A Novel Data-Aided Channel Estimation with Reduced Complexity for TDS-OFDM Systems

0.4 MB·English

by  Ming Liu

1
A Novel Data-Aided Channel Estimation with
Reduced Complexity for TDS-OFDM Systems
Ming Liu, Matthieu Crussie`re, Member, IEEE, and Jean-Franc¸ois He´lard, Senior Member, IEEE
Abstract—Incontrasttotheclassicalcyclicprefix(CP)-OFDM, Then, all the well established equalization techniques [6], [7]
the time domain synchronous (TDS)-OFDM employs a known for ZP-OFDM can be applied for TDS-OFDM signals.
pseudonoise(PN)sequenceasguardinterval(GI).Conventional
The usage of the PN as GI is somehow “double-edged
channel estimation methods for TDS-OFDM are based on the
2 sword”. On one hand, it improves the spectrum efficiency by
exploitation of the PN sequence and consequently suffer from
1 intersymbolinterference(ISI).Thispaperproposesanoveldata- economizing the cost of transmitting redundant data in the
0
aided channel estimation method which combines the channel CP and the pilots in the data symbols; on the other hand,
2
estimatesobtainedfromthePNsequenceand,mostimportantly, the channel memory effect introduces mutual interference

n additional channel estimates extracted from OFDM data sym-
between the PN sequence and the OFDM data symbols. That
a bols. Data-aided channel estimation is carried out using the
isto say, theinterferencefromdatasymbolscompromisesthe
J rebuilt OFDM data symbols as virtual training sequences. In
3 contrast to the classical turbo channel estimation, interleaving performanceofthePN-sequence-basedchannelestimationand
and decoding functions are not included in the feedback loop theinaccuratechannelestimateconsequentlycausesimperfect

] when rebuilding OFDM data symbols thereby reducing the PN sequence removal and further increases the difficulty to
I complexity. Several improved techniques are proposed to refine
N recover the data symbols. The channel estimation is thus the
the data-aided channel estimates, namely one-dimensional (1-
key point in the TDS-OFDM based transmissions.
. D)/two-dimensional (2-D) moving average and Wiener filtering.
cs Finally,theMMSEcriteriaisusedtoobtainthebestcombination Many papers have addressed this challenging issue in the
[ results and an iterative process is proposed to progressively past few years and can be classified into three categories:
refine the estimation. Both MSE and BER simulations using 1. Making channel estimation based only on the PN se-
1 specifications of the DTMB system are carried out to prove
quence.In [8], the time domain cross-correlationbetween the
v the effectiveness of the proposed algorithm even in very harsh
6 channelconditionssuchasinthesinglefrequencynetwork(SFN) receivedPNsequenceandthelocallygeneratedoneisusedto
8 case. makechannelestimation.Itexploitsthecorrelationpropertyof
6 the PN sequencein orderto obtain processinggain to combat
0 Index Terms—TV broadcasting, channel estimation, OFDM,
thenoiseandISI.Thecomplexitysignificantlygrowswiththe
. iterative method.
1 increase of the length of the channel delay spread. In [2], a
0 simplechannelestimatorisproposedbasedontheexpectation
2 I. INTRODUCTION (mean value) of the received PN sequence which cancels the
1
: CONVENTIONALLY, orthogonal frequency division random ISI component. However, this algorithm only adapts
v multiplexing(OFDM)adoptscyclicprefix(CP)asguard to the static channel situations and requires large storage.
i
X interval (GI) to mitigate intersymbol interference (ISI) and 2.RemovingISIfromthePNsequencewhenmakingchannel
r enable simple equalization at receiver side. However, CP is estimation.Afirstapproach[1]proposedtoiterativelyremove
a a redundant copy of the data, which reduces the useful bit- the ISI using the decision feedback method. However, much
rate and degrades the spectrum efficiency. Recently, it has complexity is spent by a series of fast Fourier transforms
been proposed to replace CP by a known pseudo-noise (PN) (FFT).In[9],itisproposedtocarryoutthechannelestimation
sequence. The main advantage of this approach is that the usingthePNsequenceanditstailspreadinthebeginningpart
known sequence, which initially serves as GI, can be reused of each OFDM data symbol. By iteratively removingthe data
as training sequence to carry out channel estimation and syn- symbol,thechannelestimationisprogressivelyimproved.The
chronization. Therefore no pilot is inserted among the useful estimation results however suffer an error floor even at low
datasymbolsinthefrequencydomainasneededintraditional signal to noise ratio (SNR) due to the existence of ISI in the
CP-OFDM. This kind of OFDM waveform is referred to as PN sequence. [10] proposed to alternately remove the mutual
time domain synchronous-OFDM(TDS-OFDM)1 [1] and has interference between the PN sequence and the OFDM data
been adopted by the Chinese digital television/terrestrialmul- symbols. A so-called partial decision is also used to reduce
timedia broadcasting(DTMB) system [4], [5]. After perfectly theerrordetectionofdatasymbols.However,theperformance
removing the PN sequence, the received TDS-OFDM signal significantly degrades when the channel delay spread is long.
is converted to the so-called zero padding (ZP)-OFDM [6]. [11] also adoptedthe partialdecisiontechniqueto removethe
interference on the PN sequence from previous data symbols.
AuthorsarewithUniversite´ Europe´ennedeBretagne(UEB),INSA,IETR, In order to avoid the interference from the following data
UMR6164, 20avenue des Buttes deCoe¨smes, F-35708 Rennes, France. e- symbols, the “tail” of the received PN sequence is estimated
mail:{ming.liu,matthieu.crussiere, jean-francois.helard}@insa-rennes.fr.
andthen used to reconstructthe interference-freereceivedPN
1Itisalsoknownaspseudorandompostfix-OFDM(PRP-OFDM)[2]and
knownsymbolspadding-OFDM(KSP-OFDM)[3]inotherliteratures. sequence for channel estimation.
2
Hˆ
(cid:4)(cid:10)(cid:14)(cid:15)(cid:16)(cid:17)(cid:12)(cid:4)(cid:4)(cid:11)(cid:10) 2 %(cid:9)(cid:11)(cid:15)(cid:11)(cid:20)(cid:17) (cid:10)(cid:11)(cid:3)(cid:11)(cid:12)(cid:13)(cid:11)(cid:10)
&(cid:9)(cid:16)(cid:18)(cid:11)(cid:20)(cid:9)(cid:15)"
(cid:1)(cid:7) (cid:3) (cid:12)(cid:13)(cid:14)(cid:15)(cid:15)(cid:11)(cid:16) (cid:7)(cid:8)(cid:9)(cid:10)(cid:11) (cid:1)(cid:7) (cid:11)(cid:12)(cid:10)(cid:18)(cid:13)(cid:9)(cid:19)(cid:14)(cid:15)(cid:14)(cid:15)(cid:18)(cid:9)(cid:11)(cid:8)(cid:16)(cid:15)(cid:17) Hˆ1 (cid:12)(cid:8)(cid:14)(cid:19)(cid:18)(cid:9)(cid:8)$(cid:15)(cid:9)(cid:15)(cid:29) H2 (cid:25)(cid:21)(cid:9)(cid:11)(cid:15)(cid:20)"(cid:14)"(cid:29) H~2 (cid:11)(cid:12)(cid:10)(cid:18)(cid:13)(cid:9)(cid:19)(cid:14)(cid:15)(cid:14)(cid:15)(cid:18)(cid:9)(cid:11)(cid:8)(cid:16)(cid:15)(cid:17) Xˆ (cid:20)(cid:11)$ (cid:28)(cid:14)(cid:9)(cid:16)(cid:18)(cid:31)(cid:14)(cid:9)(cid:15)(cid:17)"
"(cid:11)(cid:15)(cid:11)(cid:20)(cid:14)(cid:18)(cid:9)(cid:8)(cid:15)
(cid:5) (cid:6) Hˆ
(cid:1)(cid:2)(cid:3) (cid:4) (cid:10) (cid:3)(cid:2)(cid:1) (cid:3)
cˆ
(cid:31)(cid:1)(cid:14)(cid:18)(cid:14) (cid:4)(cid:5)(cid:5)(cid:6) (cid:2) (cid:31)(cid:14)(cid:18)(cid:14)(cid:1)(cid:7)(cid:22)(cid:20)(cid:17)(cid:11)(cid:23)(cid:19)(cid:24)(cid:8)(cid:25)(cid:21)(cid:14)(cid:16) (cid:7) (cid:5)(cid:5)(cid:6) (cid:8) (cid:26)(cid:30)(cid:27)(cid:14)(cid:28)(cid:18)(cid:9)(cid:14)(cid:8)(cid:16)(cid:15)(cid:9)(cid:29) (cid:9) (cid:19)(cid:14) !(cid:11)!(cid:29)(cid:9)(cid:15)" (cid:18)(cid:18)(cid:19) #(cid:8) (cid:31)(cid:11)(cid:9)(cid:15)(cid:29)"
Fig. 1. Block diagram ofTDS-OFDMsystem. Theshaded blocks are the processing used forthe proposed method. Thedashed blocks are the additional
processingneeded fortheturbochannel estimation.
3. Using the pilots in a complementary way to the PN method does not cause error propagation due to imprudent
sequence to enhance the channel estimation. It is proposed hard decisions. The uncertainty (noise) is kept in the soft
to replace some data subcarriers by pilots to improve the datasymbolsandintheresultingdata-aidedchannelestimates
channelestimationperformancein[3].However,thespectrum as well. Moreover, we propose several improved techniques,
efficiency is compromised. Another possible solution is the namelyone-dimensional(1-D)/two-dimensional(2-D)moving
data-aided channel estimation method which uses the rebuilt averageandWienerfiltering,whichexploitthetime-frequency
data symbols as “virtual pilots” to make channel estimation correlation property of the channel to suppress the noise ex-
andthusdoesnotneedanyextrapilots.In[12],itisproposed isting in the data-aided channelestimates. The cooperationof
tomakeharddecisionstotheequalizedsymbolsthatfallinthe these refining techniques and soft symbol rebuilding achieves
reliable decision region. The hard decided data symbols are satisfactory channel estimation accuracy with low computa-
used as virtual pilots for channel estimation. However, this tional complexity. The final channel estimates combine the
method requires an additional PN frame header for several results obtained from PN and from data according to MMSE
OFDM symbol to obtain a good initial channel estimate. criteria.Theproposedmethodcanadapttodifficultsituations,
Therefore,itisnotstraightforwardlyapplicabletotheexisting including higher order constellations, extremely long channel
DTMB system. In [13], a turbo channel estimation algorithm spread and channel time variations.
is proposed in the context of CP-OFDM. An obvious disad- The rest of the paper is organized as follows. In section
vantage of this method is the extremely high complexity and II, the mobile channel and TDS-OFDM signal models are
long time delay, especially in the systems with sophisticated described. In section III, the PN based channel estimation is
channeldecoderanddeepinterleaver.Forexample,theDTMB presented. The new proposed data-aided channel estimation
systemadoptsLDPCcodesandconvolutionalinterleaverwith method is presented in section IV. Computational complexity
a time delay of 170 (or even 510) OFDM frames which is evaluated in section V. Simulation results are shown in
prohibits the using of such a method. section VI. Conclusions are drawn in section VII.
The aim of this paper is to propose a low-complex but Inthispaper,()∗ denotestheconjugateofcomplexnumber,
effective algorithm to increase the robustness of the channel E is the exp·ected value, ()T and ()H are the matrix
{·} · ·
estimation in TDS-OFDM compared to the already existing transpose and Hermitian transpose, respectively.
techniques described above. The highlights of algorithm pro-
posed in this paper are (a) excluding the channel decoder, II. SYSTEMMODEL
interleaver and de-interleaver from the iterative channel es- A. Discrete Channel Model for OFDM
timation process to reduce complexity, (b) rebuilding soft
The wireless channel is modeled as an Lth order time-
symbols for channel estimation to prevent error propagation,
varying finite impulse response (FIR) filter. The parameter L
(c)exploitingthecorrelationpropertyofthechannelto obtain
is determined by the maximum excess delay of the channel.
improved estimation results, and (d) minimum mean square
Thechannelisassumedtobequasi-static,namelychannelco-
error (MMSE) combination of channel estimates obtained
efficients remain constant within one OFDM symbolduration
from PN and data.
but change from one OFDM symbol to another. The channel
More concretely, we propose to rebuild the data symbols impulse response (CIR) for the ith OFDM symbol is:
usingthelikelihoodinformationfromthedemapper.Thenthe
L−1
instantaneousdata-aidedchannelestimates are acquiredusing
h[i,m]= h(i)δ[m l], (1)
these rebuilt data symbols. As the interleaving and channel l −
l=0
decodingprocesses are not included in the feedback loop, the X
computationalcomplexityissignificantlyreducedcomparedto where δ[] is the Kronecker delta function, h(i) is the lth filter
· l
theturbochannelestimation.Thesoftsymbolsarefedbackin tap and is modeled as zero mean complex Gaussian random
theiterationsservingasvirtualpilotsinthechannelestimation. variables. Furthermore, the channel filter taps are assumed
Sincenodecisionismadeontherebuiltsymbols,theproposed to follow the wide sense stationary uncorrelated scattering
3
(cid:19)(cid:26) (cid:17)#$(cid:17)#(cid:17)(cid:26)(cid:18)(cid:17)
(cid:16)(cid:17)(cid:18)(cid:17)(cid:19)(cid:20)(cid:17)(cid:21)(cid:7)(cid:22)(cid:5)(cid:23)(cid:24)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:19)(cid:25)(cid:26)(cid:27)(cid:13)(cid:28)
(cid:1)(cid:2) (cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:7)(cid:1) (cid:1)(cid:2) (cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:7)(cid:1)(cid:14)(cid:15)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:5)(cid:1) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:5)(cid:1)(cid:12)(cid:13)
hˆ
c cˆ Fig.3. Illustration oftheOLAprocess.
(cid:29)(cid:30)(cid:31)(cid:19)(cid:20)(cid:27)(cid:13)(cid:17)(cid:26) (cid:7)!"(cid:24)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:19)(cid:25)(cid:26)(cid:27)(cid:13)(cid:28) #(cid:17)(cid:8)(cid:19)(cid:21)(cid:31)(cid:27)(cid:13)(cid:7)"%(cid:7)(cid:8)(cid:17)(cid:30)(cid:31)(cid:17)(cid:26)(cid:18)(cid:17)
(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:7)(cid:1) (cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:7)(cid:1)(cid:14)(cid:15) After passing the multipath fading channel, the received
signal is a linear convolution of the transmitted signal and
Fig.2. PNremovaloftheTDS-OFDMsignal. the channel as given in (8) which is shown in the top of next
page,
where [n] is the residue of n modulo N and w is the
N
additive white Gaussian noise (AWGN) with a variance of
(WSSUS) assumption, namely different taps are statistically
σ2. From (8) and Fig. 2, it can be found that there are some
independent, while a specific tap is correlated in time. The w
channel frequency response (CFR) for the kth subcarrier of mutualinterferencebetweenthe OFDM data symbolsand the
the ith OFDM symbol can be obtained via an N-point FFT PN sequencesdue to the channelmemory.In orderto recover
the data symbols, it is necessary to remove the PN sequence
over the CIR:
from the received signal first. Since the PN sequence c(i)[n]
N−1
H[i,k]= h(i)e−j2Nπlk. (2) is perfectly known by the receiver, the channel-distorted PN
l sequence can be estimated by making a linear convolution of
Xl=0 PN sequence c(i)[n] and the estimated channel response hˆ(i):
Thetime-frequencycorrelationfunctionoftheCFRis[15]:
L−1
φH[p,q],E H[i+p,k+q]H∗[i,k] =rt[p]rf[q], (3) cˆ(i)[n]= hˆ(i)c(i)[n l], ν n<L 1. (9)
{ } l − − ≤ −
where rt[p] and rf[q] are the time and frequency domain Xl=0
correlation functions of the CFR, respectively. Concretely, Usingcˆ(i)[n],thePNsequenceisremovedfromthereceived
taking the Jakes’ mobile channel model, r [p] is [15]:
t signal as depicted in Fig. 2. If the channel is perfectly
estimated, the PN sequence and its tail can be completely
r [p]=J (2πpf T ), (4)
t 0 d b
removed from the received signal. Otherwise, there will be
whereJ0() isthe zero-orderBessel functionofthe first kind, someresidualcontributionofthe PN sequencein thereceived
·
and fd is the maximumDoppler frequencyrelated to velocity signal. The PN sequence removal is expressed in (10) which
vandcarrierfrequencyfc byfd =vfc/c,wherecisthespeed is given in the next page, where ∆h(i) = h(i) ˆh(i) is the
oflight,Tb isthetimedurationofoneOFDMblockandTb = estimation error of the lth channel tapl. l − l
Tg+T given Tg and T the durations of GI and OFDM data After removingthe PN sequence,the TDS-OFDM signalis
parts, respectively.The frequencydomaincorrelationrf[q] is: turned to an equivalent ZP-OFDM signal. Thus, the so-called
L−1 overlap and add (OLA) [3] process is performed by adding
rf[q]= σl2e−j2Nπql. (5) the following GI to the beginning part of the OFDM symbol
as shown in Fig. 3. More precisely, the OLA process can be
l=0
X
written as:
where σ2 is the power of the lth path. Without loss of
l
generality, the power of the channel is normalized so that y(i)(n)=r¯(i)(n)+r¯(i+1)(n ν), 0 n<L 1. (11)
L−1σ2 =1. − ≤ −
l=0 l
Suppose that the length of GI exceeds that of the channel,
P
there is no ISI between two adjacent OFDM symbols. Taking
B. TDS-OFDM Signal Model
(10) intoaccount,the receivedsignalafterremovingthe GI is
Fig. 1 presents the baseband model of the TDS-OFDM
written as:
based system. The ith OFDM data symbol is formed by N-
point inverse fast Fourier transform (IFFT): L−1
r(i)[n]= h(i)x(i)[n l] +w′[n]+ξ[n],0 n<N, (12)
N−1 l − N ≤
x(i)[n]= 1 X[i,k]ej2Nπnk,0 n N 1. (6) Xl=0
√N k=0 ≤ ≤ − where w′(n) is the noise after OLA which is slightly colored
X
A ν-length PN sequence c(i)[n] −1 is then inserted and boosted in the OLA process. The equivalent noise power
before x(i)[n] N−1 as GI. T{he ith t}rann=s−mνitted time domain is σw2′ = NN+νσw2 [3]. ξ[n] is the contribution of the residual
{ }n=0 PN sequence in the receivedsignal. From (12), it can be seen
signal is thus:
that the linear convolutionof the channeland data becomes a
c(i)[n] ν n<0 circular one after OLA process. Therefore, after fast Fourier
t(i)[n]= − ≤ . (7)
x(i)[n] 0 n N 1 transform (FFT), the received frequency domain TDS-OFDM
(cid:26) ≤ ≤ −
4
L−1
r(i)[n]= h(i)t(i)[n l]+w[n]
l −
l=0
X
n+νh(i)c(i)[n l]+ L−1 h(i)x(i−1)[n l] +w[n] ν n< ν+L 1
l=0 l − l=n+ν+1 l − N − ≤ − −
 PL−1h(i)c(i)[n l]+Pw[n] ν+L 1 n<0
=  Plnl==00h(lli)x(i)[n−−l]+ lL=−n1+ν+1hl(i)c(i)[n−l]+w[n] 0−≤n<−L−≤1 (8)
PL−1h(i)x(i)[n l]+Pw[n] L 1 n<N
 Pl=0 l − − ≤
r¯(i)[n]=r(i)[n] cˆ(i)[n]
−
n+ν∆h(i)c(i)[n l]+ L−1 h(i)x(i−1)[n l] +w[n] ν n< ν+L 1
l=0 l − l=n+1 l − N − ≤ − −
 PL−1∆h(i)c(i)[n l]+Pw[n] ν+L 1 n<0
=  Pnll==00h(li)xl(i)[n−−l]+ lL=−n1+1∆hl(i)c(i)[n−l]+w[n] 0−≤n<−L−≤1 (10)
PL−1h(i)x(i)[n l]+Pw[n] L 1 n<N
 Pl=0 l − − ≤
signal has finally a similar representation as CP-OFDM: As mentioned before, the channel estimation error results in
interference to the OFDM data symbols. From the analysis
N−1
1
Y[i,k]= y(i)[n]e−j2Nπnk=H[i,k]X[i,k]+W′[i,k] (13) given in the appendix, the power of the interference is com-
√N puted as:
n=0
X
where W′ is AWGN with the same variance as w′. The 1 L−1 ν−1
TDS-OFDM signal can thus be easily equalized by a one-tap σI2[k] = N σ∆2hl" |c[n]|2
equalizer: Xl=0 nX=0
Y[i,k] ν−1 2π ν−1−q
Z[i,k]= . (14) + 2cos kq c [n]∗c [n+q] .(18)
H[i,k] N l l
q=1 (cid:18) (cid:19) n=0 #
X X
III. PN-BASED CHANNEL ESTIMATION The part in the bracket of the above equation is only de-
As specified in [4], the ν-length PN sequence in the GI is termined by the PN sequence and is constant for a given
composed of an N -length PN sequence, more specifically sequence. Thus, the power of the interference is determined
PN
a maximum-lengthsequence (m-sequence),as well as its pre- by the length of channel L and the MSE of CIR estimation.
andpost-circularextensions.Sinceanyshiftofanm-sequence Hence, the worse the channel estimation, the more interfer-
is itself an m-sequence, the GI can also be treated as another ence will be introduced to the OFDM data symbols, which
N -length m-sequencewith its CP. If this CP is longer than motivates us to propose additional processing to improve the
PN
the length of CIR, the N -length PN sequence is ISI-free. channel estimation results.
PN
Using the ISI-free PN sequence, a least square (LS) channel
estimation is made for the ith OFDM symbol: IV. DATA-AIDEDCHANNEL ESTIMATION
S[i,k] W[i,k] A. Instantaneous Data-aided Channel Estimate
H¯ [i,k]= =H[i,k]+ ,0 k <N , (15)
1 P[i,k] P[i,k] ≤ PN In contrast to the classical turbo channel estimation al-
gorithm like [13], the new proposed method excludes the
where P and S are obtained through N -point FFT applied
PN
deinterleaving,channeldecodingand interleaving processings
onthetransmittedandreceivedISI-freePNsequences,respec-
fromthefeedbackloopasshowninFig.1.Inotherwords,the
tively. The CIR estimate is
soft data symbols used for data-aided channel estimation are
hˆ[i,l]= N1 NPN−1H¯1[i,k]ejN2PπNkl. (16) rebTuhilet usosifnt-gouthtpeultikdeelimhoaopdpeirnfdoermmoadtiuolnatfersomthethecodmemplaepxpdera.ta
PN
Xk=0 symbolsintoLog-likelihoodratio(LLR)ofbits[16].TheLLR
Consequently, the N-length CFR estimation Hˆ1 is obtained λl[i,k] corresponding to the lth bit of the (i,k)th equalized
by applyingN-pointFFT on ˆh[i,l]. Themean squareerrorof data symbol Z[i,k] is defined as:
Hˆ is:
1 P (b[i,k,l]=1Z[i,k])
λ [i,k] , log | , (19)
1N−1 Lσ2NPN−1 1 l P (b[i,k,l]=0Z[i,k])
ε = E H[i,k] Hˆ [i,k]2 = w . |
Hˆ1 N | − 1 | NPN P[i,k]2 where the P (b[i,k,l]=1Z[i,k]) is the conditional proba-
Xk=0 n o Xk=0| |(17) bility of the lth bit equal| to 1 given Z[i,k]. The sign of
5
the LLR decides the corresponding bit equal to 1 or 0, correlation of the CFR. Several channel estimate refinement
and its absolute value gives the reliability of the decision. approachesare proposedin the followingsections. According
Based on the LLR, the probabilities of a bit equal to 1 and to the time-frequency range that data-aided approaches work,
0 are P (b[i,k,l]=1) = eλl[i,k] and P (b[i,k,l]=0) = they are catalogued into 1-D (frequency domain) and 2-D
1+eλl[i,k]
1 P(b[i,k,l]=1), respectively. Then they are used as a (time-frequencydomain) ones.
−
priori probabilities to estimate the data symbols. First, the
probability that the transmitted symbol X[i,k] is equal to a
B. 1-D Refinements
specific constellation point α is computed as the product of
j
the probabilitiesof all the bits belongingto this constellation: The proposed 1-D refinement approaches process all the
instantaneousdata-aidedchannelestimates within one OFDM
log µ
2
symboltogetanimprovedestimationresultateachtime.Only
P(X[i,k]=α )= P b[i,k,l]=κ (α ) , (20)
j l j
the frequency domain correlation property of the channel is
l=1
Y (cid:0) (cid:1) exploited. As the 1-D refinement approaches are carried out
whereΨisthesetoftheconstellationpointsofagivenmodu-
ina (OFDM)symbol-by-symbolfashion,theycantracka fast
lation scheme, µ is the modulation order and κ (α ) 0,1
l j ∈{ } variationofthechannelandrequireminimumstoragecapacity.
is the value of the lth bit of the constellation point α . The
j The OFDM symbol index i is omitted in this section for the
soft data symbol is an expected value taking the a priori
sake of notation simplicity.
probabilities (20) into account:
1) Moving Average: Since the channel frequency response
Xˆ[i,k]= α P(X[i,k]=α ). (21) is almost identicalwithin coherencebandwidth[17], the most
j j
·
αXj∈Ψ straightforwardwaytoimprovethedata-aidedestimationisto
performamovingaverageovertheinstantaneouschannelesti-
Note that, being different from the classical decision feed-
mateswith a lengthless or equalto the coherencebandwidth.
back channel estimation methods such as [10] and [15], no
More specifically, the instantaneous channel estimates within
decision is made here in order to prevent error propagation.
a particular range, namely within a “window”, are averaged
Directlyusingthesoftdatasymbols,aninstantaneouschannel
to get a more precise estimate for the central position of the
estimate is obtained over all active subcarriers by:
window.Afterthewindowslidingoverallactivesubcarriers,a
H˜ [i,k]= 1 Xˆ[i,k]∗Y[i,k] refinedchannelestimationisobtained.Concretely,themoving-
2
ηXˆ[i,k] averaged CFR for the kth subcarrier is expressed as:
Xˆ[i,k]∗X[i,k] 1
= H[i,k]+ Xˆ[i,k]∗W′′[i,k],(22)
ηXˆ[i,k] ηXˆ[i,k] H¯ [k]= 1 H˜ [m]
2 2
where W′′[i,k] is the noise and interference component with M
a variance σW2 ′′ = σW2 ′ + σI2, ηXˆ[i,k] = |Xˆ[i,k]|2 is the H[k] Xˆ[mm]X∗∈XΘ[km] 1 Xˆ[m]∗W′′[m]
powerof the (i,k)th softdata symbolwhich is used as power +
≈ M η [m] M η [m]
normalizationfactor. Note that, the power of the constellation mX∈Θk Xˆ mX∈Θk Xˆ
is a constant and known value in the uniform power constel- 1 Xˆ[m]∗W′′[m]
H[k]+ ,0 k N 1, (24)
lation cases such as BPSK or QPSK. Hence, the η [i,k] can
beapproximatedbythepoweroftheconstellationηXˆα inorder ≈ MmX∈Θk ηXˆ[m] ≤ ≤ −
to reduce computational complexity. If the data symbols are where Θ = k M−1 ,k M−1 +1,...,k+ M−1
perfectly rebuilt, e.g. SNR is high, namely Xˆ[i,k]= X[i,k], k { −⌊ 2 ⌋ −⌊ 2 ⌋ ⌊ 2 ⌋}
is the set of subcarrier indices within the moving average
(22) turns to an LS estimator:
windowwith thekth subcarrierits centralfrequency,M isthe
W′′[i,k] length of the moving average window and W′′ is the noise
H˜ [i,k]=H[i,k]+ . (23)
2 η [i,k] andinterferencecomponent.ThemovingaveragelengthM is
X
chosenlessthanorequaltothecoherencebandwidth.Itcanbe
Unlike the turbo channel estimatipon, the proposed method either empirically pre-selected according to the “worst case”
does not include any error correction before rebuilding the
or be adaptively chosen by computing the coherence band-
data. Therefore the rebuilt soft data symbols, i.e. Xˆ’s, are
width using the estimated CIR from initial PN based channel
affected by the noise as well as the channel fades. It is quite
estimation.The variance of the data-aidedCFR estimate for a
possible that the instantaneous channel estimate (22) is inac-
specific subcarrier is:
curate and even erroneous for some subcarriers. Fortunately,
as both the time delay spread and Doppler spectrum of the
channel are limited, the CFR is highly correlated, i.e. almost σ2 [i,k]=E H[i,k] H¯ [i,k] 2
identical within the coherence bandwidth and coherence time H¯2 − 2
[17].Moreover,thecoherencebandwidthspreadsoverseveral = E 1 Xˆn[i(cid:12)(cid:12),m]W′′[i,m] 2 (cid:12)(cid:12) o
adjacentsubcarriersintheOFDMsystemwithlargeFFTsize, M η [i,m]
asynmdbthoelcdouhrearteionncsetiinmeloiwsnaonrmdamllyedloiunmgervtehloancistyevcearaslesO.FTDhMis = σnW2(cid:12)(cid:12)(cid:12)′′ mX∈Θ|kXˆ[i,mX]ˆ|2 =σW2 ′′ (cid:12)(cid:12)(cid:12) o 1 . (25)
enablesustorefinethedata-aidedchannelestimationusingthe M2mX∈Θk ηXˆ[i,m]2 M2mX∈Θk ηXˆ[i,m]
6
(cid:5)(cid:6)(cid:4)(cid:7)(cid:8)(cid:4)(cid:9)(cid:10)(cid:11)
(cid:15)(cid:1)(cid:16) (cid:16)(cid:3)(cid:21)(cid:22)(cid:9)(cid:15)(cid:1)(cid:16)
(cid:17)(cid:18)(cid:19)(cid:10)(cid:20)(cid:21)(cid:19)(cid:3)(cid:11)(cid:9)(cid:15)(cid:1)(cid:16) H~(k) (cid:23) (cid:23) (cid:23) (cid:23) (cid:23)
(cid:15)(cid:1)(cid:16)(cid:9)(cid:18)(cid:21)(cid:20)(cid:23)(cid:22)(cid:3)(cid:18)(cid:9)(cid:10)(cid:6)(cid:9)(cid:19)(cid:25)(cid:3)(cid:9)(cid:23)(cid:10)(cid:22)(cid:24)(cid:19)(cid:18) H(k)
p
(cid:24)
(cid:24)
(cid:20)(cid:21)(cid:4)(cid:6)(cid:14)(cid:22)(cid:2)(cid:9)(cid:22)(cid:16)(cid:6)(cid:4)(cid:22)(cid:2)(cid:18)(cid:9)
(cid:24)
(cid:5)
(cid:2)
(cid:5)
(cid:3) (cid:1)
(cid:2) (cid:2)
(cid:12)(cid:2)(cid:6)(cid:13)(cid:8)(cid:14)(cid:15)(cid:16)(cid:17)(cid:2)(cid:15)(cid:18)(cid:13)
(cid:7)(cid:24)(cid:25)(cid:3)(cid:2)(cid:3)(cid:6)(cid:7)(cid:3)(cid:9) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:3)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:6)(cid:11)(cid:3)(cid:12)(cid:9)(cid:13)(cid:1)(cid:14) (cid:24) (cid:2)(cid:9)(cid:19)(cid:13)(cid:14)(cid:9)(cid:13)(cid:14)(cid:9)(cid:4)(cid:18)(cid:8)(cid:19)(cid:16)(cid:4)(cid:19)(cid:13)(cid:2)(cid:3)(cid:14)(cid:13)(cid:4)
(cid:26)(cid:21)(cid:6)(cid:11)(cid:27)(cid:10)(cid:11)(cid:19)(cid:25) (cid:23)(cid:10)(cid:22)(cid:24)(cid:19)(cid:9)(cid:23)(cid:24)(cid:18)(cid:10)(cid:19)(cid:10)(cid:24)(cid:6)(cid:9)(cid:1)(cid:3)(cid:4) (cid:1)(cid:3) (cid:1)(cid:2)(cid:3)(cid:4)
(cid:4)
Fig.4. 1-Daveragingandinterpolation.
Fig.5. 2-Daveraging andinterpolating. Theaveraging isperformed inthe
2-D averaging region (shaded area). The interpolation is first carried out in
thefrequency domain((cid:13)1)andconsequently inthetimedomain((cid:13)2).
The MSE of the data-aided CFR estimate for the ith OFDM
symbolcanbeestimatedbyaveraging(25)overN subcarriers:
vectorisHˆ = Hˆ [0],Hˆ [1],...,Hˆ [N 1] T andthevector
N−1 2 2 2 2 −
εH¯2,1D = N1 E H[i,k]−H¯2[i,k] 2 fcooremfficoifenCtsFoRf Wi(cid:2)sieHn2er=filteHr ω[0],aHre[1e]x,p.r.e.s,sHed(cid:3)[Nas:− 1] T. The
kX=0 n(cid:12) (cid:12) o (cid:2) f (cid:3)
= σW2 ′′ N−1 1(cid:12) . (cid:12) (26) ωf =Φ−f1θf, (29)
NM2 η [i,m]
Xk=0 mX∈Θk Xˆ where ωf is the Kf N coefficient matrix of Wiener filter
Specifically, given the uniform power constellation with a with the (m,n)th ele×ment ω [m,n], Φ = E H¯ H¯H =
power of ηα, (R(1)+σ2 I) is the K K fautocorrelaftionma{trix2 o2f C}FR
εH¯2,1D =(MσηW2 )′′2NN−1 |Xˆ[k]|2=MσW2η′′2η¯Xˆ, (27) tehsetfimvaartiiaonnHc¯es2aomfpthleeseosntimpfial×toiotnpfoesrirtoiornH¯s2odbetariivneeddiinn((2264)),,IσiH2¯s2thies
dwahtaerseyη¯mXˆbo=ls.N1 Nkα=−01|XˆkX[=k0]|m2X∈isΘtkhemeanpoweαroftherebuilt icRdo(fer1nr)etilatayntidomnRatm(fr2i)axt.arirθxefoth=feCEaFu{RtH¯oc2eoHstri}rme=laatteiRosn(fH2¯)m2iasatnrtihdxetohKfeftrhe×ealrNeCaFlcRrCoFsHsR-.
2) Wiener FiPltering: The proposed Wiener filtering based inthefrequencydomain,anditscomponentscanbecomputed
refinement is depicted in Fig.4. It consists of two steps: by (5). Note that the coefficients can be computed in either
averaging and interpolation. non-adaptive [18] or adaptive manners [19]. The MSE of the
A bunch of subcarriers are first selected as “virtual pilots”. CFR estimate after frequency domain filtering is:
Ttehrmesvirotfuaslupbiclaortrsiearrse)eiqsusaelllyecstepdacesdubasntadnttihaellyspfauclifinlglinLgf t(hine εHˆ2,1D = N1 Tr R(f3)−R(f2)TΦ−f1R(f2)∗ , (30)
sampling theorem [18]. More concretely,with a 2 oversam- (cid:16) (cid:17)
pling ratio, L is determined so that L L/N 1×/4. Denote where Tr() is the trace operation, R(3) is the N N
f f ≤ · f ×
Ξtheset ofvirtualpilotsindices,i.e. Ξ= k k =pL ,0 autocorrelation matrix of CFR.
p p f
{ ≤
p N 1 . The cardinality of Ξ (the quantity of virtual
≤ ⌊Lf⌋− } (cid:12)
pilots) is K . (cid:12)
f C. 2-D Refinements
The instantaneous channel estimates within the coherence
bandwidtharounda virtualpilot k Ξ are averagedto get a As presented in above, 1-D refinement approaches only
p
more accurate channel estimate H¯ [k∈]. Its expression can be exploit the frequency domain correlation property of the
2 p
obtained by setting k = k in (24). Repeating the averaging channel. More processing gain can be acquired if the time
p
process in all virtual pilot positions, we can get K accurate domain correlation property is also taken into account.
f
CFR estimation samples H¯ [k ], k Ξ. 1) 2-D Moving Average: Expanding the average range in
2 p p
To obtain the N-length CFR∀est∈imation Hˆ , a Wiener (24) to 2-D, namely to several consecutive OFDM symbols,
2
filtering [18] based interpolation is performed on these CFR more instantaneous channel estimates can be involved in the
estimation samples: movingaverageprocess.Withaproperselectionoftheaverag-
inglengthinthetimedomainwithrespecttothetimevariation
Hˆ [k]= ω [k,k ]H¯ [k ], 0 k N 1, (28)
2 f p 2 p ≤ ≤ − of the channel, the 2-D moving averaged results are expected
kXp∈Ξ to be better than the 1-D counterpart. More specifically, the
where ω [k,k ]’s are the Wiener filter coefficients com- subcarrier indices within the 2-D averaging region with the
f p
puted to minimize the estimation MSE E H(k) kth subcarrier of the ith OFDM symbol its central position
Hˆ (k) 2 . Rearrange the samples in vector{f|orm H¯ =− is given by the set Θ = (p,q) i Mt−1 p
H¯22[k0],|H¯}2[k1],...,H¯2[kKf−1] T. Accordingly, the ou2tput i + ⌊Mt2−1⌋,k − ⌊Mf2−i1,k⌋ ≤ q(cid:8)≤ k(cid:12)+−⌊M⌊f2−21⌋ ⌋. T≤he 2-≤D
(cid:12)
(cid:2) (cid:3) (cid:9)
7
moving-averagedCFR estimates are written as: optimum 2-D Wiener filter [18]. The 2 1-D Wiener filtering
×
is represented as:
1
H¯ [i,k]= H˜ [p,q]
2 MtMf p,qX∈Θi,k 2 Hˆ2[i,k]= ωt[i,k,ip] ωf[k,ip,kp]H¯2[ip,kp], (34)
1 Xˆ[p,q]∗W′′ Xip Xkp
H[i,k]+ . (31)
≈ M M η [p,q] timedomain frequencydomain
t f p,qX∈Θi,k Xˆ where ωt’s an|d ωf’{szare t}h|e coeffi{czients o}f the 1-D Wiener
The variance of the estimation error in (31) is then: filter in the time and frequency domains, respectively. The
coefficients of the frequency domain Wiener filter are the
σ2 [i,k]=E H[i,k] H¯ [i,k]2
H¯2 {| − 2 | } same as those givenin (29). Let us define the filtered channel
== Enσ(cid:12)(cid:12)(cid:12)W2MW′t′M′′fp,qX∈Θi,kηXˆXˆ[[pi1,,qk]](cid:12)(cid:12)(cid:12).2o (32) fiiiessslttHeig¯mri2vai[esmtned,eminnna]o.t(tr2Teix9dh)eHa.¯soT2uahontepfuNsctioz×orefrKeKtshtpefomf×nradetKiqrniuxgtewnHˆMchf2ySo=Esdeoωom(fmTfaitH,¯nhne21),t-ewhDstheiWemleremaietωineonefnrt
(MtMf)2 p,qX∈Θi,k ηXˆ[p,q] aftTerhefrecqouefefincciyendtosmoafitnheWtiiemneerdfiolmteariinngWisiesnheorwfinlteinr a(r3e0)c.om-
The MSE of the 2-D moving averaged CFR is: puted as:
= ε(HM¯2t,σ2MWD2f′=′)2NN1 NXkNkX=−=−0101p,EqX∈nΘ(cid:12)(cid:12)iH,kη[iXˆ,k[1p],−q]H.¯2[i,k](cid:12)(cid:12)2o (33) wiaEsuhttHeoˆhrcefeoTrvΦrHaertl∗iaa=tnio=cEneR{moH(ˆfa2f2)ttrThiiexsHˆωteof2htsf∗et=}itmhK=Φeatfi−ti(ol1RtnθeB(trt1ee,)rcdr+rooCrsσFsdH-2Rˆec2froeiIrvs)reteidilmsatiaitntohene(s3mKH0ˆ)af2t.t,r×θiσ(xt3HK2ˆo5=2ftf)
2) 2-D Wiener Filtering: The 2-D estimate refinementand { 2,k t} t t×
interpolation is carried out over a number of OFDM symbols CFR estimates for the kth subcarrier with different time Hˆf
2,k
within an interpolation block as shown in Fig. 5. The block andtherealCFRforaparticularsubcarrierwithdifferenttime
size B, i.e. the number of OFDM symbols in the block, is Ht.Finally,R(t1) andR(t2) aretheautocorrelationmatrixofthe
chosen according to the constraints of latency, storage and realCFRinthetimedomain,anditscomponentsarecomputed
complexity. by (4).
For low-complexityconsideration,some time-frequencyin- The MSE of the CFR estimate after time domain filtering
dices (i ,k ) Ω are pre-selected as virtual pilots. L and is:
L are tpheqvir∈tual pilot spacings in the frequency andftime ε = 1Tr R(3) R(2)TΦ−1R(2)∗ . (36)
dotmains, while K = N and K = B are the number Hˆ2,2D B t − t t t
f ⌊Lf⌋ t ⌊Lt⌋ According to the Jakes(cid:16)’ model, the coefficients(cid:17)of the time
of virtual pilots within one OFDM symbol and the number
domain Wiener filter are only determined by the Doppler
of OFDM symbols including virtual pilots, respectively. The
frequency. Note that, since the time domain interpolation
selectionofvirtualpilotsinthefrequencydomainisdiscussed
lengthis notverylarge,the computationof the coefficientsof
in the previous section. The selection in the time domain
time domain Wiener filter is not prohibitive.It should be also
should also satisfy the sampling theorem.In a similar manner
noted that the same coefficients are used for all subcarriers,
as in the frequency domain, the spacing between virtual
which indicates that the storage spent for these coefficients is
symbols in the time domain L (in terms of OFDM symbols)
t
negligible compared with the size of interleaver.
is selected so that L T f 1/4. Hence, the set of indices of
t b d
≤ Concerning the frequency domain Wiener filter, the coef-
virtualpilotsisΩ= (i ,k ) i =pL ,0 p K 1;k =
p q p t t q
≤ ≤ − ficients can be pre-computed according to the uniform delay
qL ,0 q K 1 .
f f
≤ ≤ −(cid:8) (cid:12) powerspectrumassumptionwhichrepresentsthe“worstcase”
Then a refined CFR estim(cid:12)ate for the virtual pilot located
(cid:9) of the mobile channel [18]. Given a virtual pilot pattern,
at (i ,k ) is computed by averaging all the available CFR
p p
the values of the coefficients only depend on the maximum
estimates within the coherence region Θ . The averaged
ip,kq delay spreadof the channelwhich can be measuredin reality.
estimate can be obtained from (31) by setting i = i and
p
Therefore, the coefficients can be pre-computed with some
k = k . Repeating this process over all virtual pilots in
p
typical channel situations. Even more complexity reduction
the interpolation block, K K refined CFR estimates are
t f
· can be achieved by limiting the Wiener filtering on several
acquired. With these more reliable estimates, the overallCFR
neighboring pilots [20].
estimate can be obtained via interpolation.
The 2-D Wiener filtering outperforms other interpolation
D. MMSE Combination
techniques, e.g. linear interpolation, FFT-based interpolation
etc. [20]. The use of two concatenated 1-D Wiener filters, When both PN-based and data-aided channel estimates are
i.e. one in the frequency domain and the other in the time obtained, a linear combinationis proposed to get a final CFR
domain, significantly reduces the computational complexity estimate:
with negligible performance degradation compared to the Hˆ =βHˆ +(1 β)Hˆ , (37)
1 2
−
8
TABLEI
COMPLEXITYANDSTORAGECOMPARISON
Method Complexity Storage
PNbasedmethod O(ν·logν) ν complexsymbols
Proposed Movingaverage O(N) OneOFDMsymbolfor1-Dmethods,B
method Wienerfiltering O(N)toO(N2) OFDMsymbolsfor2-Dmethods.
MUCK03[2] O(ν·logν)whenM ≪ν,O(ν2)otherwise M OFDMsymbolsa
YANG08[11] O(K·logK)b OneOFDMsymbolandoneGI
WANG05[1] O(N·logN) TwoOFDMsymbols
TANG07[9] O((N+ν)·log(N+ν)) OneOFDMsymbolandoneGI
STEENDAM07 [3] O(N3) OneOFDMsymbol
(O(N)+complexityofdecoding)foriteration, Storageshouldbegreaterthantheinterleav-
ZHAO08[13] O(N2)orO(N3)forfinalstage ingdepth. c
aThe parameter M is the length of the averaging window. It is set to 20 to 40 OFDM symbols for BPSK and QPSK, 40 to 72
OFDMsymbolsfor16QAMand120to240for64QAM.
bKisthesizeofFFT/IFFTusedtobuildthereceived PNsequence andmakechannel estimation. Itcanbeselected fromν+Lto
N orevenlarger. Kissetto2048in[11].
cAsfarastheDTMBsystemisconcerned, theinterleaving depthis170or510OFDMsymbols.
where Hˆ is a generic expression of the data-aided channel estimation method. The complexity is evaluated in terms of
2
estimations which can be obtained from (24), (28), (31) or requiredrealmultiplicationsandrealadditionsforeachOFDM
(34)usingdifferenttechniques.Thecombinationiscarriedout symbolperiteration.Inthispaperonecomplexmultiplication
onlyfortheactivesubcarrierswhiletheCFRestimatesfornull is counted as 2 real additions and 4 real multiplications al-
subcarriersare keptasthe resultsobtainedfromthePN-based thoughthereexistsomesmarterwaysrequiringfewermultipli-
one. The optimum weight values β can be obtained using cation times. The data rebuilding process including (19), (20)
opt
the MMSE criteria: and(21)needs(N µlog µ+N 2log µ)multiplicationsand
· 2 · 2
N 2log µadditions.Theinstantaneousdata-aidedestimation
β =argmin E H Hˆ 2 · 2
opt β {| − | } (22) needs 8N multiplications and 3N additions.
n o The computational complexities required by the estimate
= argmin β2ε +(1 β)2ε . (38)
β Hˆ1 − Hˆ2 refinementvary with respect to differentstrategies. For the 1-
n o D moving average method, the averaging for each subcarrier
TheaboveequationusesthefactthatHˆ andHˆ areobtained
1 2 with an averaging length of M requires 2(M 1) additions
from different sources and thus uncorrelated. Since the MSE −
and 2 multiplications neglecting the edge effect. Hence, the
function is convex, the β is obtained by setting the deriva-
opt moving averaging over N subcarriers requires 2(M 1)N
tive with respect to β equal to zero and the solution is: −
additionsand2N multiplications.Thecombinationofthetwo
β = εHˆ2 , (39) channel estimates requires 2N additions and 4N multiplica-
opt ε +ε tions.Theoverallbasicoperationsare (µ+2)log µ+14 N
Hˆ1 Hˆ2 2
multiplications and (2log µ+2M +3)N additions for each
where ε is MSE of the PN-based estimation obtained 2 (cid:0) (cid:1)
Hˆ1 iteration.GivenM N,theadditionalcomplexityofthe1-D
from (17), while ε is the MSE of the data-aided channel ≪
Hˆ2 moving average based channel estimation is (N).
estimation and is computed from (26), (30), (32) or (36) O
The 2-D moving average method, on the other hand, has
depending on different methods.
generally the same computational complexity except that the
The proposed method can be carried out in an iterative
averagingprocessforeachsubcarrierrequires2(M M 1)N
manner. More precisely, if it has not achieved the preset t f−
additions and 2N multiplications and the overall required
maximum iteration times yet, the combined CFR estimates
additions turns to (2log µ + 2M M + 3)N. Given the
(37) are used as the initial channel estimates of the next 2 t f
conditionM M N fulfilled,thecomplexityisstill (N).
channel estimation iteration for PN subtraction and symbol t f ≪ O
As far as the Wiener filtering based approaches are con-
equalization. The equalized data symbols using the updated
cerned, for the K virtual pilot in each OFDM symbol, the
channel estimates are more accurate than previous iterations.
averaging of the instantaneous estimates in the coherence
Hence, more reliable data-aided channel estimates can be
bandwidth requires 2(M 1)K real additions and 2K real
acquired in the new iteration. If the the maximum iteration −
multiplications. As the coefficients of the Wiener filter is
times are achieved, the combined channel estimates output as
real[18], the Wienerfilteringneeds2KN multiplicationsand
the final channel estimates for the data equalization and FEC
2KN additions. Taking the symbol rebuilding and combi-
decoding.
nation into account, the overall operations for 1-D Wiener
filteringbased methodis (2log µ+5+2K)N+2(M 1)K
V. COMPLEXITY ANALYSIS additionsand (µ+2)log µ+212+2K N+2K mult−iplica-
2
In this section, we analyze the additional computational tions, which is between (N) and (N2).
(cid:0) O O (cid:1)
complexity introduced by the proposed data-aided channel For the 2-D Wiener filtering case, in each block consisting
9
100 10−1
TU−6
SFN
SNR = 10 dB
10−1 SFN SSNNRR == 2300 ddBB
10−2
10−2
E E
S S
M M
10−3
10−3
PN based estimation
1−D Moving Average
10−4 1−D Wiener filtering
1st iteration
2nd iteration TU−6
3rd iteration
10−5 10−4
5 10 15 20 25 30 1 3 5 7 9 11 13 15
SNR (dB) Moving averge length (subcarriers)
Fig.6. MSEoftheproposeddata-aidedchannelestimationusing1-DMoving Fig. 7. MSE ofthe 1-D Moving average method before combination with
Averageand1-DWienerfilteringwithQPSK,intheTU-6channelandSFN different averaging lengths.
channels withvelocity of30km/h.
frequency.Thesignal fromthese two transmittersexperiences
of B OFDM symbols, the averaging and 1-D frequency
independent fading. The equivalent CIR of the SFN channel
domain Wiener filtering is repeated K times which counts
t is the combination of the CIR’s of two independent TU-6
2(N+M M 1)K K additionsand2(N+1)K K multipli-
t f f t f t channels.Thepropagationdistancedifferencebetweenthetwo
−
cations.Then,thetimedomainWienerfilteringneeds2K BN
t signalscausestimedelayandpowerattenuationonthesecond
multiplicationsandadditions.Therefore,theoveralloperations
CIR [14]. In this paper, the distance difference is set to 7
perOFDMsymbolperiterationfor2-DWienerfilteringbased
km corresponding to 23.33 µs time delay which makes the
methodis (µ+2)log µ+12+2Kf+2K N+2Kf multipli-
cations and(cid:0)(2log2µ+2 5+2KLft +Lt2Kt)Nt(cid:1)+2(MtLMtf−B1)KtKf oPvNe.raTllhelenpgotwheorfatthteenuCaItRionlonisgesretthtaon1th0atdBof. FthoelloCwPinogf tthhee
additions, which is, similar to the 1-D Wiener filtering case, computation in [17], when the frequency correlation function
between (N) and (N2). Even lower complexity can be is 0.9, the coherence bandwidths of the TU-6 channel and
O O
achieved by reducing the size of the Wiener filter. the SFN channel are 18.8 kHz and 2.94 kHz, respectively.
The computational complexities of proposed method and Given the 2 kHz subcarrier spacing in the DTMB system, the
several typical existing methods [2], [3], [7], [9], [11], [13] frequencydomain averaging length M is accordinglyset to 9
are shown in Table I. From the comparison, we find that and3fortheTU-6andSFNchannels,respectively.Thevirtual
the methodMUCK03 achievesleast computationalcomplexity pilotspacingsinthefrequencyandtimedomainsaresetequal
but requires a large amount of storage. The proposed method to the averaging lengths in each domain, respectively.
using moving average needs less complexity than rest of
other methods. In the meantime, the complexity and storage
B. MSE Performance
costs of proposed method using Wiener filtering are close to
the methods WANG05, TANG07 and YANG08. The methods Fig.6 presents the MSE performance of the proposed al-
STEENDAM07andZHAO08spendmorecomplexitythanother gorithm with QPSK, using 1-D moving average and 1-D
techniques. Wiener filtering in the TU-6 and SFN channels, respectively.
It can be observed that the accuracy of the channel esti-
mation is progressively improved. The iterative estimation
VI. SIMULATION RESULTS
process converges very fast. A significant improvement can
A. Simulation Settings
be obtained after only two iterations. More specifically, in
Simulation parameters are chosen from the DTMB sys- the TU-6 channel, when the 1-D moving average is used,
tem [4]. Baseband signal bandwidth is 7.56 MHz. FFT size the proposed data-aided channel estimation method acquires
is 3780 which results in a subcarrier spacing of 2 kHz. All about 4.1 dB gain in terms of required SNR to achieve
subcarriers are active. The length of the GI is set to ν =420. an MSE level of 1 10−2 compared with the PN-based
×
The power of the PN sequence is twice as muchas data sym- one. If the more powerful 1-D Wiener filtering technique is
bols.TheCOST207TypicalUrban(TU-6)channelmodel[21] adopted, the gain increases to 5.1 dB. The higher the SNR,
is employed in the simulation. The proposed algorithm is the more efficientthe Wiener filtering. Moreover,it should be
alsoevaluatedinthesinglefrequencynetwork(SFN)scenario noted thatthe performanceof using Wiener filtering after one
whichisaspectrumefficientsolutionwidelyusedinbroadcast iterationisasgoodasthebestperformancethatusingmoving
networks. In this case, the same signal is sent from two averagetechniquecanachieve.Thisprovidesalessprocessing
different transmitters at the same time on the same carrier delay (less iterations) trade-off with higher computational
10
100 100
10−1 SFN 10−1 SFN
10−2 10−2
MSE MSE
10−3 10−3
PN based estimation
10−4 P2−ND b Masoevdin egs Atimveartaiogne 10−4 1664QQAAMM
2−D Wiener filtering 6km/h
16QAM TU−6 30km/h
64QAM
10−55 10 15 20 25 30 10−5 80km/h TU−6
5 10 15 20 25 30
SNR (dB)
SNR (dB)
Fig.8. MSEperformanceoftheproposedmethodaftertwoiterationsusing
Fig.9. MSEperformanceoftheproposedmethodusing2-DWienerfiltering
T62k-UDm-6/mhcofhvoairnnngbeoaltvhaenTradUgMe-6atna=nddW2S,iFeMnNefrchfi=altne3nreifnlosgr.mtheethSoFdNs.cMhatn=nel2.,VMelofc=ity9isfosretthtoe mtheethToUd-6afctehrantwneoliatnerdatMionts=w2it,hMdifffe=ren3tfvoerlothceitiSeFs.NMchta=nne2l,. Mf =9 for
with such a short averaging length in the time domain, the 2-
complexity for each iteration. On the other hand, in the SFN
D method can still provide effective estimation. For instance,
channel,since the delayspreadismuchlongerthan theCP of
the proposed method using 2-D Wiener filtering acquires 8.4
the PN sequence, there is a strong ISI on the PN sequence.
dB gain over the PN-based method in terms of the required
This can be observed from the fact that the performance of
SNRtoachieveanMSElevelof1 10−3with16QAMinthe
the PN-based channel estimation is seriously degraded and ×
TU-6 channel. In the SFN channel, the improvement is also
appears an estimation error floor at high SNR. Furthermore,
significant.Theestimationerrorfloorisreducedfrom2 10−2
as the averaging length is much shorter in the SFN case, the to 3 10−3 with 16QAM at a SNR of 30 dB. Given×longer
noise mitigation ability is limited in the data-aided channel ×
time domain averaging length, more gain can be expected in
estimation. Even though in such a harsh channel, the data-
a static channel.
aidedmethodhoweveroffers6.9dBand8.1dBgainin terms
Fig.9 presents the changing of the MSE performance with
of required SNR to achieve MSE of 5 10−2 compared to
× different velocities of the receiver in the TU-6 and SFN
the PN based method, when using the 1-D moving average
channels.Withtheincreaseofthevelocity,thevariationofthe
and Wiener filtering, respectively. Moreover, the estimation
channelamongconsecutiveOFDMsymbolsismoreandmore
performanceisimprovedapproximatelytentimesathighSNR
notable, which limits the accuracy in the averaging results
region.
in (31). In low SNR region (e.g. SNR less than 10 dB), the
Fig.7 depicts the impact of the averaging length to the
channelvariationis a less significantinfluencethataffectsthe
performance of 1-D moving average based method. At a low
estimation performance compared to the noise. Whereas in a
SNR, e.g. 10 dB, the MSE is monotonically decreasing with
higherSNR regionwhere the noise is no longer the dominant
the increase of the averaging length. However, at a higher
factor, the channel variation compromises the performance of
SNR, e.g. at 30 dB, the MSE of the averaged estimation
the proposed method. However, it should be noted that the
results is degraded with a long averaging length. Hence, a
proposedmethodcanstill provideadequateimprovement.For
moderateaveraginglength,sayM =7 9,isaproperchoice.
∼ instance, in the TU-6 channel with a velocity of 30 km/h, the
Considering that the data-aided channel estimation is more
proposed method obtains 8.3 dB gain with 16QAM in terms
crucial in lower SNR region, it is better to bias our selection of required SNR to achieve MSE of 1 10−3. While in SFN
to a greater length. Therefore,M =9 is a good trade-off that ×
channel,astheISIisthedominantfactorthataffectstheMSE
suitsallnoiselevelfortheTU-6channel,whichcoincideswith
results. Therefore, the impact of the channel variation is not
the selection according to the coherence bandwidth. Similar
significant.
conclusion can be drawn in the SFN channel. M = 3 is the
best trade-off of the averaging length in the SFN channel.
C. BER Performance
Fig.8 shows the MSE of proposed 2-D method after two
iterations. As the 1-D method is proved to be effective with In this subsection, we present the bit error rate (BER) per-
QPSK, the 2-D method is only evaluated with higher order formanceof the DTMB system using the proposeddata-aided
constellations, namely 16QAM and 64QAM. The averaging channelestimationmethod.Boththeconvolutionalinterleaver,
length in the time domain is selected to M = 2 which BCH code and LDPC code are included in the simulation
t
is a very conservative setting that only requires the channel in order to give a system level evaluation. The convolutional
keepingsimilarwithintwoconsecutiveOFDMsymbols.Even interleaver is set to (52,240) which corresponds to a time