Carrier Frequency Offset Estimation for PUCCH in High Speed Train Environment

Xiaona Ren The State Key Laboratory of ISN

Xidian University Xi’an, CHINA

Guangliang Ren The State Key Laboratory of ISN

Xidian University Xi’an, CHINA

Chunhui Le Huawei Technologies

Shanghai, CHINA

Abstract—An iterative carrier frequency offset (CFO) estimation method is proposed for the physical uplink control channel (PUCCH) of 3GPP-LTE in high speed train environment. In the algorithm, the signal of one user in the received multi-user signals is separated by despreading, and the despreaded pilot signals of the user are employed in the cross-correlation operation to estimate the coarse CFO in frequency domain. The data signals compensated by the estimated coarse CFO, are employed to estimate the fine CFO by the cross-correlation operation. Simulation results show that the proposed scheme has high accuracy in low SNR and low complexity, and improve the performance of the system greatly.

Keywords-LTE; PUCCH; carrier frequency offset estimation; high speed train; multi-user

I. INTRODUCTION The goal of next generation wireless communication is to

realize the mobile multimedia transmission with high quality and high data rate. Long Term Evolution (LTE) of 3GPP, or E-UTRA supports peak rates up to 300Mbps in downlink and 75Mbps in uplink. With the development of the high speed train, the speed of the train can up to 350Km/h, and LTE has already been a communication standard in high speed train environment. However, there are many problems due to the high speed environment, such as fast-varying channel and large Doppler shift (e.g. when users are moving at a speed of 350km/h, the Doppler shift will come up to 1490Hz in LTE uplink system).

The PUCCH is a code-multiplexed narrow band channel where more than one user is multiplexed by means of CDMA on the same set of carriers. The control information carried by PUCCH is important to the performance of the system, so the performance of PUCCH should be guaranteed even when it works under very low SNR environment, e.g. some users are located at the edge of the cell. The large Doppler shift, will cause the decrease of the detection probability of PUCCH for multi-user in low SNR environment, and further lead to the loss of the performance of the LTE system. Thus, a new frequency offset estimator, which can cover large frequency range and has high accuracy for multi-user in low SNR, is required to maintain the link quality for PUCCH in high speed train environment. LTE is usually used in low-speed environment. Therefore, there aren’t any research about carrier frequency offset estimation on PUCCH in recent years.

However, there are many algorithms about CFO estimation in OFDM system. The available CFO estimation algorithms in OFDM system are generally classified into two categories, i.e., time-domain estimation algorithm [1][2], e.g. the cyclic-prefix-based (CPB) scheme and the training-symbol-based method, and frequency-domain estimation algorithm [3][4]. However, both of [1] and [2] estimate the CFO in time-domain, and the multi-user occupy the same resource both in frequency-domain and in time-domain on PUCCH, on which we can’t separate the signal of each user in time-domain. Therefore, these two methods are not applicable for PUCCH of LTE. The frequency-domain estimation algorithm, e.g. pilot-tone-aided method [3][4], can’t directly apply to the PUCCH of LTE either, because multi-user occupy the same subcarriers in frequency domain.

To estimate CFO on PUCCH, and get high estimation accuracy for multi-user in low SNR, we propose an iterative carrier frequency offset (CFO) estimation algorithm for PUCCH formats 1a/1b. The following sections are organized as: In section Ⅱ, system model is described and in section Ⅲ, CFO estimation algorithm is introduced for PUCCH formats 1a/1b. In section Ⅳ, simulation results are presented. Finally, basic conclusions are drawn in section Ⅴ.

II. SYSTEM MODEL

A. Pucch Structure In LTE uplink, a 1 ms subframe consists of two 0.5ms slots,

each of which has 7 SC-FDMA symbols in case of normal cyclic prefix, and which is placed at the edges of the system bandwidth. The PUCCH consists of 12 subcarriers over 2 resource blocks, between which slot-based frequency hopping is adopted. The ACK/NACK signals from different UEs are multiplexed by means of CDMA on PUCCH, and each ACK/NACK signal is code spread by the cyclic shift sequences and orthogonal cover sequences [5]. PUCCH has two basic transmission formats called formats 1a/1b and format 2, each of which can multiplex multiple users. In this paper, we mainly talk about PUCCH formats 1a/1b.

Reference signal (RS) symbols and data symbols are time-division multiplexed within a subframe. Multiple users are code-division multiplexed with different length-12 orthogonal sequence mapped to the 12 subcarriers. UE generates one ACK/NACK signal corresponding to the transmission result of

This work was supported in part by the State Natural Science Foundation of China, Grant No.61072102, and National Major Specialized Project of Science and Technology, Grant No.2011ZX03001-007-01, and was partly funded by Huawei Technologies Co., Ltd.

the downlink data, and this signal is code spread onto the 1st, 2nd, 6th and 7th SC-FDMA symbols, while the RS is code spread onto the 3rd , 4th and 5th SC-FDMA symbols.

B. Signal model Consider the uplink of an 3GPP-LTE based SC-FDMA

system supporting N subcarriers, and accommodating a maximum of K simultaneously active users on PUCCH. We suppose kb the modulated control information for the kth

active user, and , , , ,[ (0), (1), , (11)]Tk i k i k i k iC C C=C … is the

kth active user’s length-12 orthogonal sequence during the ith SC-FDMA symbol. Then ,k iC will map onto

, , , ,[ (0), (1),..., ( 1)]k i k i k i k iA A A N= −A . kS are the modulated information for the kth user during each SC-FDMA symbol in a subframe, following

[ (0), (1), , (13)] [ , ,1,1,1, , , , ,1,1,1, , ]k k k k k k k k k k k kS S S b b b b b b b b= =S … (1)

The orthogonal cover sequence for the kth user used in a subframe is described as

,0 ,1 ,0 ,1 ,2 ,2 ,3

,0 ,1 ,0 ,1 ,2 ,2 ,3

[ (0), (1), , (13)] [ , , , , , ,

, , , , , , , ]k k k k k k k k k k k

k k k k k k k

p p p w w w w w w w

w w w w w w w

= =P …

(2)

where orthogonal covers sequences ,0 ,1 ,2 ,3[ , , , ]k k k kw w w w and

,0 ,1 ,2[ , , ]k k kw w w of the kth user, which are used for data symbols and pilot symbols respectively, are known at the receiver.

At the receiver, the received complex baseband signal during the ith symbol can be expressed as follows:

1 1

,0 0

( )( ) ( ) ( ) ( ) exp 2 exp( 2 ) ( )

K Ng s

i k k k i m k ik m

t N iN Tr t S i p i A m H j m j f t n t

NTπ π

− −

= =

− +⎡ ⎤= +⎢ ⎥

⎣ ⎦∑∑

(3)

where mH is the frequency domain channel response, which we may reasonably consider a const on PUCCH during a symbol. gN is the samples of the CP for the elimination of

the inter-symbol interference, and sN indicates the samples

during one SC-FDMA symbol, s gN N N= + . kf is the

carrier frequency offset of the kth user, and ( )in t is additive

white Gaussian noise with zero mean and variance 2wσ .

After sampling, removing the CP and FFT process, the ith symbol is given by

12 /

,0

, , , ,

( ) ( )

exp 2 ( ) ( ) ( ) ( ) ( )

Nj nl N

k i in

g sk l k k k i i l k i k i

Z l r n e

N iNj H S i p i A l I l u l

N

π

πε α

−−

=

=

+⎛ ⎞= + +⎜ ⎟

⎝ ⎠

∑ (4)

where kε is the normalized CFO of the kth user, , ( )k iI l means

the ICI of the kth user, and , ( )k iu l is the inter-user

interference and noise. ,i lα is a attenuation coefficient caused

by the residual carrier frequency offset, and , 1i lα → .

III. PROPOSED SECHEME In this section, The proposed CFO estimation algorithm is

described in detail. According to previous analysis, we assume that , ( )k iZ l and , 1( )k iZ l+ are the ith and i+1th SC-FDMA symbol for the kth user in a slot in frequency domain, respectively, following as

12 /

,0

, , , ,

( ) ( )

exp 2 ( ) ( ) ( ) ( ) ( )

Nj nl N

k i in

g sk l k k k l i l k i k i

Z l r n e

N iNj H S i p i A i I l u l

N

π

πε α

−−

==

+⎛ ⎞= + +⎜ ⎟

⎝ ⎠

∑ (5)

and

12 /

, 1 10

, 1, , 1 , 1

( ) ( )

( 1)exp 2 ( 1) ( 1) ( 1) ( ) ( )

Nj nl N

k i in

g sk l k k k l i l k i k i

Z l r ne

N i Nj HS i p i A i I l u l

N

π

πε α

−−

+ +=

+ + +

=

+ +⎛ ⎞= + + + + +⎜ ⎟

⎝ ⎠

∑(6)

A. Despreading According to the orthogonal of the cyclic shift sequences,

users’ signal can be separated by despreading. After separating users, each of the SC-FDMA symbol becomes one sample, expressed as

*, , ,

, ,

( ) ( )

12exp 2 ( ) ( )

k i k i k il

g sk k k k i k i

B Z l A l

N iNj HS i p i I u

Nπε

=

+⎛ ⎞= + +⎜ ⎟

⎝ ⎠

∑ (7)

and

*, 1 , 1 , 1

, 1 , 1

( ) ( )

( 1)12exp 2 ( 1) ( 1)

k i k i k il

g sk k k k i k i

B Z l A l

N i Nj HS i p i I u

Nπε

+ + +

+ +

=

+ +⎛ ⎞= + + + +⎜ ⎟

⎝ ⎠

∑ (8)

where ,k iI is ICI of the kth user during the ith symbol in

frequency domain, which is almost eliminated. ,k iu is the inter-user interference and noise, and the inter-user interference can be ignored.

B. Coarse CFO Estimation In this algorithm, the CFO is estimated in frequency

domain. The coarse CFO is achieved by cross-correlation operation between pilots symbols, between which the interval is one symbol in a slot, following

*,4

, *,2

(4)ˆ

4 (2)k k

k coarsems k k

B pN angleN B p

επ

⎧ ⎫⎪ ⎪= ⎨ ⎬⎪ ⎪⎩ ⎭∑ (9)

where m is the index of slot in a subframe. This method can get large estimation range.

The CFO is large, if CFO is directly estimated by fine CFO estimation according to data signals correlation without estimating coarse CFO first, the large estimation range will not be obtained, and there will occur ‘phase ambiguity’ for fine CFO estimation. Thus, coarse CFO is estimated for large estimation range and fine CFO is evaluated for high accuracy.

C. Fine CFO Estimation After compensating part of the coarse CFO estimations,

there will not occur ‘phase ambiguity’ for fine CFO estimation, and can reduce the influence of the noise. The fine CFO is estimated according to the cross-correlation between the data symbols, between which the interval is four symbols. Thus, it can be obtained as

* *,5 ,6

, * *,0 ,1

(5) (6)ˆ

10 (0) (1)k k k k

k finems k k k k

B p B pN angleN B p B p

επ

⎧ ⎫⎡ ⎤⎪ ⎪= +⎢ ⎥⎨ ⎬⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

∑ (10)

where m is the index of slot in a subframe.

Therefore, the total CFO estimation for the kth active user becomes

, ,ˆ ˆ ˆ*k k coarse k fineε α ε ε= + (11)

Where α is a coefficient, and 0 1α< ≤ 。This algorithm is named as twice iterative CFO estimation scheme.

The Cramer-Rao bound of the CFO is given as [6]

2 2 20

1ˆ( )4 ( / ) /s p rxs block s

MSEN N N n N D E N

επ

=⋅ ⋅ ⋅ ⋅

(12)

Where rxsn is the number of receiver antenna, and

blockN means the number of subcarriers in a resource block,

and D is the interval of the cross-correlation between data symbols.

IV. SIMULATION RESULTS The performance of the proposed twice iterative CFO

estimation algorithm has been investigated by computer simulation.

A. High Speed Train (HST) Scenario For simulating the HST scenario [7], we adopt the

propagation models, which are described in TABLE 1. The maximum Doppler shift is given as

max /cf f v c= (12)

where cf is the carrier frequency in Hz, v is the velocity of the train, and c is the speed of light ,both in m/s.

In HST scenario, Doppler shift is described as

max cos ( )df f tθ= (13)

where cos ( )tθ is written by

002 2

0

cos ( ) , 0 2 /( )B

d vtt for t d vd d vt

θ −= < <+ +

(14)

where 0d is the initial distance of the train from the eNodeB,

and Bd is the distance between the eNodeB and the railway track, both in meters, and t is time in seconds.

TABLE I. PROPAGATION MODELS FOR HST SCENARIO

Scenario Open space Tunnel with leaky cable

Tunnel for multi-

antennas Model Static with

Doppler shift Single tap

Ricain fading Static with

Doppler shift ISD 1000m infinity 300m

BS-track distance 50m - 2m Rician factor - 10 - Train speed 350km/h 300km/h 300km/h Considering

maximum Doppler shift

1340 Hz 1150 Hz 1150Hz

B. Simulation Parmeters The parameters used in the LTE PUCCH, which is an SC-

FDMA system with one transmit antennas and two receive antenna, are from [5]. In this simulation, The length of FFT is 1024. And the number of the user K = 1,2,4,8,12, respectively, and α is set to be 0.5.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

K=1K=2

K=4

K=8

K=12CRB

Figure 1. MSE of CFO estimation vs. SNR with different users (HST scenario 3)

Fig. 1 and Fig. 2 show the MSEs of the carrier frequency offset estimation by the proposed method with different users in the SC-FDMA system, of which the channel model are HST scenario 1 and HST scenario 3, respectively , and compared with the CRB. It can be seen from the curves that with the increasing of users’ number, the MSE of the CFO estimation increase on a fixed SNR due to the multi-user interference. However, performance degrades a little with the increasing number of users. Therefore, the proposed algorithm is robust to the number of users. Figures also indicate that the performance of the proposed algorithm has high accuracy in low SNR.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 010

-6

10-5

10-4

10-3

10-2

SNR(dB)

MS

E

K=1K=2

K=4

K=8

K=12CRB

Figure 2. MSE of CFO estimation vs. SNR with different users (HST

scenario 1)

Fig. 3 shows the miss detection rate on PUCCH with CFO estimation and without CFO estimation, respectively. It can be seen from the curves that large CFO lead to high miss detection rate in low SNR, which cause performance degradation, and the proposed method can decrease the miss detection rate ,which improve the performance greatly.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 010

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

mis

s de

tect

ion

rate

no CFO estimation

CFO estimation and compensation

Figure 3. PUCCH miss detection rate vs. SNR with no CFO estimation and CFO estimation

V. CONCULTION To estimate the CFO in the high speed train environment,

we proposed an twice iterative CFO estimation algorithm for PUCCH. The despreaded pilot signals of the user are employed in the cross-correlation operation to estimate the coarse CFO in frequency domain. The data signals compensated by the estimated coarse CFO, are employed to estimate the fine CFO by the cross-correlation operation. The simulation results shows that the scheme is robust to the number of users, and it has high estimation accuracy in low SNR. The proposed method also decrease the miss detection rate on PUCCH in low SNR, which improve the performance greatly.

REFERENCES [1] H. Chen and G. J. Pottie, “A comparison of frequency offset tracking

algorithms for OFDM,” in Proc. IEEE GLOBECOM, 2003, pp. 1069-1073.

[2] N. Lashkarian and S. Kiaei, “Class of cyclic-based estimators for frequency-offset estimation of OFDM systems,” IEEE Trans. Commun., vol. 48, no. 12, pp. 2139-2149, Dec. 2000.

[3] S. Kapoor, D. J. Marchok, and E.-F. Juang, “Pilot assisted synchronization for wireless OFDM systems over fast time varying fading channels,” in proc. 48th IEEE VTC, May 18-21, 1998, vol. 3, pp.2077-2080.

[4] W. Lei, J. Lu, and J. Gu, “A new pilot assisted frequency synchronization,” in Proc. IEEE ICASSP, Apr. 6-10, 2003, vol. 4, pp. IV-700-IV-703.

[5] 3GPP, TS 36.211, Physical Channels and Modulation, V8.7.0 May 2009.

[6] K. Shi, E. Serpedin, and P. Ciblat, “Decision-directed fine synchronization in OFDM systems,” IEEE Trans. Commun., vol. 53, no. 3, pp. 408-412, Mar. 2005.

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