TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214ll11/19llpp487-491 Volume 14, Number 4, August 2009

Interference-Cancellation-Based Carrier Frequency Offset Estimation for OFDMA Uplink Transmissions*

SU Huan ( ), ZHANG Chao ( )†, LU Jianhua ( )**

Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; † School of Aerospace, Tsinghua University, Beijing 100084, China

Abstract: A carrier frequency offset (CFO) estimator was developed based on an interference cancellation

scheme for an orthogonal frequency division multiplex access uplink. An initial CFO estimate was first ob-

tained based on the received training signals at each user’s prescribed subcarrier positions. Then, the re-

ceived training signals were compensated by using the initial CFO estimates in the frequency domain and

the multi-user interferences were estimated. Finally, the interference-cancelled training signals were used to

reliably estimate each user’s CFO. The CFO estimator performance was evaluated by the bit error rate per-

formances of the CFO compensation-based receivers at the base station. Simulations show that with this

optimal interference-cancellation-based CFO compensation receiver, the performance gain with the esti-

mated CFO values is approximately 3 dB better at the 0.1% bit error rate than the initial CFO estimates.

Key words: orthogonal frequency division multiplex access (OFDMA); uplink; carrier frequency offset esti-

mation; compensation; interference cancellation

Introduction

In orthogonal frequency division multiple access (OFDMA), signals from different users overlap in the frequency domain but occupy different subcarriers. The orthogonality among subcarriers prevents inter- carrier interference (ICI), which eliminates multiple access interference (MAI) among users. OFDMA has been recognized as a promising technology for wire-less metropolitan area networks (WMANs)[1], satellite communications[2], cable TV transmissions[3], and long-term evolution (LTE) of 3G[4].

As with orthogonal frequency division multiplexing (OFDM), OFDMA is sensitive to the carrier frequency offset (CFO) between the transmitter and the receiver.

Inaccurate CFO estimates result in the loss of or-thogonalilty among subcarriers, thus leading to severe performance degradation. Particularly in the uplink transmission, when each user suffers from different frequency offsets, the CFO introduces not only ICI but also MAI or multiple user interference (MUI)[5].

For OFDMA uplink transmissions, the sub-band- based subcarrier assignment scheme has been stud-ied[6,7], in which signals from different users occupy non-overlapping frequency bands in a similar fashion as traditional frequency division multiple access (FDMA). Guard subcarriers at the edge of each sub-band minimize the MAI. Signals from different users can, thus, be separated by filter banks with exist-ing synchronization algorithms for OFDM applicable for the signal on each sub-band.

The carrier frequency offsets of multiple users in the interleaved OFDMA uplink have been estimated[8]. These algorithms are based on the algebraic signal structure in the OFDMA uplink when using the

Received: 2008-07-02; revised: 2009-02-23

* Supported by the National Key Basic Research and Development(973) Program of China (No. 2007CB310601)

** To whom correspondence should be addressed. E-mail: lujh@wmc.ee.tsinghua.edu.cn; Tel: 86-10-62792550

Tsinghua Science and Technology, August 2009, 14(4): 487-491 488

interleaved carrier assignment scheme with a complete subspace-based method to estimate multiple users’ CFOs.

Another synchronization scheme proposed for OFDMA uplinks[9] does not rely on any specific sub-carrier assignment scheme. However, it assumes that only one user is asynchronous with the uplink receiver. Hence, it applies only to the single-user synchroniza-tion error problem.

A CFO estimator presented in this paper is based on an interference cancellation scheme for OFDMA up-links. The estimator requires that all users send training symbols at the beginning of the uplink transmission process which are composed of two identical OFDM symbols in the time domain. Each user transmits its training symbols in the prescribed subcarrier set, thus, the CFO method is applicable to any subcarrier as-signment scheme.

1 System and Signal Model

Consider an OFDMA uplink with M users, where each user communicates with the base station through an independent multipath channel. For simplicity, assume that both time synchronization and sampling frequency are ideally performed. Further, assume that there are N subcarriers in each OFDM symbol. Only one subcar-rier can be assigned to one user. The information sym-bol for the i-th user at the k-th subcarrier is denoted by

( )ikX , ik , where i is the set of subcarriers as-

signed to user i. Then, 1 0,1,..., 1Mi i N and

i j for i j . In the OFDMA uplink, the

length of the guard interval is equivalent to gN and is

assumed to be longer than the maximum channel delay spread. After inverse discrete Fourier transform (IDFT) processing and guard-interval insertion at the transmit-ter, the time domain sequence of the i-th user is given by

j2( ) ( )1 ei

nki i N

n kk

x XN

, g 1N n N (1)

After passing through the channel, the i-th user’s signal is

( ) ( ) ( )i i in n ny x h (2)

where “ ” denotes linear convolution and ( )inh is the

i-th user’s channel impulse response (CIR). Further,

assume that ( )inh is nonzero only for 0,1,..., 1n L ,

where L is the maximum channel delay spread. By taking into account the CFOs and the additive noise, the received signal is given by

( )j2( )

1

ei nM

i Nn n n

i

r y z (3)

where (i), i=1,…,M denotes the i-th user’s CFO nor-malized by the subcarrier spacing and zn is the additive white Gaussian noise.

2 CFO Method

Assume that each user transmits training symbols over its pre-assigned subcarriers at the beginning of the up-link transmission process. Since the received signal power for a specific user is mainly concentrated in the prescribed subcarrier positions, the training symbols for different users can be transmitted simultaneously. Two OFDM symbols are utilized to estimate the CFO[10]. Let {Y1, k | k m} and {Y2, k | k m} denote the received signals at the m-th user’s subcarrier posi-tions for the first and second received training OFDM symbols. Then, the initial CFO for the m-th user is given by

2, 1,( )

2, 1,

Im( )1 arctan

2 Re( )m

m

k km k

k kk

Y Y

Y Y (4)

Note that Eq. (4) was originally developed for single-user systems and, therefore is not resistant to MAI. The following utilizes the CFO compensation scheme at the base station to estimate the MAI and then uses an MAI cancellation scheme to reliably ob-tain the CFOs.

In a single-user detector, for the m-th user, the re-ceived sequence rn is multiplied by a time domain se-quence exp( j2 (m)n/N) before the discrete Fourier transform (DFT) processing[11]. After the multiplication, the signal at the m-th branch is given by

( )( ) j2 /emm n N

n nr r ( ) ( ) ( )( ) ( ) j2 ( ) / j2 /

1

e ei m m

Mm i n N n N

n n nii m

y y z (5)

Here, the first term is the signal for the m-th user, the second term is the MUI, and the third term is the addi-tive noise.

In the single-user detector, one DFT block is needed

SU Huan ( ) et al. Interference-Cancellation-Based Carrier Frequency Offset … 489

for each user to detect the information symbols. To reduce the required number of DFT blocks, the CFOs can be compensated for in the frequency domain. In the post-DFT processing method proposed by Choi et al.[12], the received signal after the guard-interval re-moval and the DFT processing is

( )( ) j2

1DFT e

ii

nMN

k N n ni

R y z ( ) ( )

1

Mi i

k k ki

Y C Z

(6) where denotes circular convolution, ( )i

kY ( )DFT ( )i

N ny , ( )( ) j2 /DFT (e )ii n N

k NC , DFT ( )k N nZ z ,

and 1 j2 /0

DFT ( ( )) (1 / ) ( )eN nk NN n

f n N f n for any

function f (n). Equation (6) can be written into vector form as

( ) ( )

1

Mi i

iR Y C Z

( ) ( ) ( ) ( )

1

Mm m i i

ii m

Y C Y C Z (7)

where T0 1 1[ , ,..., ]NR R RR , ( ) ( ) ( ) ( ) T

0 1 1[ , ,..., ]i i i iNY Y YY ,

( ) ( ) ( ) ( ) T0 1 1[ , ,..., ]i i i i

NC C CC , and T0 1 1[ , ,..., ]NZ Z ZZ .

In Eq. (7), the first term is the m-th user’s received signal, the second term is the MUI, and the third term is the additive noise. The m-th user’s received signal can then be represented by an N×1 vector ( )mY

( ) ( ) ( ) T0 1 1[ , ,..., ]m m m

NY Y Y as ( ) ( ) ( )m m mY Y C (8)

Since C (m) is the frequency-domain representation of exp(j2

(m)n/N), n=0,1,…,N 1, Y (m) can be restored from Y (m) as

( ) ( ) ( )m m mY Y C (9) where ( ) ( ) ( ) ( ) T

0 1 1[ , ,..., ]m m m mNC C CC and ( )m

kC ( )j2 /DFT (e )m n N

N . When the CFOs are small compared with the sub-

carrier spacing, the received m-th user’s power is mainly concentrated in the prescribed subcarrier posi-tions. Then, Y (m) can be replaced by A(m)R to obtain Y(m) , where A(m) is the diagonal matrix,

( ) 1, ;( 1, 1)

0, mm

m

ii i

iA (10)

where m is the set of subcarriers assigned to user m. As a result, the m-th user’s signal for the post-DFT

processing method is given by ( ) ( ) ( ) ( )ˆ (( ) )m m m mY A A R C

( ) ( ) ( ) ( ) ( )(( ( )) )m m m m mA A Y C C

( ) ( ) ( ) ( ) ( )

1

Mm m i i m

ii m

A A Y C C

( ) ( ) ( )(( ) )m m mA A Z C (11) In Eq. (11), the first term includes both the signal for

the m-th user and the ICI, the second term is the MUI, and the third term is the additive noise. Huang and Le-taief proposed an interference-cancellation (IC) scheme to further reduce the MUI[13]. The interference cancel-lation algorithm is iterative with ( ),ˆ m jY denoting the restored signal at the j-th step as follows.

Initiation: Set j=0 and ( ), ( ) ( )ˆ (( )m j m mY A A R ( ) )mC , for m=1,2,…,M.

Loop: j=j+1 Set

( ), ( ), 1 ( )

1

ˆM

m j i j i

ii m

Y R Y C ,

for m=1,2,…,M (12) ( ), ( ) ( ) ( ), ( )ˆ (( ) )m j m m m j mY A A Y C ,

for m=1,2,…,M (13) Go back to Loop. Let {Y1, k | k m} and {Y2, k | k m} denote the re-

stored signal ( ),ˆ m jY of the first and second received training OFDM symbols at the m-th user’s subcarrier positions, then, the CFO for the m-th user at the j-th step is

2, 1,

( ),

2, 1,

Im( )1 arctan

2 Re( )m

m

k km j k

k kk

Y Y

Y Y (14)

3 Simulations and Discussion

The simulation parameters used a carrier center fre-quency of 2 GHz, a system bandwidth of 5 MHz, and a sampling frequency of 7.68 MHz. The fast Fourier transform (FFT) size was 512 and the cyclic prefix was 40 samples. The number of active subscribers was M=16. The interleaved subcarrier assignment scheme was used with a total of 512 sub-carriers divided into 16 sub-channels with each sub-channel composed of 32 sub-carriers equally spaced in the total system bandwidth. Each user was allocated to one sub-channel. The average received signal powers at the base station

Tsinghua Science and Technology, August 2009, 14(4): 487-491 490

from all the users were assumed the same. The channel was a 3GPP M.1225 Pedestrian channel B and all sub-scribers’ channels were assumed to be statistically in-dependent and known perfectly at the base station. Each user’s data used quaternary phase shift keying (QPSK) modulation and channel coding/decoding at a rate-1/2 turbo code with a constraint lengh of 3/max-log-MAP decoding with 8 iterations. Each frame consisting of training symbols and 7 OFDM data symbols used a 30×50 data block bit interleaver. The normalized CFOs for 16 users were randomly assigned to 0.2 or 0.2. Both the CFO estimator and the inter-ference cancellation receiver used only one iteration.

The CFO estimator performance was quantified using the normalized root mean square error (RMSE) defined as

( )( ) 2

1 1

1 ˆNormalized RMSE= ( )k

Kk

kK (15)

where K is the number of active users, is the total number of tests, and ( )ˆ k is the estimate of ( )k . The subscript denotes the index of the test.

The normalized RMSEs of the initial CFO estimates (initial estimate) and the interference cancellation- based CFO estimates (current method) are plotted in Fig. 1. The results show that the MAI results in an er-ror floor for the initial CFO estimates. Removal of the MAI in the current CFO estimator gives much more accurate CFO estimates.

Fig. 1 Root mean square errors of the carrier frequency offset estimate

The bit error rate (BER) performances for the CFO compensation-based receiver at the base station are compared in Fig. 2 for receivers with ideal CFOs compensation by using a single-user detector, a post-DFT processing receiver, and an interference

cancellation receiver. The interference-cancellation scheme gives the best BER of the three CFO compen-sation receivers. The BER of an interference cancella-tion receiver compensated with ideal CFOs, the initial CFO estimates, and the estimated CFO estimates by the current method shown in Fig. 3 shows that com-pensation using the estimated CFOs in the current method gives an interference cancellation receiver with almost the same performance as when compensated with ideal CFOs. Furthermore, the performance gain of the interference cancellation receiver with the current CFO estimator is approximately 3 dB better at 0.1% BER than the initial CFO estimates.

Fig. 2 Bit error rates of interference cancellation receivers with ideal CFOs

Fig. 3 Bit error rate performance of interference cancellation receivers with ideal CFOs compensation and with the current CFO compensation

4 Conclusions

This paper presents a CFO estimator based on inter-ference cancellation for uplinks in OFDMA systems. The performance of this CFO estimator based on bit error rates of the receiver at the base station shows that

SU Huan ( ) et al. Interference-Cancellation-Based Carrier Frequency Offset … 491

with the optimal interference-cancellation-based CFO compensation receiver, the performance gain with the estimated CFOs by the current estimator is approxi-mately 3 dB better at the 0.1% bit error rate than with the initial CFO estimates.

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