A New Type of Comb Pilot in FBMC/OQAMChunling Hao, Shaochuan Wu, Xiaoqing Liu, Kangjian Ma

School of Electronics and Information EngineeringHarbin Institute of Technology

Harbin, Chinahithcl@sina.com, scwu@hit.edu.cn, liuxiaoqing0608@163.com, kangjianma@gmail.com

Abstract—Scattered pilot-aided channel estimation in offsetQAM-based filter bank multicarrier (FBMC/OQAM) systems hasso far been only considered for slow fading channels. In moredemanding scenarios, the classical auxiliary pilot (AP) idea hasbeen shown to result a severe error. This paper proposes novelchannel estimation techniques for FBMC/OQAM systems forfast fading channels. Unlike the conventional auxiliary pilot, theFBMC/OQAM systems’ transmitter adopts the proposed combpilot arrangement mode based on auxiliary pilot. Meanwhilefeedback interference estimation algorithm and feedback inter-ference calculation algorithm are proposed at receiver, whichcan eliminate the imaginary interference of all the pilot symbols.Numerical results show that the FBMC/OQAM systems with theproposed channel estimation algorithms based on the proposedpilot have a better bit error rate (BER) performance compared tothat with the auxiliary pilot algorithm. And compared with AP,the greater the Doppler frequency is, the greater performancesuperiority the proposed channel estmator achieves.

Index Terms—Filter-Bank Multi-Carrier, Offset QuadratureAmplitude Modulation, Channel Estimation, Pilot Design

I. INTRODUCTION

Multicarrier communication system can transmit high-speeddata flow by many parallel low-speed data flows simulta-neously over many orthogonal subcarriers, so multicarriercommunication system has better flexibility and high resis-tance to frequency selective fading channel. One of the mostwidely adopted multicarrier communication systems is OFDM,famous for its high spectrum efficiency, low computationalcomplexity and easiness to combine with MIMO.

The fifth generation mobile communication technology (5G)requires the physical layer waveform technology to be moreflexible and have higher frequency utilization efficiency. How-ever the conventional OFDM adds cyclic prefix (CP) in orderto increase the systems resistance to multipath interference,which has side effects as a waste of spectrum resources, anda large side lobe of the filter, resulting in a less flexibilityof the system. FBMC is a candidate for 5Gs waveformtechnology. Compared with OFDM, FBMC’s prototype filterhas a better time-frequency characteristic, so it does not needCP to resist channel fading, which makes FBMC systems tobe more spectrum efficient, and has more flexibility to takeadvantage of some of the existing non-continuous spectrumresources[1]. Further more , FBMC has a good compatibilitywith OFDM, which means some of the techniques in OFDMcan be applied directly to FBMC. But in order to obtain bettertime-frequency characteristics, FBMC sacrifices orthogonalitybetween subcarriers[2].

Fading channel estimation and equalization techniques arecrucial for coherent symbol detection at the receiver. In theframework of multicarrier systems, many channel estimationtechniques were proposed in the literature particularly forOFDM systems [3–6], which can be classified as trainingsequence/pilot symbols based techniques and blind methods.In this paper, with a faster convergence speed and a lowercomputational complexity compared with blind methods, wewill focus our attention on the former.

In recent years, many researchers have studied the problemof channel estimation of FBMC/OQAM systems. Focusingon pilot-based channel estimation schemes, [7] proposed anauxiliary pilot scheme (AP), which applies an auxiliary pilot toneutralize the interference on the prime pilot. Mestre X studiedthe auxiliary pilot design in a highly frequency selectivefading channel, which approximates the signal model with theTaylor series to simulate various scenarios, and the resultedchannel estimates can be considered to be multiple parallelanalysis filters linear combination[8]. Cui W proposed a codedauxiliary pilot method that linearly encodes the auxiliary pilotto carry information, thereby further improving the spectralutilization of the FBMC systems[9]. Because the value ofthe auxiliary pilot depends on the main pilot in the originalauxiliary pilot algorithm, Yu B proposed a dual correlationpilot design algorithm, by sending two related pilots to neu-tralize the respective interference[10]. Nissel R proposed alinear precoding of the symbols around the pilot symbols toeliminate the interference of the surrounding symbols to thepilot symbols[11].

Through the analysis of the current research situation, it isclear that almost all of the researches on channel estimation arefocused on channel estimation in slow fading channels. Thismotivates that a fast fading pilot design scheme and channelestimation algorithms for FBMC.

This paper proposes a new comb pilots of FBMC/OQAMin fast fading channel. On the basis of the original auxiliarypilot algorithm, we insert pilots in the interval of auxiliarypilots to form comb pilots. Corresponding channel estimationalgorithms are proposed simultaneously, which are namedfeedback interference estimation algorithm and feedback in-terference calculation algorithm respectively and introduced tocalculate the imaginary interference of pilots without auxiliarypilot. We also proved that the BER performance of theproposed feedback channel estimation algorithms are betterthan AP algorithm.

0( )c l

1( )c l

1( )

Mc l

C2R

C2R

C2R

IFFT

M/2

M/2

M/2

Z

1

Z

1

d n0

d n1

Md n

1

Mn

1

n1

n0

n0

n1

Mn

1

P Z0

P Z1

MP Z

1

S m

Synthesis

polyphase filteringTransform blockOQAM mapping

P/S

consversation

Fig. 1. Block diagram of the FBMC/OQAM transmitter

The paper is organized as follows. In Section II, the conven-tional FBMC/OQAM system and AP algorithm are introduced.Section III presents the proposed new comb pilot arrangementand feedback channel estimation algorithms. Simulation re-sults are presented in Section IV. Section V concludes thispaper.

II. FBMC/OQAM COMMUNICATION SYSTEMThe generalized block diagram of the FBMC/OQAM trans-

mitter is illustrated in Fig.1.In the Fig.1, ck (l) represents the complex symbol after

the process of constellation mapping, and C2R representsthe transformation of a complex to real. Introducing a phaserotation operation θk (n) = jk+n to ensure the interferencebetween neighboring subcarriers is pure imaginary. The over-lap factor is K, and the number of subcarriers is M. The lengthof the prototype filter is L, and L = KM . In the modulatedfilter banks, the number of prototype filter branches dependson the periodic of modulation function εk (m).

εk (m) = (−1)knej

2πkM (m−L−1

2 )

= (−1)kne−j

2πkM (L−1

2 )ej2πkmM

= βkγk (m)

(1)

whereγk (m) = e j 2πkm

M (2)

βk = (−1)kne−j

2πkM (L−1

2 ) (3)

The existence of (−1)kn in (3) leads to the frequency offset

of all subcarrier signal near the zero frequency, in favor offurther process.

The output of a synthesis filter bank can be expressed by:

s (m) =M−1∑k=0

∞∑n=−∞

dk (n)θk (n) p(m− nM

2

)εk (m) (4)

where dk (n) is the collection of real-valued data symbols atsubcarrier k. dk (n) is transmitted at a rate of 2/T , with thesignaling period T = 1/∆f where ∆f denotes the subcarrier

spacing. The pair of symbols dk (n) and dk (n+ 1) representthe in-phase and quadrature parts of the complex-valued inputsymbol ck (l), respectively.

dk (n) = dk (2l) =

Re (ck (l)) , k evenIm (ck (l)) , k odd

dk (n) = dk (2l + 1) =

Re (ck (l)) , k oddIm (ck (l)) , k even

(5)

where l is the sample index at OQAM mapping input.In order to achieve high spectral efficiency, complex mod-

ulated filter banks are usually used, which means that all sub-channel filters are frequency shifted versions of the prototypefilter p (m) . So, the synthesis subchannel filters are:

gk (m) = p (m) εk (m) (6)

with m = 0, 1, · · · , L− 1.As shown in Fig.2, the conjugate multiplicative factors

θ∗k (n) and β∗k (n) of the receiver correspond to θk (n) andβk (n) of the transmitter.

The analysis subchannel filters can be expressed as:

fk (m) = g∗k (L− 1−m) (7)

It should be noted that the design of the prototype filtermust satisfy perfect reconstruction (PR) conditions or at leastprovide nearly perfect reconstruction (NPR) characteristics.However, the PR property is only achieved under the con-dition of ideal transmission channel. As interferences in thewireless channel are unavoidable, there is no way to meet PRconditions. Thus, prototype filters are designed to satisfy NPRcharacteristics. In this paper, we take PHYDYAS prototypefilter[12] as NPR prototype filter. The finite impulse response(FIR) of the low-pass prototype filter can be expressed as:

p (t) = 1 + 2K−1∑k=1

(−1)kPk cos

(2π kt

KT

)(8)

where K is overlap factor, Pk is the filter coefficient, satisfyingthe following conditions.

FFT

M/2

M/2

M/2

Z

1

Z

1

R2C

R2C

R2C r m

Q Z0

Q Z1

MQ Z

1

*n

0

*n

1

*

Mn

1

*n

0

*n

1

*

Mn

1

d n0

d n1

ˆM

d n1

c l0

c l1

ˆMc l1

S/P

consversation

Analysis

Polyphase filteringTransform block OQAM demapping

Fig. 2. Block diagram of the FBMC/OQAM receiver

P0 = 1P 2k + P 2

K−k = 1;PL−k = Pk; 1 ≤ k ≤ K − 1Pk = 0;K ≤ k ≤ L−K

(9)

where 1 ≤ k ≤ K− 1.When K = 4, the prototype filterfrequency response is shown in Fig.3.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Normalized Frequency

0

0.2

0.4

0.6

0.8

1

Norm

ali

zed A

mpli

tude

P(f)

Fig. 3. K = 4 The prototype filter frequency response

dominant pilot

data symbol

auxiliary pilot

f

t

Fig. 4. Auxiliary pilot arrangement

Because there is interference between adjacent filters in theFBMC, there will be interference information leaked to usefulinformation after the complex channel. Meanwhile there will

also be data leakage to interference. Thus it can not distin-guish between signal and interference. With complex channelresponse, channel estimation algorithms, such as auxiliarypilot based algorithm, are needed to obtain accurate channelinformation. Fig.4 shows the arrangement of auxiliary pilotsand the AP window selection is shown in Fig.5.

The interference generated between adjacent filters canbe represented by an interference filter. The time domaininterference coefficients of the interference filter are shownin Fig.5.

-4 -2 0-3 -1 1 32 4ft

-2

-1

0

1

2

0

0.0054

0

0.0054

0

0.0006

0.0006

-0.0001

0.0002

-0.0001

0

0

0

0

0

0

-0.0001

0.0002

-0.0001

0.0006

0.0006

0

0.0054

0

0.0054

0

10.5644 0.5644

-0.0429j

0.0429j

0.0429j

-0.0429j

-0.0668-0.0668

-0.125-0.125

-0.125-0.125 -0.2058j

-0.2058j

0.2058j

0.2058j

0.2393

0.2393

Fig. 5. Interference weights and AP window choice

In Fig.5, the red part represents the dominant pilot position(kp, np), and the gray represents the optional position ofauxiliary pilot (ka, na). The black frame is the window forcalculating the auxiliary pilot, i.e Ωkp,np .

dka,na = −∑

(k,n)

dk,n tkp−k,np−n

tkp−k,np−n

(10)

where (k, n) ∈ Ωkp,np , (k, n) 6= (ka, na) , (k, n) 6= (kp, np),dka,na represents the auxiliary pilot at the position (ka, na),and tkp−k,np−n is interference weights in Fig.5.

III. A NEW TYPE OF COMB PILOT

Since the prototype filter is an approximate reconstructionfilter, regardless of the frequency offset and time delay of the

channel, the output of transform block can be written as (11).

yk,n =k+1∑i=k−1

∞∑l=−∞

xi,lqi,k,n−l + wk,n

= xk,n +k+1∑i=k−1

∞∑l=−∞

(i,l) 6=(k,n)

xi,lqi,k,n−l + wk,n(11)

where xi,n = di,nθi,n represents the signal after the OQAMmapping, and wk,n represents channel additive noise. qi,k,n−lrepresents a two-dimensional impulse response that dependson subcarriers, including the influence from the subcarrierk− 1 to the subcarrier k+ 1 and the influence of the channel.Since the frequency domain characteristics of the filter inFBMC are excellent, only adjacent subcarriers will generateinterferent with each other. The receiver’s signal through thephase deflection at the receiver can be written as (12).

yk0,n0= θ∗k0,n0

yk0,n0

= dk0,n0+ juk0,n0

+ θ∗k0,n0wk0,n0

(12)

where the imaginary interference is

uk0,n0=

∑(k,n)∈Ωk0,n0

dk,ntk0−k,n0−n (13)

In (13), tk,n = Im(θ∗k,ntk,n

), tk,n epresents the interference

coefficient of each symbol on the surrounding symbol, andΩk0,n0

represents the range of symbols that interfere with thesymbols around dk0,n0 . At the receiver, the estimated channelresponse of (kp, np) is

hkp,np =θ∗kp,npykp,np

dkp,np(14)

The above analysis shows that FBMC subcarriers are or-thogonal to each other only in real part, which means there isimaginary interference between subcarriers.

The high relative velocity of the transmitter and the re-ceiver will lead to a large Doppler frequency, resulting ina rapid change in the channel, i.e. the channel response isdifferent on different symbols of the same subcarrier. Thehigher the Doppler frequency is, the faster the change willbe. In general, in order to combat the rapid changes in suchchannel, the auxiliary pilot need to be adopted. Obviously,when the dominant pilot interval is too small, the windowthat calculates the auxiliary pilot will overlap, resulting inan infinite recursion of auxiliary pilot calculation. Meanwhile,the 5G scenario requires communication support velocity over300km/h, so the auxiliary pilot method cannot be applied tofast fading channel. This paper presents an AP method basedcomb pilot arrangement, as shown in Fig.6.

As shown in Fig.6, the pilot with the auxiliary pilot iscalled the dominant pilot. The secondary pilot does not havethe auxiliary pilot to help it eliminate interference. In orderto obtain more accurate channel information, it is necessaryto get the interference information of the secondary pilots.So feedback interference estimation algorithm and feedbackinterference calculation algorithm are proposed in this paper.The algorithm flow charts are shown in Fig.7 and Fig.8separately.

secondary pilot

tf

data symbol

auxiliary pilot

dominant pilot

Fig. 6. A comb pilot based on auxiliary pilot

Calculate the

dominant pilot

position channel

response

InterpolationChannel

equalizationDemodulation

Calculate the secondary

pilot position channel

response

Estimate the secondary

pilot position interference

Input Output

Fig. 7. Feedback interference estimation algorithm

Calculate the

dominant pilot

position channel

response

InterpolationChannel

equalizationDemodulation

Calculate the secondary

pilot position channel

response

Calculates The

secondary pilot position

interference

InputOutput

Fig. 8. Feedback interference calculation algorithm

The true channel response can be expressed by equation(15).

hk,n =yk,n

dk,n+juk,n≈ hk,n

1+juk,ndk,n

1+juk,ndk,n

(15)

where k, n are the time domain and frequency domain labelrespectively, uk,n represents the estimate of the imaginaryinterference uk,n. From (15) it is evident that the smaller ofthe difference between uk,n and uk,n, the better the estimatedeffect is. The traditional auxiliary pilot cannot obtain uk,n, sothe hk,n is different from the real value. Feedback interfer-ence estimation algorithm and feedback interference calcula-tion algorithm obtain approximately interference informationthrough the proposed comb pilot.

In feedback interference estimation algorithm, the entirechannel information is obtained by AP algorithm and interpo-lation in the first place. The channel response of the secondarypilots can be obtained by interpolating the channel responseof the dominant pilots. For example, if linear interpolation isused, the channel response can be expressed as

h(1)k,n=h

(1)k,nd−1

+h(1)k,nd−h(1)

k,nd−1

Np(n− nd−1) (16)

where nd−1 < n < nd. h(1)k,nd

is the dominant frequencychannel response of the preceding time near the (k, n) , whilethe h(1)

k,ndis the dominant frequency channel response at the

posterior time near the (k, n). Of course, other interpolation

algorithms can be used. For simplicity, linear interpolation isadopyed as an example in this paper.

Then in the secondary pilots position, the correspondingtransmission signal and the estimation of the interferenceinformation are obtained by using the received signal and theestimated channel information, which can be expressed as

dk,n + juk,n =yk,n

hk,n(17)

Since the pilot signal dk,n is known, the estimation of thetransmission signal obtained in (17) is corrected by dk,n. Andthen the feedback to the received signal is used to correct theestimated channel information, as shown in (18).

h(2)k,n =

yk,ndk,n+juk,n

(18)

In (16) and (18), h(1)k,n and h(2)

k,n represent the first and secondestimation of the channel response respectively. Finally, thechannel information acquired by the second estimation isinterpolated to obtain the response of the whole channelestimation, with equalization and demodulation followed.

In feedback interference calculation algorithm, the entirechannel information by AP algorithm and interpolation isfirstly achieved. The channel response of the secondary pilotscan be obtained by interpolating the channel response of thedominant pilots.

Then the interference information of the secondary pilotsis calculated by using the estimated transmission signal afterequalization and demodulation, which uses the estimated sym-bol around the secondary pilot symbol and the interferencecoefficients , as shown in equation (19). Thus, we can getdk,n + uk,n.

uk,n =∑

(k′,n′)∈Ωk,n

(k′,n′) 6=(k,n)

dk,ntk−k′,n−n′(19)

where tk−k′,n−n′ represents the interference coefficient, anddk,n represents the symbol after demodulation, Ωk,n representsthe interference calculation window around the secondarypilot, and uk,n represents the estimation of the interferenceinformation of the secondary pilot symbol.

After getting dk,n + uk,n, the channel response can beestimated once again by using (18). The channel response ofthe pilot subcarrier at each moment can be obtained, and thenthe channel information is acquired by re-interpolation, withthe equalization and demodulation are carried out again.Thefeedback interference calculation algorithm is a recursiveprocess,which can be conducted incessantly until a satisfactoryperformance. Since the focus of this article is not the numberof feedback, but in the algorithm itself, and it can be seen oncethe feedback has a better performance, so this article does notdiscuss the number of feedback.

IV. SIMULATION RESULTS

In this section, we carry out a comparative study on theestimation performance of FBMC/OQAM in fast fading chan-nel implementing the proposed the feedback channel estimate

algorithms and the AP method. After simulation analysis,there are not many performance improvements in iterativefeedback interference calculation, so the feedback interferencecalculation is followed by a feedback iterative simulation.

In all simulations, a Rayleigh multipath channel is adopted,with the multipath delay as (0 1 2 3 4)Ts, where Ts representsthe sampling time, and the fading of each path as (-2.748-4.413 -11.052 -18.500 -18.276)dB. The channel estimationuses LS estimation and linear interpolation algorithm. Inall simulations, no channel coding is added. The remainingsimulation parameters are shown in the table I.

TABLE ISIMULATION PARAMETERS

Subcarrier spacing 10.94kHzSampling frequency 11.2MHzCarrier frequency 3.5GHzSubcarrier number 1024System bandwidth 10MHzBaseband modulation order of OQAM 4Overlap factor 4Time domain interval ofthe pilot distribution 8Frequency domain interval ofthe pilot distribution 4

Fig.9 shows the performance comparison at the speed on300km/h. It is obvious that feedback interference estimationalgorithm and feedback interference calculation algorithmbased estimator provide much better estimation than AuxiliaryPilot based estimator. This is due to the insertion of pilot-intensive channel information obtained more, secondary pilotsalso use the inherent interference will reduce the interferenceerror, so the performance becomes better.

0 5 10 15 20 25 30

SNR(dB)

10 -2

10 -1

10 0

BE

R

Feedback Interference Calculation

Feedback Interference Estimation

Auxiliary Pilot

Fig. 9. Comparison of BER of Auxiliary Pilot and the feedback channelestimate algorithms at 300km/h

Fig.10 shows the performance comparison at differentspeeds. It can be seen that the BER performance has signifi-cantly improvement after adding feedback compared with thatusing AP. At low speeds, the channel Doppler frequency issmall and the channel change rate is low. The feedback channelestimation algorithms only calculate the interference of some

signals beside it, and the symbols far from it also interfere withit. Only relatively small, but there is also a superposition, sothe differences between AP and the feedback channel estimatealgorithms are small. However the performance improves withthe increase of the speed of movement, i.e. the augment ofDoppler frequency. This confirms that the feedback channelestimate algorithms can track the variation of rapidly fadingchannels status.

50 100 150 200 250 300 350 400

velocity(km/h)

10 -4

10 -3

10 -2

10 -1

BE

R

Feedback Interference Calculation

Feedback Interference Estimation

Auxiliary Pilot

Fig. 10. Comparison of BER of Auxiliary Pilot and feedback channel estimatealgorithms at different speeds

As shown in all figures, the proposed feedback channelestimate algorithms have a better BER performance comparedwith AP. For the computational complexity, it is assumed thatthe number of total permissible pilots is NP . Compared withthe auxiliary pilot, feedback interference estimation algorithmadds 2NP multiplication. Feedback interference calculationalgorithm need to adds 20NP multiplication, 18NP addition,as well as one time-frequency interpolation, one equalizationand one demodulation operation. And there is an output delayof the K−1 symbols since the interference of the pilot symbolsis to be estimated in the both proposed algorithms. As a result,the computational complexity of the auxiliary pilot is less thanthat of the feedback interference estimation algorithm, andthe most complexity is the feedback interference calculationalgorithm.

For the spectrum utilization, it is assumed that the numberof total permissible pilots for auxiliary pilot is NP . Feedbackinterference estimation algorithm and feedback interferencecalculation algorithm use the same pilot insertion mode, andtotal pilots are 4NP , so the spectral utilization of the two arethe same. It can be seen from Fig.4 and Fig.6, the comb pilotbased on auxiliary pilot inserts more pilots than the auxiliarypilots, but there is no data loss, so its spectrum utilization isless than that of the auxiliary pilot algorithm.

In practice, the appropriate algorithm should be selectedaccording to the specific application scenario. According tosimulation results, as well as the analysis of computationalcomplexity and spectrum utilization, the specific options areshown in the table II.

TABLE IIALGORITHM SELECTION

No Doppler frequency Auxiliary PilotSmall Doppler frequency Feedback Interference EstimationHigh Doppler frequency Feedback Interference Calculation

V. CONCLUSIONS

In this paper, a comb pilot based on auxiliary pilot andtwo corresponding feedback channel estimation algorithmsare proposed for the estimation of FBMC/OQAM systems inthe fast fading process. The simulation results showed thatthe BER performance of the proposed two feedback channelestimation algorithms based on the proposed pilot arrangementoutperforms auxiliary pilot at Doppler frequency.

ACKNOWLEDGMENT

This research was supported by the National Science Foun-dation of China (Under Grant: 61671173).

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