Exhibit 2027
`
`Exhibit 2027
`
`

`

`The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
`
`ANALYSIS OF PER-CHANNEL EQUALIZED FILTERED
`MULTITONE MODULATIONS OVER TIME-VARYING
`FADING CHANNELS
`Tiejun (Ronald) Wang, John G. Proakis, and James R. Zeidler*
`Center for Wireless Communications
`University of California, San Diego
`La Jolla, CA 92093-0407, USA
`
`efficiency. The trade-off between possible ICI and ISI and the
`ABSTRACT
`corresponding spectral efficiency (or data rate) ofthe FMT sys-
`We consider the performance of an FMT system with per-
`tr steeoea motn su o
`h ytmdsg n
`channel~~~~~eqaizto
`tem iS therefore an important issue for the system design and
`channel equalization over frequency-selective time-vaying
`ove frqec-eetietm-ayn
`comparison with conventional OFDM. Recently, several inter-
`fading channels. Due to the distortion caused by frequency and
`exist in Testing papers have appeared, addressing this problem from dif-
`tetivity odt
`tiFMe sel
`efadingochannel,bot
`rCIan. BSesing
`time selectivity of the fading channel, both ICI and
`ferent perspectives [7] - [12]. Assalini et al. investigated in [7]
`the effects of frequency offsets and phase noise in FMT and
`an FT sstemandcaus peformncedegrdaton.
`y uing
`Byevauain thachabe bite
`ofThe
`a per-channel equalizer at the FMT receiver with sufficiently OFD systs
`large number of equalizer taps, the ISI can be mitigated signif-
`two systems over different types of channels, they found that
`icantly, but the ICI still exists. In this paper, the effects of the
`interference caused by the time-frequency dispersive channel is FMT has a higher spectral efficiency and is more robust to
`*nf baito i
`frequency offset than OFDM. Tonello [8] calculated the ex-
`act matched filter performance bound for multitone modulated
`er-
`quantfied by analyzing the average system carrieret
`interfer
`signals in time-varying and frequency-selective fading chan-
`rtosof
`ret ading con-
`the Fy
`ence (
`
`u
`nels when optimal maximum likelihood detection is employed.
`C/I raio ad ts upper
`bound a closed
`for the
`boundeare povded fr the-fM sytwem wicrh leadcto
`In order to shorten the cyclic prefix (to reduce the overhead) in
`abte
`DMT-based systems, a design of frequency domain equalizer iS
`undrstndig oth trde-ff etwen pecraleffciecy nd
`system performance degradation. Moreover, comparisons be-
`tween FMT and OFD sytemunerheamecconsidered in [9]. In [10] [11], practical FMT systems includ-
`ming the filter bank design were investigated with the objective of
`tweenFMTand OFDM systems under the same channel cond-
`tions and spectral efficiency are also provided. Numerical and
`minimizing the ISI and ICI while at the same time maximizing
`simulation results of the system C/I ratio further confirm and
`the spectral efficiency. Wang et al. provided in [12] an analysis
`support the obtained analytical results.
`in terms of CIR ratios of FMT system over frequency-selective
`and time-varying fading channels. The authors also provided a
`detailed comparison between FMT and OFDM with the same
`I.
`INTRODUCTION
`spectrum efficiency under different channel conditions.
`Filtered multitone (FMT) modulation is a form of multicarrier
`modulation that has gained much attention recently. It has been
`In this paper, we consider the performance of an FMT
`proposed for data transmission for both very high-speed digi-
`system with a per-channel equalizer over frequency-selective
`tal subscriber lines (VDSL) [1] and for wireless communica-
`time-varying fading channels. It is known that when the base-
`tions [2] because FMT is suitable for high data rate communi-
`band filter at the transmitter and the matched filter at the re-
`cations with high spectral efficiency, and offers convenience in
`ceiver maintain orthogonality between the subcarriers but also
`spectrum management [1] - [2].
`satisfy the Nyquist sampling criterion, there is no ICI or ISI in
`OFDM is another widely used multicarrier modulation in
`the system as long as the fading channel impulse response is flat
`mobile radio applications, such as 802.1 la and DVB systems.
`and stationary. However, this is not the case for most practical
`The baseband filter of an OFDM [3] system is simply a rectan-
`wireless environments when the channel response is not only
`gular function and hence has overlapping spectra in the fre-
`frequency selective and also time variant. Basically, both ICI
`Specifically, in conventional OFDM, each
`quency domain.
`and ISI exist in an FMT system when transmitting over time-
`OFDM subchannel exhibits a Sinc shape frequency response.
`varying frequency-selective fading channels. The ICI results
`Therefore, the time variations ofthe channel during one OFDM from the time-varying channel response which destroys the
`symbol duration destroy the orthogonality of different subcar-
`orthogonality among different sub-channels. In addition, the
`riers and result in power leakage among subcarriers, known as
`frequency-selectivity of the fading channel breaks the perfect
`Intercarrier Interference (ICI), which will cause degradation in
`reconstruction (Nyquist criterion) condition of the base band
`system performance [4], [5]. As compared to an OFDM sys-
`filters, which leads to the ISI. By using a per-channel equal-
`tem using a cyclic prefix (sacrificing the spectral efficiency)
`izer at the FMT receiver of sufficient length to span the ISI,
`to remove Intersymbol Interference (ISI), an FMT system uses
`the ISI is mitigated significantly. However, the ICI still exists
`a noncritical sampling rate technique to mitigate the interfer-
`and is likely to be enhanced by the channel inversion. There-
`ence caused by the fading channel. The interference in an FMT fore, it is interesting the investigate the system performance
`system iS suppressed at the expense of choosing a larger non-
`Of a per-channel equalized FMT system compared to a regu-
`critical sampling factor and hence also sacrificing the spectral
`lar FMT system as well as a standard OFDM system. In this
`* This work was supported by the Center for Wireless Communications
`paper, we investigate the average system carrier to interference
`under the UC IUCRP CoRe research grant core 03-10148.
`(C/I) ratio of the FMT system over fading channels. A closed-
`VIS EXHIBIT 2027
`
`1-4244-0330-8/06/$20.OO®f2006 IEEE
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`Page 1 of 5
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`The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
`
`form expression of the C/I ratio and its upper bound are pro-
`vided for the FMT system, which lead to a better understanding
`of the trade-off between spectral efficiency and system perfor-
`mance degradation. Moveover, comparisons between FMT and
`OFDM systems under the same channel conditions and spectral
`efficiency are also provided. Numerical and simulation results
`of the system C/I ratio further confirm and support the analyti-
`cal results obtained.
`
`The number of fading taps L is given by TmaxI(TIK), where
`Tmax is the maximum multipath delay, and W = K/T is the
`entire channel bandwidth of the FMT system. The parameter
`Q controls the coherence bandwidth of the channel. The 3dB
`channel coherence bandwidth is given by fcoh = v/3rK
`In
`the time domain, the fading coefficients g, (kT/K) are corre-
`lated and have a Doppler power spectrum density modelled as
`in Jakes [14], given by
`
`II.
`
`SYSTEM MODEL FOR FMT MODULATION
`
`f < Fd
`
`e j2 rrfo kT/K
`
`ej2nK
`
`ej2kT
`
`Noise
`Noise
`
`e j27 fo kT/K Ao(nT)
`
`2 fkT
`
`1
`f
`)
`D(f) = <
`Fd \ 1- (
`O-(kT)
`ljFd
`otherwise
`klllJ 4Kwhere Fd is the maximum Doppler bandwidth.
`g(kT/K) has a autocorrelationfunctiongivenby
`)
`
`(4)
`
`Hence
`
`e
`
`e2w7fil lkT/K | | j2fffisllTK E[gi(mjK).gi(mjK)]
`
`cv.exp(-a l).JO (27(n-m)Fd)
`
`Figure 1: System model of the filtered multitone (FMT) mod-
`ulation system
`
`As illustrated in Fig. 1, the complex valued QAM symbols
`Am(ThT), m 0,1,
`7
`, M-1, are provided atthe symbol rate
`-T=K
`of l/T. AfterAupsamplingbyafactorofK,eachsymbolstream
`is filtered by a baseband filter with frequency response H(f) kw-°°c
`T IE RnaE ANLYIS OF t
`and impulse response h(k). The transmitted signal x(kT/K)
`iS obta1ned by adding the frequency shifted versions of the M
`filtered outputs from the filters at the transmission rate of K/T,
`In this section an analysis of the interference generated under
`which is given by
`different channel conditions is provided. As a comparison, the
`analysis of FMT systems with ideal per-channel equalizers is
`~~T ~ K_
`also provided and used to investigate the trade-offs between
`T M-1
`oo
`T
`is~~~~ ~ ~ ~ ~ ~ ~ ~~~~~ecobtheebyq1s perfectthelnfrequency shifedhersiosseband
`] ej22mATkK Aspectrum efficiency and system performancebdegradation.
`Am(ThT)h[(k-
`E2
`_(kK=
`E
`mO
`When the FMT system is transmitting over a frequency-
`selective time-varying fading environment, the spectrum of the
`( )
`where K/MT is the frequency spacing between adjacent sub-
`received signal is shaped by the channel frequency response.
`h
`AmLYIn cn T
`OfteAsebN
`Hence ThEN
`(kT/K) is transmitted over a
`carriers. The obtained signal
`p
`dilspersve channel. At the receiver end, the sampled receIved
`filters of the FMT system is no longer satisfied, and cnse-
`shigna maybiven expressedfquently, we have 11. Furthermore, due to the time variance of
`Tthe fading channel, the orthogonality among different subchan-
`L-1
`T1 9 T)
`nels is destroyed and the transmitted signal is also distorted by
`T
`xK)
`AmnT.oknKL
`the ICI. In this case, by substituting (2) and (1) into (6), the
`output signal from the FMT demodulator can be represented
`where gK(kT/K) repreqsents the channel response of the 1th
`as,
`path at time kT/K, L represents the total number of paths of
`ti
`the frequency-selective fading channel, andwe(kaT/K) repre-Aiivn'T)tGi,i(sn', in')
`sAy in'T) +El Gi,i(in, n') -A(incT)
`sents the additive Gaussian noise with zero mean and variance
`n=-oo
`E[ w(kT/Kf) 212 =2 =NO/Es.*n7n
`The fading channel coefficients gt(kT/K) are modelled as
`M-1
`oo
`(in,in')s s (ignT) + wI'
`S
`zero mean complex Gaussian random variables. Based on the
`+E
`ry a
`1'Kh
`
`sents~ ~~theaddtiv Gassa nos wit zero mean
`vaiac
`syste
`n= by
`tbino
`wide sense stationary and uncorrelated scattering (WSSUS) as-
`igelp
`sumption, the fading channel coefficients in different delay taps
`frequency domain channel
`are statistically independent. We alsoassumethattheyhave an
`The (time-variant)
`Ker1encmlxGasinrno vaibls eBp(-L on th)
`Gi,i('
`(n1n Ain,in') +j~\w,
`(n') ote, FMT stei
`exponential power delay profile, which iS given by
`given by
`(3)~
`E[gl(kTK) 2] =a7exp( -1),
`i)L')
`exp-
`nn1-
`
`= E
`
`tjk2,
`MKiKK
`
`(2)
`
`-
`
`*
`
`(7)
`
`response
`(8)
`
`The sampled signal y(kT/K) at the receiver is first fre-
`quency shifted and generates M substreams. Each stream is
`then filtered by a matched filter h(k), followed by subsampling
`by a factor of K. Therefore, the it
`output of the substream
`Ai (n'T) at time n' is given by
`( T _e2+ [m'-r
`K
`
`A^mT,
`
`k) T1
`6
`K(6 )
`MODULAtION
`
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`

`The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
`
`with signal g
`
`(1, n, n') defined as the following form
`
`g
`
`F
`Tl
`, T
`-
`(l, in, in') = E 91(kjK) h [(k-i-inK) Kf]
`k=-oc
`
`_i_i__k
`T
`h* (k - n/K) K
`ej27(rA1)
`Ki
`It is evident from equation (7) that the first term is the desired
`signal (to be demodulated), the second term represents the ISI,
`the third term represents the ICI, and the last term represents
`the additive Gaussian noise.
`
`(9)
`
`equation (14), the first term is the desired signal, and the sec-
`ond term is the interferences from the other sub-channels in an
`FMT system. Therefore, the ideal per-channel equalizer elimi-
`nates the ISI completely by using a filter with sufficiently large
`number of equalizer taps. However, the residual interference
`from adjacent sub-channels due to the loss of orthogonality
`In order to investigate the effects of per-channel
`still exists.
`equalization on the system performance, we provide the C/I ra-
`tio analysis of the FMT system over different fading channel
`conditions in the next section.
`
`IV. PER-CHANNEL EQUALIZED FMT MODULATION
`Compared with an OFDM system with sufficient long cyclic
`prefix, where the transmitted signal is free of ISI, it is clear
`from equation (7) that both ICI and ISI exists in an FMT
`Therefore, it is interesting to study the effects of
`system.
`per-channel equalizers in an FMT system over time-varying
`frequency-selective fading channels.
`A. FMT Modulation with Per-Channel Equalizer
`In this paper, we consider an ideal per-channel equalizer with
`a infinite number of equalization taps. The mnth tap coefficient
`of the ith sub-channel at time instant n' is denoted as Ci,n/ (m)
`for 0 < i < M-1. In this case, the output signal from the
`per-channel equalizer is given by
`00
`
`Al,((n/T) =
`
`ci,n(m) Ai((n' - m)T) ,
`
`(10)
`
`=-oo
`where AEq with superscript ()Eq represents the received sig-
`i
`nal after equalization. It is evident that the Z-transform of the
`channel equalizer, which is defined by the following form
`
`Analysis ofPer-Channel Equalized FMT System
`B.
`From equation (14), it can be established that the ICI of the
`per-channel equalized system, which is denoted as ui, can be
`expressed as follows:
`M-1 oo
`oo
`E cin/(m)Gi(i(n,in'-m)Ai/(nT). (15)
`ui=N
`?
`i'=On=zoim=-o
`il:Ai
`Therefore, the instantaneous variance ofthe interference signal
`can be represented in the following format:
`M-1 oC
`ci,n, (m)G,i, (n, n'
`i/=on=-oom=-oo
`i'7(i
`By assuming the input signal Ai/ (nT) is i.i.d. with unit vari-
`ance and by using the property of the Z-transform, it can be
`shown that
`SE E ci,n (in)
`n=-oo m=-oc
`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1
`f Ci,(j27f) Fii,i/,n(j27f) 2 df .
`J
`J
`'
`By substituting equation (12) into equation (17), the following
`lower bound on the instantaneous ICI variance is obtained
`27)2
`M-1
`(j2f)
`
`E[wui 21=2E=
`
`2
`
`m)
`
`Gi,i/ (n, in' - m) 2
`
`(17)
`
`'
`
`1
`
`E[Zui J]
`
`E
`i/=0
`
`d
`
`00
`
`(11)
`
`Ci,n/ (z) = E Ci,n/ (m) Z-m
`m=-CX0
`is the inverse of the Z-transform of the equivalent channel re-
`sponse Gi,i (n, n'), given by
`Ci,n/ (z) = Fi,i,n (z)]
`(12)
`,n/ (z) given by the following form
`with the Z-transformF
`
`Fi,i/,n/ (z) =
`
`(13)
`
`Bysubstituting equatn(7) into (10) we obtain the following
`
`M1 f2 7f(j2wf) df 2
`Zi70
`Fi,i,n/(j2iFf)2d2f Z>EXDo
`=
`i,#Ai
`
`(in', in') 2
`in') 2
`
`(18)
`
`3 Oi,i/ (n' + m, n') z-m
`m-oo
`By substituting equation (18) into the C/I definition, the aver-
`age CIR ratio of the per-channel equalized FMT system can be
`By susiuigequation (7 no(0,w bantefloig bounded in the following form:
`result after some manipulations
`iEq (in'T) - A (i(n'T)+5 S
`
`S ci,n'(m)
`
`I
`
`AI-1 C tCA E [i-0 En= _ lGi,i(n,rl')|~~~~1
`K I)
`1
`--1
`
`F [lz
`
`2]
`
`In' 2]
`
`x ~ (in,in'-m)~ (inT)
`
`v
`
`For the sake of simplicity, we can denote the nominator and
`where v is an additive Gaussian noise with zero mean and vani-
`the denominator of the R.H.S. of equation (19) as the Cup and
`ance given by (J2 =O f-4 cir,' (j2wf) 2 d f. Note that in Ip respectively. By substituting the definition of Gii (in, in')
`
`(14)
`
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`

`The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
`
`and FMT have the same type of interference, i.e., ICI from
`given by equations (8) and (9) into (19), we obtain the follow-
`The performance comparison between
`other sub-channels.
`ing result after some manipulations
`these two modulation forms in terms of CIR ratios, which are
`1
`1
`cup = a ff
`(20)
`given by equations (19) and (25), provides a better understand-
`Jo-a Jo
`,ing of the trade-offs between spectrum efficiency and system
`y
`performance of different multi-carrier modulations.
`where Scp(f, s) is the general power spectrum density of the
`upper bound of the average signal power, which is given by
`V. NUMERICAL AND SIMULATION RESULTS
`In this section, we assume that the baseband filter h[nT/K] has
`a root raised cosine frequency response, which is given by
`
`(f s) Dg(s)
`c upv,,
`g v,
`
`df ds
`
`1 K-1
`k
`k
`SC,up(f s) K S H(f - K H(f- K -s)
`k=o
`xH*(f) H(f-s)-
`
`(j;¼f
`K
`21)
`) 2K
`2K
`-
`C-(O+j27rk/K)HW ~ ~ ~ ~ ~ ~ ~~~f <
`~(1-a)
`f < (1+a)
`0
`
`K-M
`
`and Dg (f) is the discrete Doppler spectrum, given by
`K < FdT
`K
`fK
`Dg(fV=
`.D(TV{ 7rFdT
`Ds(f)=T D( T )= dT 1
`0O
`
`(FdT)d
`fT
`
`Similarly, It,p iS given by
`l
`l
`l
`
`UP=a
`
`S,up(f', f, s) Dg(s) df' df ds
`
`(23)
`
`where
`
`Si,up(f f, s)
`
`/ i/
`M-1
`5 H(f - M H(f
`i'=o
`
`H(f ) H*st)
`xH(f - s) H*(f
`
`1 -eL(O+j±2-(f
`- e-(+i2(f-f))(24)
`By substituting the signal power Cup given by equation (20)
`and the interference power Iup given by equation (23) into the
`C/I ratio definition, the upper bound ofthe CIR ratio of the per-
`channel equalized FMT system over frequency-selective time-
`varying channel is obtained.
`
`))
`
`~~~~~~~~~~~~~~~~(26)
`where the roll-off factor a is given by a = M
`I < Fyf
`K
`We demonstrate in Fig. 2 the CIR graphs of an FMT system
`otherwise
`having 64 subcarriers and several different upsampling factors
`(22) K = 91, 80 and 71. The spectral efficiency r = M/K, de-
`fined as the ratio of the subcarrier number over the upsampling
`factor, varies from r = 0.7 to r = 0.9, which parameter-
`izes the CIR curves. The FMT system has a total bandwidth
`W = 0.5MHz, where adjacent subcarriers have frequency
`spacing 7.81KHz. The FMT system is transmitting over a
`frequency selective L = 4 taps fading channel with 3dB co-
`herence bandwidth W3dB = 0.125MHz. For comparison pur-
`poses, the upper bounds of the CIR graph of the same FMT
`system with per-channel equalizer is also shown in the plot.
`It can be observed that the per-channel equalizer significantly
`improves the performance of an FMT system. As indicated in
`Fig. 2, while Doppler frequency increases, CIR is nearly con-
`stant for any Doppler frequency of FMT system; however, the
`CIR degrades dramatically although that of the equalized FMT
`system exceeds that of the conventional FMT.
`
`C
`
`1
`(k-i)2
`
`100
`
`200
`
`400
`300
`Doppler Frequency (Hz)
`
`500
`
`600
`
`Performance Comparisons with OFDMSystems
`C.
`It is insightful to compare the performance of both FMT and70---------------------------
`OFDM systems with the same spectral efficiency under the
`same channel conditions. In practical OFDM systems, we se-
`lect the length of the cyclic prefix to be longer than the channelA=
`maximum multipath delay spread, and thus, the system is ISI
`free. According to the ICI analysis of an OFDM system in a
`time-varying fading channel as provided in [4] [6], the carrier
`to interference (ICI only) ratio of the OFDM system can be
`represented as
`
`FMT system of M=64 subcarriers with subcarrier spacing 7.81 KHz
`
`90
`
`-t Per-Channrel Equalized FMT.
`
`60
`
`4
`
`30
`
`20
`
`0=M/K_0.7
`
`=M/ K=
`
`0.9
`
`=MIK-=.8
`=/
`i=MI---
`
`0.9
`
`2
`(MTFdIK)2 <
`ki
`Figure 2: CIR graphs of an FMT system with M =64 subcar-
`where MT/K is the OFDM symbol interval.
`In this paper, we extend the interference analysis to FMT riers under different upsampling factors.
`modulations with a per-channel equalizer. Instead of designing
`specific channel equalizers for the FMT system, we investigate
`the ideal system performance ofthe per-channel equalized sys-
`In order to compare the performance of the per-channel
`tem with a sufficiently large number of equalizer taps. There-
`equalized FMT system with an OFDM system, we compare in
`fore, with the help of per-channel equalization, both OFDM Fig. 3 the CIR graph of the same FMT system with that of an
`
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`

`The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
`
`lines," IEEE Journal on Selected Areas in Communica-
`tions, vol.20, pp. 1016-1028, June 2002.
`
`[3]
`
`0
`
`60
`
`FMT system of M=64 subcarriers with subcarrier spacing 7.81 KHz
`
`90
`
`<
`
`80
`70 k b<> I
`
`< Per-Channel Equalized FMT
`\
`
`OFDM system having 64 subcarriers and the same subcarrier
`frequency spacing over the same fading channel conditions as
`in Fig. 2. The simple rectangular pulse shape in OFDM mod-
`ulations causes more severe ICI effects comparing with FMT [2] N Benvenuto, G. Cherubini, and L. Tomba, "Achievable
`systems. By contrast, FMT systems resort to noncritically sam-
`bit rates of DMT and FMT systems in the presence of
`phase noise and multipath," Vehicular Technology Confer-
`pled filter-bank design that achieves tight subchannel spectral
`containment. Therefore, the sidelobes of spectral characteris-
`ence Proceedings, vol.3, pp. 2108-2112, May 2000.
`tics (Sinc function) for each OFDM subchannel attenuate much
`S. B. Weinstein and P. M. Ebert, "Data transmission by
`slower than the FMT systems. Without per-channel equalizer,
`frequencydivision multiplexing using the discrete Fourier
`transform," IEEE Trans. Comm. Technol., Vol. COM-19,
`the previous results in [12] had shown that OFDM performance
`exceeded that of FMT at low Doppler range but FMT was bet-
`pp. 628-634 Oct. 1971.
`ter at high Doppler, but this paper shows that with the elimina-
`p
`[4] T. Wang, J. Proakis, E. Masry, and J. Zeidler, "Performance
`tion of the ISI with per-channel equalizer, FMT is better than
`OFDM at all Doppler rates with a convergence to equal perfor-
`degradation of OFDM system due to Doppler spreading,"
`mance as M/K approaches unity at high Doppler rates.
`IEEE Trans. on Wireless Comm., vol. 5, pp. 1422-1432,
`June 2006.
`[5] P. Robertson and S. Kaiser, "Analysis of the loss of or-
`thogonality through Doppler spread in OFDM system,"
`in Proc. IEEE Global Telecommunications Conference,
`Globecom'99, pp. 701-706, Dec 1999.
`l[6] T. Wang, J. Proakis, and J. Zeidler, "Perfornance analy-
`sis of high QAM OFDM System over frequency selective
`time-varying fading channel," in Proc. 14th IEEE PIMRC,
`vol. 1, pp. 793-798, Sep., 2003.
`[7] A. Assalini, S. Pupolin, and A. M. Tonello, "Analysis ofthe
`Effects of Phase Noise in Filtered Multitone (FMT) Modu-
`lated Systems," In IEEE Global Telecommunications Con-
`ference, Globecom '04, vol. 6, pp. 354 1-3545, Dec., 2004.
`A
`l
`Promnelmt f
`i
`ae
`[8] A.Tonello, "Perfoancelimitsofmulticarrierbasedsys-
`tems in fading channels with optimal detection," The 5th
`International Symposium on Wireless Personal Multimedia
`Communications, vol. 3, pp.1005-1009, Oct., 2002.
`[9] Van Acker et al., "Per tone equalization for DMT-based
`systems ," IEEE Trans. on Comm., vol. 49, pp. 109-119,
`Jan. 2001.
`[10] B. Boma and T. N. Davidson, "Efficient filter bank de-
`sign for filtered multitone modulation," 2004 IEEE Inter-
`national Conference on Communications, vol. 1, pp.38-42,
`June, 2004.
`
`l
`
`\
`
`-
`
`40
`
`60
`
`=M/K = 0.7
`0.8
`
`............=M.K=..9-
`
`=
`
`0.9
`
`..=..
`1OFD.MOFDLM
`0.9
`
`
`20____L___OFDM :
`400
`200
`300
`Doppler Frequency (Hz)
`
`__M_
`
`9
`
`_= 0
`
`_
`
`500
`
`600
`
`50
`
`30
`
`20
`100
`
`system
`
`CONCLUSION
`VI.
`We considered the performance of an FMT system with
`per-channel equalization over frequency-selective time-varying
`fading channels. Due to the distortion caused by the time-
`frequency dispersive channel response, both ICI and ISI ex-
`ist in an FMT system and cause performance degradation. By
`using a per-channel equalizer at the FMT receiver with a suf-
`ficiently large number of equalizer taps, the ISI is mitigated
`significantly, while the ICI still exists. In this paper, the effects
`of the ICI and ISI on the FMT system performance was quan-
`tified by analyzing the average system carrier to interference
`(C/I) ratio under different fading conditions. A closed-form
`expression of the C/I ratio and its upper bound were provided,
`which led to a better understanding of the trade-off between
`spectral efficiency and performance degradation. Moveover,
`comparisons between FMT and OFDM systems under the same
`channel conditions andl spectral effciency were also providledl. ''''
`[13] J. G. Proakis, Digital Communications, 2nd ed., New
`Numerical and simulation results ofthe system C/I ratio further
`confirmed the obtained analytical results.
`York: McGraw-Hill, 1989.
`
`[11] A. Tonello, R. M. Vitenberg, "An efficient implemen-
`tation of a wavelet based filtered multitone modulation
`scheme," The 4th IEEE International Symposium on Sig-
`nal Processing and Information Technology, pp.225-228,
`Dec., 2004.
`[12] T. Wang, J. Proakis, and J. Zeidler, "Interference analysis
`of filtered multitone modulation over time-varying fading
`channels," in Proc. IEEE Global Telecommunications Con-
`'05 v.
`1., 2005.
`6 pp 3586-359
`
`REFERENCES
`[1] G. Cherubini, E. Eleftheriou, and S. Olcer,"Filtered mul-
`titone modulation for very high-speed digital subscriber
`
`[14] W. C. Jakes, Microwave Mobile Communications, IEEE
`prs,Rritd194
`
`Page 5 of 5
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