improper frequency synchronization. In Sections 3 and4, we will explain why frequency offsets have detrimentaleffects on the received signal’s spectrum. We will quantify theoffset with respect to the carrier frequency spacing and willconsider the two cases where the offset is either an integermultiple of the carrier spacing or not. Depending on thiscondition, we will see how the orthogonality among thecarriers may be destroyed. We will then turn to study theeffects of phase noise. We will characterize phase noise bydescribing the 2 types of phase error that it induces, namely,common phase error (CPE) and intercarrier interference
(ICI). The description will fully explain the modificationinduced by each type on the received signal’s spectrum. InSection 7, we will briefly discuss the common approaches toremove the effects of CPE.
2. OFDM SYSTEMS
The main reasons OFDM was adopted in the wireless localarea network (WLAN) standards IEEE 802.11a [1] and g[2] are its high spectral efficiency and ability to deal withfrequency-selective fading and narrowband interference.However, the main disadvantage that might result is theinduced intersymbol interference (ISI). OFDM addresses thisproblem within the more general framework of multicarriermodulation. The bit-stream is divided into substreams thatare each sent with a lower data rate on an individualsubchannel.
As in all digital communication systems, OFDM requiresproper synchronization between the transmitter and thereceiver. Both time and frequency synchronization influencethe performance of OFDM systems. The subdivision of theinitial symbol into N parallel symbols results in a longersymbol duration. This will cause the system to be lesssensitive to timing offsets. However, frequency offsets mayheavily degrade the system’s performance [1].
2 Journal of Computer Systems, Networks, and Communications
3. IMPLEMENTATION OF QAM TRANSCEIVER
By implementing a QAM-based transceiver, the OFDMsignal is formed by first converting the frequency samplesinto time samples through the use of the inverse Fouriertransform represented before by the IFFT [3].
The output time samples take the following form:
Sn = 1√N
N−1∑
k=0
Skej2πnk/N , n = 0, 1, . . . ,N − 1. (1)
These generated parallel time samples are then convertedto a serial stream through a parallel-to-serial converter.The last step required before transmitting the stream overthe channel is to add a cyclic prefix code. Indeed, one ofthe major properties of the continuous Fourier transformis the duality between convolution in time domain andmultiplication in frequency domain. This property doesnot completely extend to the discrete case. For it to becorrectly applied, one should carry circular convolutioninstead of the more common linear convolution in thetime domain. To this end, we assume that the discretechannel impulse response has length k. Adding the cyclicprefix corresponds to appending the last k symbols of eachblock [s0, s1 · · · sN ] to the beginning of the same block. Weget the following block: [sN−k, sN−k−1 · · · s0, s1 · · · sN ]. Thisoperation preserves the desired property of multiplicationin the frequency domain. The resulting sequence is passedthrough a digital-to-analog converter and then up convertedto a higher carrier frequency. The signal is then sent throughthe channel.
On the receiver end, noise introduced by the channel willbe superimposed on the received signal. The signal is firstdown converted to base-band and then passed through alowpass filter to remove the effects of high-frequency terms.The time samples are retrieved by passing the resulting signalthrough an analog-to-digital converter. The cyclic prefix isfirst removed from each stream and then the stream isconverted to a parallel stream through a serial-to-parallelconverter. The DFT is then performed to recover the originalcoefficients. These are then converted to a serial stream toform the symbol that was originally sent.
As can be clearly seen from Figure 1, the required overallbandwidth of an OFDM system is equal to NB/2. In thissense, OFDM systems make better use of the available systembandwidth.
4. FREQUENCY SYNCHRONIZATION
As in all digital communication modems, OFDM requiresproper synchronization between the transmitter and thereceiver. Both time and frequency synchronizations influencethe performance of OFDM systems. The subdivision of theinitial symbol into N parallel symbols results in a longersymbol duration. This will cause the system to be lesssensitive to timing offsets. However, frequency offsets mayheavily degrade the system’s performance. To see this, wefirst derive the spectrum of an OFDM symbol from itstime domain representation. The time domain version of the
fn−1 fn fn+1 f
A( f )
(a)
fn−1 + δ f fn + δ f fn+1 + δ f f
A( f )
(b)
Figure 1: Effects of frequency shift on OFDM spectrum.
symbol is the one transmitted over the channel. We representthe transmitted OFDM symbol as follows:
S(t) =N−1∑
k=0
Skej2π( f0+kΔ f )trect
(t
NTs
), (2)
Sk denotes the complex amplitude of the kth carrier, Δ f is thecarrier spacing, and f0 is the frequency of the 0th carrier. Themultiplication by the window function is due to the fact thateach OFDM symbol is time limited to a duration Ts.
We then compute the Fourier transform of the aforemen-tioned time signal to get
S( f ) =N−1∑
k=0
Sk sin c(NTs f
)∗δ( f − ( f0 + kΔ f)). (3)
Now, we note that the total bandwidth is equal to NΔ f
and so the symbol time Ts is equal to 1/NΔ f . Replacing NTsby 1/Δ f , we get
S( f ) =N−1∑
k=0
Sk sin c
(f − ( f0 + kΔ f
)
Δ f
). (4)
It might happen that on the demodulator’s side, thecarriers get shifted by an amount δ f . The spacing between thecarriers is still equal to Δ f . This can be seen from Figure 2.
In this case, we have 3 subcarriers and the symbols on the3 different curves correspond to the different contributionsof each of the subcarriers to the sum of the sampling points.
Mourad Melliti et al. 3
0 10 20 30 40 50 60 70
Index
0
0.5
1
1.5
Mag
(F1)
Symbol to be transmitted (magnitude spectrum)
(a)
0 10 20 30 40 50 60 70
Index
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
Rea
l(T
1)
I-channel signal (after IFFT)
(b)
0 10 20 30 40 50 60 70
Index
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
Rea
l(RT
1)
Demodulated I-channel signal
(c)
0 10 20 30 40 50 60 70
Index
0
0.5
1
1.5
Mag
(F1)
Recovered symbol contains ICI
(d)
Figure 2: ICI effects on OFDM signal.
In Figure 1, the configuration is optimal since no offset ispresent between the receiver and the transmitter. However, inFigure 2, an offset of δ f is introduced and causes the differentsubcarriers to interfere.
The amount of shift might either be an integer multipleof the subcarrier spacing Δ f , in which case, the configurationwould be similar to Figure 1. However, the received datasymbols are now in the wrong position and so this willinduce a bit-error rate of 0.5 [1]. However, the orthogonalityamong the subcarriers is still maintained. Indeed, thespectrum would now become
S( f ) =N−1∑
k=0
Sk sin c
(f + CΔ f −
(f0 + kΔ f
)
Δ f
), (5)
where C is an integer constant.The shift does not affect the location of the points of
intersection of the different sin c waveforms that constitutethe spectrum of the OFDM symbol. Orthogonality is thuspreserved. If the shift is not an integer multiple of thecarrier spacing, then we end up with interference among thedifferent subcarriers. This interference may be quantified inthe following way:
Il =N−1∑
k=0, k /= 1
Sk sin c
(δ f + (l − k)Δ f
Δ f
). (6)
It represents the amount of contribution other carriershave on the waveform associated with carrier l. So, Il isobtained by evaluating S( f ) at the frequency of interest,namely, the one associated with subcarrier l. Note that if theshift is zero or an integer multiple of the carrier-spacing,the aforementioned interference term would evaluate tozero. A nonzero value for Il can be interpreted as a lossof orthogonality of the basis functions because this wouldsuggest that the projection of the waveform associated withcarrier l has nonzero components in the direction of thewaveforms associated with the other carriers. In this sense,ICI is also referred to as the effect of loss of orthogonality. Wewill see this effect more in details in Section 5 in the contextof phase noise.
5. EFFECTS OF PHASE NOISE
Signals are usually transmitted in the radio frequency range;but this is not compatible with the range of frequenciesover which modulators/demodulators operate. Indeed, theyoperate at a much lower frequency usually referred to as theintermediate frequency. Converting the RF frequency to IFis thus crucial for proper demodulation of the signal. Thisdown-conversion is performed by local oscillators whichturn out to have the detrimental effect of introducingnoise that will be superimposed on the received signal[4].
4 Journal of Computer Systems, Networks, and Communications
The introduced noise is caused by random variationsof the phase about the steady-state sinusoidal waveform. Inwhat follows, we assume that the transmitted OFDM signalhas the same form as mentioned before, that is,
s(t) =N−1∑
k=0
Skej2π( f0+kΔ f )t . (7)
In ideal conditions (if the local oscillator does not intro-duce noise), the received signal would be of the followingform:
r(t) =N−1∑
k=0
HkSkej2π( f0+kΔ f )t, (8)
where Hk denotes the complex frequency response of thechannel in the kth subchannel.
On the other hand, if the local oscillator is not ideal, weneed to take into account the effect of noise. The latter ismodeled as a complex random process and denoted by e jϕ(t).We get the following received signal:
r(t) =N−1∑
k=0
HkSkej2π( f0+kΔ f )t
=N−1∑
k=0
Rkej2π( f0+kΔ f )te jφ(t),
(9)
where Rk = HkSk.At the receiver, we project the received signal over each
one of the possible carrier waveforms to determine thedemodulated carrier amplitudes. This is translated in thefollowing:
Al = 1Ts
∫ Ts
0r(t)e− j2π( f0+lΔ f )tdt
= 1Ts
∫ Ts
0e jφ(t)
N−1∑
k=0
Rkej2π(k−l)Δ f tdt,
(10)
where Ts denotes an OFDM symbol time and is equal to Ts =1/NΔ f and N is equal to the number of different subcarriers.In a practical design, the afore-mentioned integral wouldbe replaced by a summation [5], but the authors decidedto use the integral because it makes the derivation closer tointuition even though nothing would change if they replaceit by a summation.
The afore-mentioned expression denotes the projectionof the received signal on the waveform associated with thecarrier:
2π f1 = 2π f0 + 2πlΔ f . (11)
The perturbations introduced by the random processϕ(t) are assumed to be relatively small so that the followingapproximation is justified:
e jφ(t) ≈ 1 + jφ(t). (12)
Now, we can write Al in the following way:
1T
∫ Ts
0(1 + jφ(t))
N−1∑
k=0
Rkej2π(k−l)Δ f t dt
= 1Ts
N−1∑
k=0
Rk
∫ Ts
0e j2π(k−l)Δ f t dt
+1Ts
N−1∑
k=0
Rk
∫ Ts
0jφ(t)e j2π(k−l)Δ f t dt.
(13)
The second term will be denoted by Yl.This separation of the two terms is justified by the fact
that the first part is what we would have received in theabsence of noise while the second term includes the effect ofnoise.
Now, we write
1Ts
N−1∑
k=0
Rk
∫ Ts
0jϕ(t)e j2π(k−l)Δ f t dt (14)
in the following way:
1Ts
N−1∑
k=0, k /= lRk
∫ Ts
0jφ(t)e j2π(k−l)Δ f t dt +
RlTs
∫ Ts
0jφ(t)dt. (15)
The second term of the afore-mentioned summation repre-sents the contribution of the lth carrier to the summationand is the one that we expect since we are projecting thereceived signal on the waveform associated with the lthcarrier. It evaluates to jφ0Rl, where ϕ0 is a real constant thatresults from the integration.
We note that the constant ϕ0 is independent of l and soit is the same for all symbols of the signal constellation. Werefer to this error as the CPE, which is directly proportionalto the received amplitude Rl of carrier l. We conclude thatthe physical meaning of this contribution is a rotation of thesignal constellation by an angle equal to
φ0 = 1Ts
∫ Ts
0jφ(t)dt. (16)
We now characterize the other term that contributes tothe previous summation, namely,
1Ts
N−1∑
k=0, k /= lRk
∫ Ts
0jφ(t)e j2π(k−l)Δ f t dt. (17)
This term represents the remainingN−1 contributions ofthe other carriers. This contribution consists in first shiftingthe spectrum of ϕ(t) by 2 2π(k − l)Δ f and then scalingit by the received amplitude of the corresponding carrier.This amplitude is complex and thus this noise term will alsobe complex. It is commonly referred to as ICI or loss oforthogonality [6]. This is due to the fact that the orthogonalproperty of the basis functions that was used to produce theOFDM signal is no longer preserved. Indeed, the projectionof the received signal on the waveform associated with the
Mourad Melliti et al. 5
lth subcarrier now contains a new term which is completelyrandom. Because of this randomness, it cannot be corrected.
More generally, we define ϕm to be equal to
φm = 1Ts
∫ Ts
0φ(t)e jmΔ f t dt. (18)
The noise effect can then be represented by the followingmatrix:
⎡⎢⎢⎢⎢⎢⎢⎢⎣
Y0
Y1
Y2
:YN−2
YN−1
⎤⎥⎥⎥⎥⎥⎥⎥⎦
= j
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
ϕ0 ϕ1 ϕ2 · · · ϕN−2 ϕN−1
ϕ−1 ϕ0 ϕ1 · · · ϕN−3 ϕN−2
ϕ−2 ϕ−1 ϕ0 · · · ϕN−4 ϕN−3...
......
......
...ϕ−(N−2) ϕ−(N−3) ϕ−(N−4) · · · ϕ0 ϕ1
ϕ−(N−1) ϕ−(N−2) ϕ−(N−3) · · · ϕ−1 ϕ0
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
×
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
R0
R1
R2...
RN−2
RN−1
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
.
(19)
The diagonal of the afore-mentioned matrix is constantbecause, as was explained before, this constitutes the CPE,which is the same for all carriers. The off-diagonal elementsare the weighting coefficients that multiply each of the com-plex amplitudes of the received signals. The nomenclatureintercarrier interference is thus clear from the structure ofthe afore-mentioned matrix.
ϕ0 can be considered to be the output of a filter with thefollowing impulse response:
h(t) = rect(t/Ts
)
Ts. (20)
The impulse response is zero except for a rectangle of height1/Ts for a duration of Ts seconds.
Taking the Fourier transform of h(t), we get
H( f ) = sin c(f
Δ f
). (21)
It is very common to assume that the random process is azero-mean Gaussian process. From this, we conclude that therandom variables ϕm are also Gaussian zero-mean. To fullycharacterize these random variables, we need to computetheir variances.
For ϕ0, we find that its power spectral density is givenby |Φ( f )H( f )|2, where Φ( f ) denotes the power spectraldensity of ϕ(t). Its variance may then be computed as follows:
σ20 =
∫∞
−∞
∣∣Φ( f )H( f )∣∣2df
=∫∞
−∞sin c2
(f
Δ f
)∣∣Φ( f )∣∣2df .
(22)
More generally, ϕm is a zero-mean Gaussian randomvariable with variance equal to
σ20 =
∫∞
−∞sin c2
(f
Δ f
)∣∣Φ(f −mΔ f
)∣∣2df . (23)
In fact, CPE can be accounted for as will be described inSection 7. The component we are left with is ICI.
We rewrite it for ease of reference:
1Ts
N−1∑
k=0, k /= lRk
∫ Ts
0jφ(t)e j2π(k−l)Δ f t dt. (24)
Using the afore-described filter, this can be rewritten as
1Ts
N−1∑
k=0, k /= lRk
∫∞
−∞jΦ(f − (k − l)Δ f
)sin c
(f
Δ f
)df . (25)
We make the change of variable u = f − (k − l)Δ f andget
ICI = 1Ts
N−1∑
k=0, k /= lRk
∫∞
−∞jΦ(u) sin c
(u
Δ f+ k − l
)du. (26)
We assume that the kth subcarrier has average power = 2.We can then compute the power of the ICI term and find itto be equal to
N−1∑
k=0, k /= lσ2k
∫∞
−∞
∣∣Φ(u)∣∣2
sin c2(u
Δ f+ k − l
)du. (27)
From the afore-mentioned expression, we can see thatif the power spectral density of ϕ(t) is decreasing withfrequency, then the major contribution to ICI will be thatof subcarriers that are near the subcarrier of interest. We canalso say that subcarriers near the center of the frequency bandwill suffer more from ICI than subcarriers at the edge of theband because contribution from adjacent subcarriers will behigher in the former case. In [5], it is stated that subcarriersnear the center of the frequency band will be subject to moreinterference than subcarriers at the band edge by up to afactor of two.
Another important observation is that interferenceincreases as the spacing between the subcarriers decreases.
From the power of the ICI, we can compute the noise-to-signal ratio. For a subcarrier near the middle of the band,assuming equal power on all subcarriers, the noise-to-signalratio is given in [2] as
ICI2
σ2l
= 2N/2−1∑
k=0
σ2k
∫∞
−∞
∣∣Φ(u)∣∣2
sin c2(u
Δ f+ k − l
)du.
(28)
We have seen that the effect of ICI increases as the relativespacing of the subcarriers decreases. So in this case, ICIeffect may be considered small as compared to that of CPE.However, ICI is still present because the symbols in theconstellation tend to have the shape of a cloud which depicts
6 Journal of Computer Systems, Networks, and Communications
the random perturbation introduced by ICI. However, wecan appreciate more the effect of CPE because it can be seenthat the constellation has undergone a rotation by a constantangle. CPE can be corrected as will be briefly discussed inSection 7 and so after removing its effect.
6. CORRECTION
We have previously mentioned that CPE is the part of phasenoise that can be accounted for and thus can be corrected.
The ability to do so stems from the fact that the effect ofCPE is a simple rotation of the signal’s constellation by a fixedangle. Thus, if we can estimate that angle, then correctingfor CPE becomes a simple task as it would only consist inrotating back the constellation by the same angle.
One way to estimate the angle is by measuring the phasevariation of a pilot subcarrier and subtracting that rotationfrom all subcarriers. The authors in [7] use an extendedKalman filter to present an algorithm for pilot-based CPEestimation.
Another way would consist in using differential phasemodulation between the subcarriers. This method would,however, introduce a noise performance penalty whencompared to coherent demodulation. The idea behind thistechnique is to let one subcarrier have a fixed phase and tolet the information in the other subcarriers be encoded intheir relative phase differences.
In [6], the authors propose a new algorithm for CPEcorrection.
Recall that
At = 1Ts
N−1∑
k=0
Rk
∫ Ts
0e j2π(k−l)Δ f t dt
+1Ts
N−1∑
k=0,k /=Rk
∫ Ts
0jφ(t)e j2π(k−l)Δ f t dt
+RlTs
∫ Ts
0jφ(t)dt,
(29)
which can be written as
At = 1Ts
N−1∑
k=0
Rk
∫ Ts
0e j2π(k−l)Δ f t dt + ICI + CPE. (30)
The first term on the left-hand side as well as ICI are bothzero-mean. So, the authors of [6] suggest that we can get anestimate of the CPE for the lth OFDM symbol by finding themean of the phase rotations associated with the subchannelsof an OFDM symbol (because ICI and the first term havezero mean, they will not affect the expectation of Al for all l,and so we can have an estimate of the CPE by averaging overall theAl). However, some subchannels may suffer from a lowSNR, and thus including their effect in the CPE estimationwill result in undesirable errors. These channels (for whichSNR falls below a certain threshold) are discarded. We willdenote by Nd their number. The Al above the threshold willthen be passed through a frequency equalizer to remove theeffect of the channel. Note that this assumes that we alreadyknow the channel’s characteristics. The equalized version of
the Al is then passed through a slicer and we perform anaveraging over the difference of the equalized version and thesliced version of the Al.
This can be written as
CPEestimate = 1Nd
∑
l,Hl≥threshold
(Al,equalized − Al,sliced
). (31)
More generally, a tracking sequence occupying OFDMsymbol Nt (Nt is generally set to 0) is sent to allow a properdetection of the start of the OFDM frame and thus a properremoval of the cyclic prefix discussed previously. The aboveCPE estimation needs to be carried out for each symbol. CPEvariations are usually very slow and the channel estimationprocedure performed by the frequency equalizer remains thesame unless a new tracking sequence is sent. If the blockassociated with the training sequence turns to have a highCPE estimate (CPENt ), then it will affect the channel phaseestimation as described in [6]. This needs to be taken intoaccount in the subsequent estimation of the CPE of thesymbols. The authors in [6] use a moving average filter toremove the offset that might be introduced.
The algorithm proposed by the author can be formulatedin the following way.
(1) Select the subchannels that meet the threshold crite-ria (SNR above a certain critical value).
(2) Calculate the mean of the previous CPE estimatesthat are in the moving average filter. We call this meanCPEm.
(3) Use CPEm to update the phase of the coefficients(Cm−1,l) of the frequency equalizer. This would pre-vent the occurrence of the offset previously discussed.The update can be described as follows:
Cm,l = Cm−1,l + CPEm for 0 ≤ l ≤ N − 1. (32)
(4) Get the new estimate for
CPEestimate = 1Nd
∑
l,Hl≥threshold
(Al,equalized − Al,sliced
). (33)
(5) Move the previous value in the moving average filterto calculate CPEm+1.
7. CONCLUSION
OFDM is considered as a potential candidate for next-generation cellular systems. Despite all the advantages itprovides in terms of ISI suppression and efficient bandwidthuse, it suffers from the detrimental effects introduced byfrequency offset and phase noise. The interference amongthe subcarriers causes the system to loose its orthogonality.We have seen that ICI places a limit on the carrier spacingbecause it increases as the spacing decreases. Local oscillatorsintroduce phase noise that will be superimposed on thereceived signal. Many algorithms have been proposed tocorrect the CPE part of the phase noise. We have presented
Mourad Melliti et al. 7
one algorithm based on averaging previous estimates of theCPE to get a better future estimate. The algorithm trackswell the variations of the CPE even though it usually variesslowly. On the other hand, ICI has a random structure andmitigating its effects remains a challenge.
REFERENCES
[1] M. Mourad, H. Salem, and B. Ridha, “Analysis of frequency off-sets and phase noise effects on an OFDM 802.11 g transceiver,”in Proceedings of the 4th International Workshop on Wearableand Implantable Body Sensor Networks (BSN ’07), vol. 13,Aachen, Germany, March 2007.
[2] S. K. Bassam, “Frequency Synchronization Errors and Effects ofPhase Noise on OFDM Systems,” EE359-Wireless Communica-tions Class Projects Stanford University, 2004.
[3] G. Pujolle, Les Reseaux, Eyrolles, Paris, France, 4th edition,2000.
[4] H. Salem, “Contribution a la modelisation des cables mono-tones par elements finis,” thesis report ENIT, January 2000.
[5] A. R. S. Bahai and B. R. Saltzberg, Multi-Carrier DigitalCommunications. Theory and Applications of OFDM, KluwerAcademic Publishers/Plenum, New York, NY, USA, 1999.
[6] V. S. Abhayawardhana and I. J. Wassell, “Common phase errorcorrection for OFDM in wireless communication,” in Proceed-ings of the 3rd International Symposium on CommunicationSystems, Networks and Digital Signal Processing (CSNDSP ’02),Staffordshire, UK, July 2002.
[7] D. Petrovic, W. Rave, and G. Fettweis, “Phase noise suppres-sion in OFDM using a Kalman filter,” in Proceedings of the6th International Symposium on Wireless Personal MultimediaCommunications (WPMC ’03), vol. 3, pp. 375–379, Yokosuka,Japan, October 2003.
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