evaluation of preamble based channel estimation for mimo⁃fbmc

DEMAG2016-10-53VOL13F3VFTmdashmdash8PPSP

Evaluation of Preamble Based Channel Estimation forEvaluation of Preamble Based Channel Estimation forMIMOFBMC SystemsMIMOFBMC SystemsSohail Taheri1 Mir Ghoraishi1 XIAO Pei1 CAO Aijun2 and GAO Yonghong2

(1 5G Innovation Centre Institute for Communication Systems (ICS) University of Surrey Guildford Surrey GU2 7XH United Kingdom2 ZTE Wistron Telecom AB Kista Stockholm 164 51 Sweden)

Abstract

Filterbank multicarrier (FBMC) with offset quadrature amplitude modulation (OQAM) is a candidate waveform for future wirelesscommunications due to its advantages over orthogonal frequency division multiplexing (OFDM) systems However because of orthogonality in real field and the presence of imaginary intrinsic interference channel estimation in FBMC is not as straightforwardas OFDM systems especially in multiple antenna scenarios In this paper we propose a channel estimation method which employsintrinsic interference cancellation at the transmitter side The simulation results show that this method has less pilot overheadless peak to average power ratio (PAPR) better bit error rate (BER) and better mean square error (MSE) performance comparedto the wellknown intrinsic approximation methods (IAM)

channel estimation filterbank multicarrier (FBMC) multipleinput multipleoutput (MIMO) offset quadrature amplitude modulation (OQAM) wireless communication

Keywords

DOI 103969j issn 167310490205188 2016 04 001httpwwwcnkinetkcmsdetail341294TN201610140955002html published online October 14 2016

Special Topic

This work is supported by ZTE IndustryAcademiaResearch CooperationFunds under Grant No SurreyRef9953

1 Introductionrthogonal frequency division multiplexing(OFDM) has been widely used in communicationsystems in the last decade This is because of itsimmunity to multipath fading and simplicity of

channel estimation and data recovery with a low complexitysingletap equalization and also suitability for multipleinputmultiple output (MIMO) systems [1] However it suffers fromdisadvantages such as sensitivity to carrier frequency offset(CFO) significant outofband radiation and cyclic prefix overhead In the presence of CFO there is loss of orthogonality between subcarriers leading to inter carrier interference (ICI)Moreover to efficiently use the available spectrum a waveformwith very low spectral leakage is needed

Because of the OFDM shortcomings filterbank multicarrier(FBMC) modulation combined with offset quadrature amplitude modulation (OQAM) has drawn attention in the last decade [2] [3] Regardless of the higher complexity compared toOFDM FBMC (known as OFDMOQAM and FBMCOQAM inthe literature) provides significantly reduced outofband emissions robustness against CFO [4] and under certain condi

tions better spectral efficiency as there is no need to use cyclic prefix (CP) [5] These advantages come from well localizedprototype filters in time and frequency domain for pulse shaping Accordingly FBMC can be a promising alternative to conventional radio access techniques to improve wireless accesscapacity

On the other hand as orthogonality in FBMC systems onlyholds in the real field received symbols are contaminated withan imaginary intrinsic interference term coming from the neighbouring real symbols The interference becomes a source ofproblem in channel estimation and equalization processes especially in MIMO systems The pilot symbols used for channelestimation should be protected from interference as the receiver has no knowledge about their neighbours to estimate theamount of interference These protections cause overheadswhen designing a transmission frame In a preamblebased approach the preamble should be protected from the subsequentdata transmission and the previous frame by inserting null symbols which causes longer preamble and thus more overheadcompared to OFDM This is also true for scattered pilots wherethe neighbouring data symbols contribute to the interferenceon the pilots [6] In this scenario typically one or two timefrequency points adjacent to the pilots are used to cancel the interference on the pilots [7]-[10]

Interference Approximation Method (IAM) for preamble

O

October 2016 Vol14 No 4 ZTE COMMUNICATIONSZTE COMMUNICATIONS 03

1


Special Topic

Evaluation of Preamble Based Channel Estimation for MIMOFBMC SystemsSohail Taheri Mir Ghoraishi XIAO Pei CAO Aijun and GAO Yonghong

October 2016 Vol14 No 4ZTE COMMUNICATIONSZTE COMMUNICATIONS04

based channel estimation in singleinput singleoutput (SISO)systems was first introduced in [11] The preamble was namedIAMR in the literature where R denotes real valued pilotsAlternatively IAMI and IAMC were introduced in [12] [13]where I and C stand for imaginary and complex pilots Thosepreamble based channel estimation schemes were extended toFBMCMIMO systems in [14] In IAMI and IAMC pilots oneach subcarrier interfere with their adjacent subcarriers in aconstructive way That is these methods use the intrinsic interference to enhance amplitude of the pilots As a result betterperformance of channel estimation is achieved Despite goodperformance IAM methods suffer from increased pilot overhead ie a number of zero symbols are required to protect thepilot symbols from the interference of their adjacent symbolsWhile the number of pilot symbols is equal to the number ofantennas the total number of symbols in the preamble will bemore than twice the number of transmit antennas

This paper proposes a channel estimation method with reduced preamble overhead compared to the IAM family Theidea was first introduced in [15] for MIMOOFDM Applyingthis method to MIMOFBMC with spatial multiplexing needsfurther consideration to cancel intrinsic interference By usingbasic idea of zero forcing from single antenna this method hasmodest computation complexity while it can outperform IAMmethods in terms of peak to average power ratio (PAPR) bit error rate (BER) and mean square error (MSE) under perfect synchronization conditions and in presence of carrier frequencyoffset

The rest of this paper is organized as follows Section 2 reviews the MIMOFBMC systems the effect of intrinsic interference and the conventional channel estimation methods In Section 3 the new method for channel estimation is proposed andSection 4 shows the results and comparisons with IAM methods Finally conclusions are drawn in Section 5

2 MIMOFBMC System

21 System ModelFBMC systems are implemented by a prototype filter g( )t

and synthesis and analysis filter banks in transmitter and receiver side respectively The real and imaginary parts of complex symbols are separated in two different branches wherethey are modulated in FBMC modulators as real symbolsTherefore at a specific time each subcarrier in this system carries a realvalued symbol Denoting T0 as symbol duration andF0 as subcarrier spacing in OFDM systems duration and subcarrier spacing in FBMC are either τ0 = T02 ν0 =F0 orτ0 = T0 ν0 = F02 [16] For the system model in this paper theformer approach is adopted That is subcarrier spacing remains the same as OFDM while symbol duration is reduced by

halfAssuming a multiple antenna scenario with P transmit anten

nas Q receive antennas and M subcarriers the baseband signal to be transmitted over the p th branch in general form isexpressed ass( )p ( )t =sum

n = -infin

+infin summ = 0

M - 1a( )pmngmn( )t (1)

where a( )pmn is the realvalued symbol and gmn( )t is the shift

ed version of the prototype filter on the m th subcarrier and atn th symbol durationgmn( )t = jm + ne j2πmν0t g( )t - nτ0 (2)The prototype filter g( )t is designed to keep its shifted ver

sions are orthogonal only in the real field [17] ieRaeligegraveccedil

oumloslashdivideintgmn( )t g

m0n0( )t dt = δmm0δnn0 (3)

where R( ) denotes the real part of a complex number As aconsequence the outputs of the analysis filterbank have a socalled intrinsic interference term which is pure imaginary Thedemodulated signal on the q th receive antenna at a particularsubcarrier and symbol point ( )m0n0 is given byy( )qm0n0

=sump = 1

P

hqpm0n0

a( )pm0n0

+ jI ( )qm0n0

+η( )qm0n0

(4)

where hqpm0n0 is channel frequency response at ( )m0n0 be

tween qth receive and pth transmit antenna η( )qm0n0 is the noise

component at qth receive antenna and the interference termI( )qm0n0 is formed asjI

( )qm0n0

=sump = 1

P sum( )mn ne ( )m0n0

hqpmna

( )pmn g

m0n0

mn (5)In (5) g

m0n0

mn is expressed asg

m0n0

mn = intgmn( )t gm0n0( )t dt (6)

Having the prototype filter g( )t well localized in time andfrequency it can be assumed that the intrinsic interference ismostly due to the first order neighbouring points That is( )mn in (5) can take the values of Ω as follows [6]

Ω = ( )m0n0 plusmn 1 ( )m0 plusmn 1n0 ( )m0 plusmn 1n0 plusmn 1 (7)which covers the ( )m0n0 point firstorder neighbours By assuming constant channel frequency response over ( )m0n0and Ω we can simplify (5) as

jI( )qm0n0

=sump = 1

P

hpqm0n0 sum( )mn isinΩ

a( )pmn g

m0n0

mn (8)

2



Special Topic


Consequently (4) can be written as

y( )qm0n0

=sump = 1

P

hpqm0n0

aelig

egrave

ccedil

ccedil

ccedilccedilccedilccedil

ouml

oslash

divide

divide

dividedividedividedivide

a( )pm0n0

+ ju( )pm0n0

c( )pm0n0

+η( )pm0n0

(9)

whereju

( )pm0n0

= sum( )mn isinΩ

a( )pmn g

m0n0

mn (10)Table 1 shows the number of g

m0n0mn coefficients on the first

order neighbours of the point ( )m0n0 The weights of interference β γ and δ depend on the prototype filter and havebeen derived in [18] In this work the isotropic orthogonaltransform algorithm (IOTA) [19] filter is employed It exploitsthe symmetrical property of Gaussian function in time and frequency Therefore the amount of interference out of firstorderneighbouring points is negligible The weights of interferencefor this filter are β = 02486 γ = 05755 andδ = 01898 (Table 1)

The MIMOFBMC signal model can be represented asaelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

y(1)m0n0⋮y

(Q)m0n0

=aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

h11m0n0

⋯ h1Pm0n0⋮ ⋱ ⋮

hQ1m0n0

⋯ hQPm0n0

aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

c(1)m0n0⋮c(Q)m0n0

+aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

η(1)m0n0⋮

η(Q)m0n0

(11)

where c( )pm0n0 is defined in (9) To retrieve the transmitted sy

mbols from the system above it is necessary to have an evaluation of the channel coefficients which are used to detect thelinearly combined demodulated complex symbols c

( )pm0n0 at each

receiver branch using zero forcing (ZF) minimum mean squareerror (MMSE) or maximum likelihood (ML) In c

( )pm0n0 the imag

inary parts are intrinsic interference terms By taking R operation the transmitted symbols a

( )pm0n0 =R c

( )pm0n0 are recovered

22 Channel EstimationTo obtain the channel information over one frame duration

on each receive antenna we need to know the transmitted pilotsymbols The number of these pilot symbols should be equal toP to form a linear equation system with the least square estimation method For simplicity let us consider a 2by2 antenna

scenario By allocating two pilot symbols at times n = n0 andn = n1 on each antenna the equation set of the system on subcarrier m is given byaelig

egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1mn0

y( )1mn1

y( )2mn0

y( )2mn1

= aeligegraveccedilccedil

ouml

oslashdividedivide

h11mn0

h12mn0

h21mn0

h22mn0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1mn0

x( )1mn1

x( )2mn0

x( )2mn1

+

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

η( )1mn0

η( )1mn1

η( )2mn0

η( )2mn1

(12)

In (12) x( )pmn are pilot symbols We have assumed that there

is no significant variations in the channel between time slotsn0 and n1 Hence we can drop the time subscript and express(12) asYm =HmXm +ηm (13)Thus channel coefficients can be calculated by the least

square estimation methodHm =Ym( )XH

mXm

-1XH

m =Hm +ηm( )XHmXm

-1XH

m (14)or in a special case with the equal number of transmit and receive antennaHm =YmX

-1m =Hm +ηmX

-1m (15)

The preamble in the IAM methods is composed of 2P + 1symbols That is the length of the preamble grows linearlywith P The symbols with even time indices are pilots whileother symbols are all zeros to protect pilots from intrinsic interference Based on the values of pilot symbols ie real imaginary or complex valued pilots IAM R IAM I and IAM Cwere proposed In these approaches the channel coefficientscan be obtained using (12) For P=2 pilot symbols in (12) areset as x

( )1mn0 = x( )1

mn1 = x( )2mn0 = -x( )2

mn1 = xm Hence they form a systembased on (12) asYm = xmHm( )1 11 -1 +ηm = xmHmA2 +ηm (16)

where A2 =A-12 is an orthogonal matrix if omitting the co

nstant coefficient of the inverse [14] Finally the channel coefficients are obtained as followsHm = 1

xmYmA2 =Hm + 1

xmηmA2 (17)

The length of the preamble in this method is 2P+1=5 withjust two pilot symbols As a result this approach suffers fromsignificant pilot overhead which reduces the spectral efficiency Furthermore the periodic nature of the pilots in these preambles results in high PAPR at the output of the synthesis filter

Table 1 Weights of interference on the firstorder neighbours

m0 - 1m0

m0 + 1

n0 - 1( )-1 m0 δ

-( )-1 m0γ

( )-1 m0 δ

n0

-β1β

n0 + 1( )-1 m0 δ

( )-1 m0γ

( )-1 m0 δ

3



bank [14]

3 Proposed MethodIn order to reduce the preamble overhead and accordingly

increase the spectral efficiency a novel channel estimation approach with modest computation complexity is proposed Sincethere is no need to have an estimation of the channel on eachsubcarrier we can reduce the number of pilot symbols to oneIn this way each subcarrier is allocated to only one branch totransmit pilot That is while a branch is transmitting pilot on asubcarrier the other branches remain silent Therefore thechannel parameters between the receive branch and the pilottransmitting branch on that specific subcarrier can be obtained This method enables the increase of transmit brancheswith a constant length of the preamble

To elaborate the system more precisely we assume a 2x2MIMO system where preambles for branches 1 and 2 areshown in Fig 1 It can be seen that the first and third symbolsare all zero to protect the preamble from intrinsic interferencefrom data section and previous frame In the middle symbol forbranch 1 complex pilots are placed on odd subcarriers whilethe other subcarriers carry zeros On branch 2 orthogonal pilots to branch 1 are sent ie even subcarriers carry complexpilots and the rest are zero valued On a particular subcarrierm =m0 the system equations is written as followsaelig

egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1m0

y( )2m0


ouml

oslashdividedivide

h11m0

h12m0

h21m0

h22m0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1m0

x( )2m0

+ aeligegrave

ccedilccedil

ouml

oslash

dividedivide

η( )1m0

η( )2m0

(18)

On odd subcarriers m0 = 2k + 1 we have x( )1m0 =Xm0 while

x( )2m0 = 0 Then the channel coefficients h11

m0 and h21m0 are ob

tained ash11m0= y

( )1m0

Xm0

|x( )2m0

= 0

h21m0

= y( )2m0

Xm0

|x( )2m0

= 0

(19)

Likewise on even subcarriers the channel coefficients ofh12m0 and h22

m0 are given by

h12m0

= y( )1m0

Xm0

|x( )1m0= 0

h22m0

= y( )2m0

Xm0

|x( )1m0= 0

(20)

Hence we have calculated the channel parameters betweeneach pair of antennas on alternative subcarriers Channel Coefficients on the rest of subcarriers can be obtained by interpolation Due to short distance between pilots in this system linearinterpolation provides enough accuracy with the advantage of

low complexityThe technique works perfectly for MIMO OFDM systems

[15] When applying this method to MIMOFBMC intrinsic interference degrades the channel estimation performance ietransmitted pilots from one branch interfere with the receivedpilots on other branch Consequently the conditions in (19)and (20) no longer hold To tackle this problem we propose aprecoding approach in which the interference is calculated atthe transmitter side Then the zero points in pilot symbols arereplaced by Imn so that there are no interference on the corresponding points at the receiver side That is the pilots are received without any interference from other branchesFig 2 shows the precoded pilots The value of cancelling in

terference on subcarrier m is calculated by using (10) as

Imn = - sum( )mn isin Ω

a( )pmn g

mn

mn (21)

Moreover the adjacent points of the pilot Xm are filled withprecalculated values to maximize the received signal energythereby to enhance the estimation accuracy [18] DefiningXm =X R

m + jX Im These values would be

X m = - jX I

m

X Primem = -XR

m (22)

Consequently the amplitude of the real and imaginary parts

Special Topic


Figure 1 The basic preamble for two antennas

Figure 2 The preambles for two antennas after interferencecancellation of the first and third time symbols that helps the pilotsbecome stronger

000000

Xm - 3

0Xm - 1

0Xm + 1

0Branch 1

000000

000000

0Xm - 2

0Xm

0X_(m + 2)Branch 2

000000

X m - 3

0X

m - 1

0X

m + 1

0

Xm - 3

Im - 21

Xm - 1

Im1

Xm + 1

Im + 21

Branch 1

X Primem - 3

0X Prime

m - 1

0X Prime

m + 1

0

0X

m - 2

0X

m

0X

m + 2

Im - 31

Xm - 2

Im - 11

Xm

Im + 11

Xm + 2

Branch 2

0X Prime

m - 2

0X Prime

m

0X Prime

m + 2

4


of the received pilots becomes|| X R

m = ||XRm + γ ||X

m + γ ||X Im

|| X Im = ||X I

m + γ ||X Primem + γ ||XR

m

(23)

where γ is the interference weight shown in Table 1 The complete design of the preambles is displayed in Fig 2 The pilotscan take arbitrary values In this work the maximum amplitude of the used QAM modulation is used so that X R

m =X Im Inorder to avoid high PAPR the sign of the pilots should be

changed alternatively after a number of repetitions The finalvalue of the received pilots in (23) with X R

m =X Im is

Xm = ( )1 + 2γ Xm (24)The extension to Pbranch MIMO system is straightforward

In this case one subcarrier of every P subcarriers carries a pilot (nonzero) while each branchrsquos pilot symbol is orthogonalto other branches The more transmit branches the more distance between pilot subcarriers Consequently for larger number of branches the quality of channel estimation degrades

4 Simulation ResultsIn this section different preamblebased channel estimators

for a 2x2 MIMOFBMC system are simulated and comparedThe simulations are performed using 7tap EPA5Hz and 9tapETU70Hz channel models with low spatial correlations Perfect synchronization is assumed for BER and MSE comparisonie there is no timing or frequency offset errors In order to detect symbols MMSE equalizer is used Table 2 summarizesthe simulation parameters

The results are compared with IAMR and IAMC methodsintroduced in [14] For fair comparison the transmission poweris kept equal for all methods In this system Eb

N0is defined by

Eb

N0=Q SNR

α times log2( )M (25)

where M = 16 is the modulation order SNR is signaltonoiseratio and α =Ns - Np

Ns

with the frame length Ns = 14 and thepreamble length Np The length of preamble Np in the pr

oposed method is three symbols resulting in 40 overhead reduction compared to IAMs As a result a performance gain isexpected due to shorter preamble The extra symbols generatedby the synthesis filterbanks can be dropped before transmission but one of them with the most power should be kept toavoid filtering errors after demodulation ie Ns + 1 symbolsare transmitted To consider this extra symbol α can bechanged to α =Ns - Np

Ns

+ 1

41 PAPR ComparisonFig 3 shows the comparison between the proposed method

and IAMs in terms of PAPR The plots show the squared magnitude of the preambles at the output of the synthesis filter bank on branch 1 Evidently from the point of practical implementations the proposed method is preferable Whereas in theothers the signal level should be kept very low to avoid ADsaturations The PAPR levels for the pilot symbols are compared in Table 3 for the three methods42 Channel Estimation Performance ComparisonFig 4 shows the MSE comparison of the channel estimation

methods To calculate MSE the channel tap on the secondsymbol in frame is considered as reference and it is assumedconstant during the symbol duration Then the MSE is calcu


Special Topic


Table 2 Simulation parameters

EPA Extended Pedestrian A modelETU Extended Typical Urban model

FFT fast Fourier transformQAM quadrature amplitude modulation

Modulation typeFFT size

Used subcarriersSampling frequencySymbols per frame

Channel

MQAM M =16256144

384 MHz14

EPA 5 Hz ETU 70 Hz

Table 3 PAPR comparison for the three methods

IAMC Interference Approximation Methodcomplex pilotsIAMR Interference Approximation Methodreal valued pilots

PAPR peak to average power ratioPAPR

IAMC175

IAMR93

Proposed72

Figure 3 Squared magnitude of the preambles on output ofthe branch 1

150010005000

151050

The proposed preamble

150010005000

151050

IAMR preamble

150010005000

151050

IAMC preamble

Time (Samples)

Transm

itsign

alcom

parison


5



lated using the estimated channel H as Eaeligegrave

oumloslash( )H - H H( )H - H

It can be seen that the proposed preamble outperforms IAMRand has approximately the same performance as IAMC in bothchannel models In the EPA5Hz scenario the proposed method gradually reaches an error floor This is due to dominationof errors from ISI and interference cancellation residual However the performance is still as good as IAMC In the ETU70Hz scenario because of rapid variation of the channel tapsthe assumption of constant channel over Ω in (8) is invalidConsequently the performance of all the methods degradesand reaches an error floor in higher SNRs This is a generalproblem in channel estimation for FBMC systems where the receiver should necessarily have an estimation of intrinsic interferences for channel estimation However the degradation onIAMs is more significant as the channel is estimated using twosymbols with one zero symbol in between Therefore as thechannel is not constant over the two pilot symbols degradationis higher than the proposed method with only one symbol forchannel estimation The CramerRao lower bound (CRLB) forthe proposed method derived in Appendix A has also beenplotted in the figure for benchmark comparison It can be seenthat the proposed scheme achieves closest performance to thetheoretical lower bound in comparison to the other schemes

Fig 5 shows the MSE comparisons in terms of residualCFO It is assumed that the CFO has been estimated and compensated before channel estimation As the estimated CFO isnot perfect the residual CFO affects the quality of channel estimation Therefore the methods are compared in presence of residual CFO in the two channel scenarios without added whiteGaussian noise When the CFO is zero the MSEs show the error floor of the methods in Fig 4 at very high SNRs It can be

seen that in EPA channel the error floor of the proposed method is higher than IAMC while it has the best performance under ETU channel This is also true for the other values of CFOwhere the degradation of MSE in the proposed method is lowerthan the other two in both channels43 Bit Error Rate Performance Comparison

The BER performance comparison with respect to Eb

N0is il

lustrated in Fig 6 Evidently the proposed method performs

Special Topic


CRLB CramerRao lower boundEPA Extended Pedestrian A modelETU Extended Typical Urban model

IAM Interference Approximation MethodSNR signaltonoise ratio CFO carrier frequency offset

EPA Extended Pedestrian A modelETU Extended Typical Urban modelIAM Interference Approximation Method


IAM Interference Approximation Method

Figure 4 MSE performance of the channel estimation methods Figure 5 MSE performance of the channel estimation methods inpresence of residual CFO

Figure 6 BER performance of the channel estimation methods

30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4

ProposedEPA 5 HzIAMCEPA 5 HzIAMREPA 5 HzProposedETU 70 HzIAMCETU 70 HzIAMRETU 70 HzProposedCRLB

150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150

ProposedEPA 5 HzIAMCEPA 5 HzIAMREPA 5 HzProposedETU 70 HzIAMCETU 70 HzIAMRETU 70 Hz

22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6


better compared to the others in low mobility EPA5Hz scenario In the high mobility ETU70Hz channel the performancedeteriorates as the channel varies significantly during theframe time Consequently the preamblebased channel estimation is not a proper choice for high mobility applications andthere is an error floor for all the curves showing around six percent bit error rate

5 ConclusionsIn this paper we proposed a novel channel estimation algo

rithm with much reduced pilot overhead compared to the existing IAM based approaches Our results show that the proposedmethod has better PAPR property The system performance under low mobility and high mobility channels as well as in thepresence of CFO has been simulated and compared According to the results the proposed method achieves comparablechannel estimation performance to the IAM methods and better BER performance due to shorter preambleAppendix ACramerRao Lower Bound for the Proposed Channel Estimation

In this section a lower bound for the proposed channel estimator is derived We simplify the system using equations (13)(18) (19) and (20) asY =XH +η (26)

where Y = [ ]y1 y2 is the received signal vector η = [ ]η1 η2 isthe noise vector H = [ ]h1 h2 is the channel vector to be estimated X is the pilot symbol The subcarrier index has alsobeen dropped for simplicity

The CRLB is a bound on the smallest covariance matrix thatcan be achieved by an unbiased estimator H of a parametervector H as

J-1 leCH=E ( )H - H ( )H - H

J =Eigraveiacuteicirc

iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide

part ln p( )Y HpartH

aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)

where ( )∙ denotes conjuagate transpose operation J is theFisher information matrix and ln p( )Y H is the loglikelihoodfunction of the observed vector Y The vector Y is a complexGaussian random vector ie YsimCN( )XHN0I with likelihood function and loglikelihood function as

where K is a constant Taking the complex gradient [20] ofln p( )Y H with respect to H yields

part ln p( )Y HpartH = - 1

N0[ ]XXH -X

Y (29)

The above equality holds sincepartY2

partH = 0 partHXYpartH = 0

partYXHpartH = ( )XY

partHXXHpartH = ( )XXH

(30)

Thus we can derivepart ln p( )Y H

partH = aeligegraveccedilccedil

ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)

This proves that the minimum variance unbiased estimatorof H isH = ( )XX

-1XY = Y

X (32)

It is efficient in that it attains the CRLB The Fisher information matrix J( )H and covariance matrix C

H of this unbiasedestimator are

J( )H =Eeacuteeumlecircecirc

ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)

In (33) Ex is the pilot energy The CRLB for each diagonalelement of J-1( )H is

var( )h1 = var( )h2 = diag[ ]CH i

= N0Ex

(34)As the pilots in this system are amplified exploiting intrinsic

interference by the factor of 1 + 2γ Ex should be replacedby E

x = ( )1 + 2γ 2Ex Assuming Ex

N0is approximately equal to

SNR and considering (25) (34) becomesvar( )h1 = var( )h2 = N0

Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0

2 expeacuteeumlecircecirc

ugrave

ucircuacuteuacute- ( )Y -XH ( )Y -XH

N0=

1( )πN0

2 expeacuteeumlecirc

ugraveucircuacute-Y2 -HXY -YXH +HXXH

N0

ln p( )Y H =K - Y2 -HXY -YXH +HXXHN0

(28)References[1] A Sahin I Guvenc and H ArslanldquoA survey on multicarrier communications

Prototype filters lattice structures and implementation aspectsrdquoIEEE Communications Surveys Tutorials vol 16 no 3 pp 1312-1338 Mar 2014

7



Special Topic


[2] B Farhang BoroujenyldquoOFDM versus filter bank multicarrierrdquoIEEE SignalProcessing Magazine vol 28 no 3 pp 92-112 May 2011

[3] F Schaich and T WildldquoWaveform contenders for 5GmdashOFDM vs FBMC vsUFMCrdquoin 6th International Symposium on Communications Control and Signal Processing Athens Greece 2014 pp 457 - 460 doi 101109ISCCSP20146877912

[4] Q Bai and J NossekldquoOn the effects of carrier frequency offset on cyclic prefixbased OFDM and filter bank based multicarrier systemsrdquoin IEEE Eleventh International Workshop on Signal Processing Advances in Wireless Communications Marrakech Morocco Jun 2010 pp 1-5 doi 101109SPAWC20105670999

[5] M Sriyananda and N RajathevaldquoAnalysis of self interference in a basic FBMCsystemrdquoin IEEE 78th Vehicular Technology Conference Las Vegas USA Sept2013 pp 1-5 doi 101109VTCFall20136692102

[6] J Javaudin and Y JiangldquoChannel estimation in MIMO OFDMOQAMrdquoinIEEE 9th Workshop on Signal Processing Advances in Wireless CommunicationsRecife Brazil Jul 2008 pp 266-270 doi 101109SPAWC20084641611

[7] J Javaudin D Lacroix and A RouxelldquoPilot aided channel estimation forOFDMOQAMrdquoin 57th IEEE Semiannual Vehicular Technology Conference Jeju South Korea Apr 2003 pp 1581-1585 doi 101109VETECS20031207088

[8] C Lele R Legouable and P SiohanldquoChannel estimation with scattered pilotsin OFDMOQAMrdquoin IEEE 9th Workshop on Signal Processing Advances inWireless Communications Recife Brazil Jul 2008 pp 286-290 doi 101109SPAWC20084641615

[9] Z Zhao N Vucic and M SchellmannldquoA simplified scattered pilot for FBMCOQAM in highly frequency selective channelsrdquoin 11th international symposiumon Wireless communications systems Barcelona Spain Oct 2014 pp 819-823doi 101109ISWCS20146933466

[10] J Bazzi P Weitkemper and K KusumeldquoPower efficient scattered pilot channel estimation for FBMCOQAMrdquoin 10th International ITG Conference on Systems Communications and Coding Hamburg Germany Feb 2015 pp 1-6

[11] C Leacuteleacute J Javaudin R Legouable A Skrzypczak and P SiohanldquoChannel estimation methods for preamble based OFDMOQAM modulationsrdquoTransactions on Emerging Telecommunications Technologies pp 741-750 Sept 2008doi 101002ett1332

[12] C Leacuteleacute P Siohan and R Legouableldquo2 dB better than CPOFDM with OFDMOQAM for preamblebased channel estimationrdquoin IEEE International Conference on Communications Beijing China 2008 pp 1302-1306 doi 101109ICC2008253

[13] J Du and S SignellldquoNovel preamble based channel estimation for OFDMOQAM systemsrdquoin IEEE International Conference on Communications Dresden Germany 2009 pp 1-6 doi 101109ICC20095199226

[14] E Kofidis and D KatselisldquoPreamble based channel estimation in MIMO OFDMOQAM systemsrdquoin IEEE International Conference on Signal and Image Processing Applications Kuala Lumpur Malaysia 2011 pp 579-584 doi101109ICSIPA20116144161

[15] J Siew R Piechocki A Nix and S Armour (2002)ldquoA channel estimationmethod for MIMOOFDM systemsrdquoLondon Communicaitons Symposium (LCS)[Online] Available httpwwweeuclacuklcspreviousLCS2002LCS087pdf

[16] J Du P Xiao J Wu and Q ChenldquoDesign of isotropic orthogonal transformalgorithmbased multicarrier systems with blind channel estimationrdquoIET communications vol 6 no 16 pp 2695- 2704 Nov 2012 doi 101049iet com20120029

[17] P Siohan C Siclet and N LacailleldquoAnalysis and design of OFDMOQAMsystems based on filterbank theoryrdquoIEEE Transactions on Signal Processingvol 50 no 5 pp 1170-1183 May 2002

[18] E Kofidis and D KatselisldquoImproved interference approximation method forpreamblebased channel estimation in FBMCOQAMrdquoin 19th European signal processing conference (EUSIPCO2011) Barcelona Spain 2011 pp 1603-1607

[19] J Du and S SignellldquoTime frequency localization of pulse shaping filters inOFDOQAM systemsrdquoin 6th International Conference on Information Communications Signal Processing Singapore 2007 pp 1-5

[20] S Kay Fundamentals of Statistical Signal Processing Upper Saddle RiverUSA Prentice Hall 1998

Manuscript received 20160404

Sohail Taheri (staherisurreyacuk) received his BS degree in electronic engineering and MSc degree in digital electronics from Amirkabir University of TechnologyIran in 2010 and 2012 respectively He is currently working towards his PhD degreefrom the Institute for Communication Systems (ICS) University of Surrey UnitedKingdom His current research interests include signal processing for wireless communications waveform design for 5G air interface and physical layer for 5G networksMir Ghoraishi (mghoraishisurreyacuk) is a senior research fellow in the Institute for Communication Systems (ICS) University of Surrey He joined the Institutein 2012 and is currently leading 5GIC testbed and proofofconcept projects Thiswork area includes several implementation and proofofconcept projects eg 5G airinterface proofofconcept distributed massive MIMO implementation wireless inband fullduplex millimeter wave hybrid beamforming system and millimeter wavewireless channel analysis and modelling He was involved in EU FP7 DUPLO project as work package leader He has previously worked in Tokyo Institute of Technology as assistant professor and senior researcher from 2004 to 2012 after getting hisPhD from the same institute In Tokyo Tech he was involved in several national andsmall scale projects in planning performing implementation analysis and modelling different aspect of wireless systems in physical layer propagation channel andsignal processing He has coauthored 100 publications including refereed journalsconference proceedings and three book chaptersXIAO Pei (pxiaosurreyacuk) received the BEng MSc and PhD degrees fromHuazhong University of Science amp Technology Tampere University of TechnologyChalmers University of Technology respectively Prior to joining the University ofSurrey in 2011 he worked as a research fellow at Queenrsquos University Belfast andhad held positions at Nokia Networks in Finland He is a Reader at University ofSurrey and also the technical manager of 5G Innovation Centre (5GIC) leading andcoordinating research activities in all the work areas in 5GIC Dr Xiaorsquos research interests and expertise span a wide range of areas in communications theory and signal processing for wireless communications He has published 160 papers in refereed journals and international conferences and has been awarded research fundingfrom various sources including Royal Society Royal Academy of Engineering EUFP7 Engineering and Physical Sciences Research Council as well as industryCAO Aijun (caoaijunztecomcn) is a principal architect in ZTE RampD CenterSweden (ZTE Wistron Telecom AB) He has over 17 years of experience in wirelesscommunications research and development from baseband processing to network architecture including design and optimization of commercial UMTSLTE base station and handset products HetNet and small cell enhancement etc He has alsobeen involved in standardization works and contributed to several 3GPP technicalreports He is also active in academic and industrial workshops and conferences related to the future wireless networks being as panelists or (co)authors of publishedpapers in refereed journals and international conferences In addition he holdsmore than 50 granted or pending patents His current focus is 5G technologies related to the new energyefficient unified air interface and network architecture egnew waveform design nonorthogonal multiple access schemes random access challenges and innovative signaling architecture for 5G networksGAO Yonghong (gaoyonghongztecomcn) received his BEng degree in electronicengineering from Tsinghua University China in 1989 and PhD degree in electronicsystems from Royal Institute of Technology Sweden in 2001 In 1996 he was a visiting scientist at Royal Institute of Technology and Ericsson Sweden In 1999 hejoined Ericsson Sweden to develop 3G base stations baseband algorithms and baseband ASICs He joined ZTE European Research Institute (ZTE Wistron TelecomAB Sweden) in 2002 and has been the CTO of ZTE European Research Institutetill now leading and participating the development of 3G4G commercial base stations basebandRRM algorithms and baseband ASICs 3GPP small cell enhancement and from 3 years ago focusing on 5G prestudy 5G standardization and 5G research projects in Europe He has filed 40+ patents as a main author or coauthorHis research interests include mobile communication standardssystems and solutions and algorithms for commercial wireless products

BiographiesBiographies

8


Special Topic



based channel estimation in singleinput singleoutput (SISO)systems was first introduced in [11] The preamble was namedIAMR in the literature where R denotes real valued pilotsAlternatively IAMI and IAMC were introduced in [12] [13]where I and C stand for imaginary and complex pilots Thosepreamble based channel estimation schemes were extended toFBMCMIMO systems in [14] In IAMI and IAMC pilots oneach subcarrier interfere with their adjacent subcarriers in aconstructive way That is these methods use the intrinsic interference to enhance amplitude of the pilots As a result betterperformance of channel estimation is achieved Despite goodperformance IAM methods suffer from increased pilot overhead ie a number of zero symbols are required to protect thepilot symbols from the interference of their adjacent symbolsWhile the number of pilot symbols is equal to the number ofantennas the total number of symbols in the preamble will bemore than twice the number of transmit antennas

This paper proposes a channel estimation method with reduced preamble overhead compared to the IAM family Theidea was first introduced in [15] for MIMOOFDM Applyingthis method to MIMOFBMC with spatial multiplexing needsfurther consideration to cancel intrinsic interference By usingbasic idea of zero forcing from single antenna this method hasmodest computation complexity while it can outperform IAMmethods in terms of peak to average power ratio (PAPR) bit error rate (BER) and mean square error (MSE) under perfect synchronization conditions and in presence of carrier frequencyoffset

The rest of this paper is organized as follows Section 2 reviews the MIMOFBMC systems the effect of intrinsic interference and the conventional channel estimation methods In Section 3 the new method for channel estimation is proposed andSection 4 shows the results and comparisons with IAM methods Finally conclusions are drawn in Section 5

2 MIMOFBMC System

21 System ModelFBMC systems are implemented by a prototype filter g( )t

and synthesis and analysis filter banks in transmitter and receiver side respectively The real and imaginary parts of complex symbols are separated in two different branches wherethey are modulated in FBMC modulators as real symbolsTherefore at a specific time each subcarrier in this system carries a realvalued symbol Denoting T0 as symbol duration andF0 as subcarrier spacing in OFDM systems duration and subcarrier spacing in FBMC are either τ0 = T02 ν0 =F0 orτ0 = T0 ν0 = F02 [16] For the system model in this paper theformer approach is adopted That is subcarrier spacing remains the same as OFDM while symbol duration is reduced by

halfAssuming a multiple antenna scenario with P transmit anten

nas Q receive antennas and M subcarriers the baseband signal to be transmitted over the p th branch in general form isexpressed ass( )p ( )t =sum

n = -infin

+infin summ = 0

M - 1a( )pmngmn( )t (1)

where a( )pmn is the realvalued symbol and gmn( )t is the shift

ed version of the prototype filter on the m th subcarrier and atn th symbol durationgmn( )t = jm + ne j2πmν0t g( )t - nτ0 (2)The prototype filter g( )t is designed to keep its shifted ver

sions are orthogonal only in the real field [17] ieRaeligegraveccedil

oumloslashdivideintgmn( )t g

m0n0( )t dt = δmm0δnn0 (3)

where R( ) denotes the real part of a complex number As aconsequence the outputs of the analysis filterbank have a socalled intrinsic interference term which is pure imaginary Thedemodulated signal on the q th receive antenna at a particularsubcarrier and symbol point ( )m0n0 is given byy( )qm0n0

=sump = 1

P

hqpm0n0

a( )pm0n0

+ jI ( )qm0n0

+η( )qm0n0

(4)

where hqpm0n0 is channel frequency response at ( )m0n0 be

tween qth receive and pth transmit antenna η( )qm0n0 is the noise

component at qth receive antenna and the interference termI( )qm0n0 is formed asjI

( )qm0n0

=sump = 1

P sum( )mn ne ( )m0n0

hqpmna

( )pmn g

m0n0

mn (5)In (5) g

m0n0

mn is expressed asg

m0n0

mn = intgmn( )t gm0n0( )t dt (6)

Having the prototype filter g( )t well localized in time andfrequency it can be assumed that the intrinsic interference ismostly due to the first order neighbouring points That is( )mn in (5) can take the values of Ω as follows [6]

Ω = ( )m0n0 plusmn 1 ( )m0 plusmn 1n0 ( )m0 plusmn 1n0 plusmn 1 (7)which covers the ( )m0n0 point firstorder neighbours By assuming constant channel frequency response over ( )m0n0and Ω we can simplify (5) as

jI( )qm0n0

=sump = 1

P

hpqm0n0 sum( )mn isinΩ

a( )pmn g

m0n0

mn (8)

2



Special Topic



y( )qm0n0

=sump = 1

P

hpqm0n0

aelig

egrave

ccedil

ccedil


ouml

oslash

divide

divide


a( )pm0n0

+ ju( )pm0n0

c( )pm0n0

+η( )pm0n0

(9)

whereju

( )pm0n0

= sum( )mn isinΩ

a( )pmn g

m0n0





egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

y(1)m0n0⋮y

(Q)m0n0

=aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

h11m0n0

⋯ h1Pm0n0⋮ ⋱ ⋮

hQ1m0n0

⋯ hQPm0n0

aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

c(1)m0n0⋮c(Q)m0n0

+aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

η(1)m0n0⋮

η(Q)m0n0

(11)



( )pm0n0 at each


( )pm0n0 the imag


( )pm0n0 =R c





egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1mn0

y( )1mn1

y( )2mn0

y( )2mn1


ouml

oslashdividedivide

h11mn0

h12mn0

h21mn0

h22mn0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1mn0

x( )1mn1

x( )2mn0

x( )2mn1

+

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

η( )1mn0

η( )1mn1

η( )2mn0

η( )2mn1

(12)




mXm

-1XH

m =Hm +ηm( )XHmXm

-1XH


-1m =Hm +ηmX

-1m (15)


( )1mn0 = x( )1

mn1 = x( )2mn0 = -x( )2




xmYmA2 =Hm + 1

xmηmA2 (17)



m0 - 1m0

m0 + 1

n0 - 1( )-1 m0 δ

-( )-1 m0γ

( )-1 m0 δ

n0

-β1β

n0 + 1( )-1 m0 δ

( )-1 m0γ

( )-1 m0 δ

3



bank [14]




egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1m0

y( )2m0


ouml

oslashdividedivide

h11m0

h12m0

h21m0

h22m0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1m0

x( )2m0

+ aeligegrave

ccedilccedil

ouml

oslash

dividedivide

η( )1m0

η( )2m0

(18)



m0 and h21m0 are ob

tained ash11m0= y

( )1m0

Xm0

|x( )2m0

= 0

h21m0

= y( )2m0

Xm0

|x( )2m0

= 0

(19)


m0 are given by

h12m0

= y( )1m0

Xm0

|x( )1m0= 0

h22m0

= y( )2m0

Xm0

|x( )1m0= 0

(20)






a( )pmn g

mn

mn (21)



X m = - jX I

m

X Primem = -XR

m (22)


Special Topic




000000

Xm - 3

0Xm - 1

0Xm + 1

0Branch 1

000000

000000

0Xm - 2

0Xm

0X_(m + 2)Branch 2

000000

X m - 3

0X

m - 1

0X

m + 1

0

Xm - 3

Im - 21

Xm - 1

Im1

Xm + 1

Im + 21

Branch 1

X Primem - 3

0X Prime

m - 1

0X Prime

m + 1

0

0X

m - 2

0X

m

0X

m + 2

Im - 31

Xm - 2

Im - 11

Xm

Im + 11

Xm + 2

Branch 2

0X Prime

m - 2

0X Prime

m

0X Prime

m + 2

4



m = ||XRm + γ ||X

m + γ ||X Im

|| X Im = ||X I


m

(23)




m =X Im is






N0is defined by

Eb

N0=Q SNR



Ns



Ns

+ 1





Special Topic







Channel

MQAM M =16256144

384 MHz14

EPA 5 Hz ETU 70 Hz




IAMC175

IAMR93

Proposed72


150010005000

151050


150010005000

151050

IAMR preamble

150010005000

151050

IAMC preamble

Time (Samples)

Transm

itsign

alcom

parison


5









N0is il


Special Topic









30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4


150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150


22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8



Special Topic



y( )qm0n0

=sump = 1

P

hpqm0n0

aelig

egrave

ccedil

ccedil


ouml

oslash

divide

divide


a( )pm0n0

+ ju( )pm0n0

c( )pm0n0

+η( )pm0n0

(9)

whereju

( )pm0n0

= sum( )mn isinΩ

a( )pmn g

m0n0





egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

y(1)m0n0⋮y

(Q)m0n0

=aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

h11m0n0

⋯ h1Pm0n0⋮ ⋱ ⋮

hQ1m0n0

⋯ hQPm0n0

aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

c(1)m0n0⋮c(Q)m0n0

+aelig

egrave

ccedil

ccedilccedilccedil

ouml

oslash

divide

dividedividedivide

η(1)m0n0⋮

η(Q)m0n0

(11)



( )pm0n0 at each


( )pm0n0 the imag


( )pm0n0 =R c





egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1mn0

y( )1mn1

y( )2mn0

y( )2mn1


ouml

oslashdividedivide

h11mn0

h12mn0

h21mn0

h22mn0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1mn0

x( )1mn1

x( )2mn0

x( )2mn1

+

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

η( )1mn0

η( )1mn1

η( )2mn0

η( )2mn1

(12)




mXm

-1XH

m =Hm +ηm( )XHmXm

-1XH


-1m =Hm +ηmX

-1m (15)


( )1mn0 = x( )1

mn1 = x( )2mn0 = -x( )2




xmYmA2 =Hm + 1

xmηmA2 (17)



m0 - 1m0

m0 + 1

n0 - 1( )-1 m0 δ

-( )-1 m0γ

( )-1 m0 δ

n0

-β1β

n0 + 1( )-1 m0 δ

( )-1 m0γ

( )-1 m0 δ

3



bank [14]




egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1m0

y( )2m0


ouml

oslashdividedivide

h11m0

h12m0

h21m0

h22m0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1m0

x( )2m0

+ aeligegrave

ccedilccedil

ouml

oslash

dividedivide

η( )1m0

η( )2m0

(18)



m0 and h21m0 are ob

tained ash11m0= y

( )1m0

Xm0

|x( )2m0

= 0

h21m0

= y( )2m0

Xm0

|x( )2m0

= 0

(19)


m0 are given by

h12m0

= y( )1m0

Xm0

|x( )1m0= 0

h22m0

= y( )2m0

Xm0

|x( )1m0= 0

(20)






a( )pmn g

mn

mn (21)



X m = - jX I

m

X Primem = -XR

m (22)


Special Topic




000000

Xm - 3

0Xm - 1

0Xm + 1

0Branch 1

000000

000000

0Xm - 2

0Xm

0X_(m + 2)Branch 2

000000

X m - 3

0X

m - 1

0X

m + 1

0

Xm - 3

Im - 21

Xm - 1

Im1

Xm + 1

Im + 21

Branch 1

X Primem - 3

0X Prime

m - 1

0X Prime

m + 1

0

0X

m - 2

0X

m

0X

m + 2

Im - 31

Xm - 2

Im - 11

Xm

Im + 11

Xm + 2

Branch 2

0X Prime

m - 2

0X Prime

m

0X Prime

m + 2

4



m = ||XRm + γ ||X

m + γ ||X Im

|| X Im = ||X I


m

(23)




m =X Im is






N0is defined by

Eb

N0=Q SNR



Ns



Ns

+ 1





Special Topic







Channel

MQAM M =16256144

384 MHz14

EPA 5 Hz ETU 70 Hz




IAMC175

IAMR93

Proposed72


150010005000

151050


150010005000

151050

IAMR preamble

150010005000

151050

IAMC preamble

Time (Samples)

Transm

itsign

alcom

parison


5









N0is il


Special Topic









30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4


150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150


22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8



bank [14]




egrave

ccedilccedil

ouml

oslash

dividedivide

y( )1m0

y( )2m0


ouml

oslashdividedivide

h11m0

h12m0

h21m0

h22m0

aelig

egrave

ccedilccedil

ouml

oslash

dividedivide

x( )1m0

x( )2m0

+ aeligegrave

ccedilccedil

ouml

oslash

dividedivide

η( )1m0

η( )2m0

(18)



m0 and h21m0 are ob

tained ash11m0= y

( )1m0

Xm0

|x( )2m0

= 0

h21m0

= y( )2m0

Xm0

|x( )2m0

= 0

(19)


m0 are given by

h12m0

= y( )1m0

Xm0

|x( )1m0= 0

h22m0

= y( )2m0

Xm0

|x( )1m0= 0

(20)






a( )pmn g

mn

mn (21)



X m = - jX I

m

X Primem = -XR

m (22)


Special Topic




000000

Xm - 3

0Xm - 1

0Xm + 1

0Branch 1

000000

000000

0Xm - 2

0Xm

0X_(m + 2)Branch 2

000000

X m - 3

0X

m - 1

0X

m + 1

0

Xm - 3

Im - 21

Xm - 1

Im1

Xm + 1

Im + 21

Branch 1

X Primem - 3

0X Prime

m - 1

0X Prime

m + 1

0

0X

m - 2

0X

m

0X

m + 2

Im - 31

Xm - 2

Im - 11

Xm

Im + 11

Xm + 2

Branch 2

0X Prime

m - 2

0X Prime

m

0X Prime

m + 2

4



m = ||XRm + γ ||X

m + γ ||X Im

|| X Im = ||X I


m

(23)




m =X Im is






N0is defined by

Eb

N0=Q SNR



Ns



Ns

+ 1





Special Topic







Channel

MQAM M =16256144

384 MHz14

EPA 5 Hz ETU 70 Hz




IAMC175

IAMR93

Proposed72


150010005000

151050


150010005000

151050

IAMR preamble

150010005000

151050

IAMC preamble

Time (Samples)

Transm

itsign

alcom

parison


5









N0is il


Special Topic









30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4


150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150


22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8



m = ||XRm + γ ||X

m + γ ||X Im

|| X Im = ||X I


m

(23)




m =X Im is






N0is defined by

Eb

N0=Q SNR



Ns



Ns

+ 1





Special Topic







Channel

MQAM M =16256144

384 MHz14

EPA 5 Hz ETU 70 Hz




IAMC175

IAMR93

Proposed72


150010005000

151050


150010005000

151050

IAMR preamble

150010005000

151050

IAMC preamble

Time (Samples)

Transm

itsign

alcom

parison


5









N0is il


Special Topic









30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4


150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150


22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8









N0is il


Special Topic









30

100

SNR (dB)

Mean

square

error

2520151050

10-1

10-2

10-3

10-4


150

10-1

Residual CFO (Hz)Me

ansqu

areerro

r

10-2

10-3100500-50-100-150


22

100

Eb NO (dB)

Biterro

rrate

10-1

10-2

10-32018161412108642


6








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8








J-1 leCH=E ( )H - H ( )H - H


iuml

iuml

uumlyacutethorn

iuml

iuml

aelig

egraveccedilccedil

ouml

oslashdividedivide


aelig

egraveccedilccedil

ouml

oslashdividedivide


(27)




N0[ ]XXH -X

Y (29)





(30)



ouml

oslashdividedivide


= X

Y -XXHN0

=XXN0 ( )XX

-1XY -H = J( )H [ ]H -H

(31)


-1XY = Y

X (32)




ugrave

ucircuacuteuacute

XXI2N0

= E[ ]XX I2N0

= Ex

N0I2

CH= J-1( )H = N0Ex

I2(33)



= N0Ex






Ex

1( )1 + 2γ 2 (35)


Special Topic


( )Y H = 1( )πN0


ugrave


N0=

1( )πN0



N0




7



Special Topic
























8



Special Topic
























8

evaluation of preamble based channel estimation for mimo⁃fbmc

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