This paper presents a novel blind estimation scheme for carrier frequency offset (CFO) in single-input single-output orthogonal frequency division multiplexing (SISO-OFDM) systems that overcomes limitations of existing methods. The proposed scheme, based on constant modulus signaling, shows better performance than traditional kurtosis-type schemes in terms of bit error rate, albeit with slightly higher computational complexity. Extensive simulations confirm the effectiveness of the scheme, making it applicable to all signal constellations.

1. ACEEE Int. J. on Network Security, Vol. 01, No. 03, Dec 2010
Blind Estimation of Carrier Frequency Offset in
Multicarrier Communication Systems
Arvind Kumar. Author, and Rajoo Pandey
Department of Electronics and Communication Engineering, National Institute of Technology Kurukshetra, India
arvindsharmanitk@rediffmail.com, rajoo_pandey@rediffmail.com
Abstract—Orthogonal Frequency Division Multiplexing The computational complexity of the scheme is
(OFDM) systems are very sensitive to carrier frequency offset approximately same as that of kurtosis type scheme. The
(CFO), caused by either frequency differences between CFO estimation scheme of [9] can be used only with
transmitter and receiver local oscillators or by frequency constant modulus signaling like M-ary PSK, but it is not
selective channels. The CFO disturbs the orthogonality among
subcarriers of OFDM system and results intercarrier
applicable for M-ary QAM (for M>4).
interference (ICI), which degrades the bit error rate (BER) In this paper, we present a novel CFO estimation scheme
performance of the system. This paper presents a new blind that overcomes the limitation of [9]. The scheme presented
CFO estimation scheme for single-input single-output (SISO) in this paper is similar to scheme of [9] but not limited to
OFDM systems. The presented scheme is based on the constant modulus signaling. The proposed scheme assumes
assumption that the channel frequency response changes that the channel frequency changes slowly in the frequency
slowly in frequency domain. In this scheme an excellent trade- domain. The effect of this assumption is that the channel
off between complexity and performance, as compared to behaves nearly same for the two neighboring subcarriers.
existing estimation schemes, is obtained. The improved We exploit this slowly changing property of channel, in
performance of the present scheme is confirmed through
extensive simulations.
frequency domain, to derive the cost function. It is shown
in [9] that the minimization of the cost function gives a
Index Terms— OFDM systems, carrier frequency offset unique estimate of CFO.
(CFO), intercarrier interference (ICI). It is shown that the performance of the proposed scheme
is better than that of kurtosis type (and similar to scheme of
I. INTRODUCTION [9]) but its computational complexity is somewhat more
than that of [9]. In the present scheme it is assumed that the
Orthogonal frequency division multiplexing has been channel frequency response changes slowly in frequency
adopted as a modulation scheme in various digital domain as was the case in [8] and [9].
communication systems, such as digital audio/video The organization of rest of the paper is as follows:
broadcasting (DAB/DVB) and several wireless local area Section II presents the SISO-OFDM system model under
networks (WLANs). OFDM is very sensitive to frequency consideration. The proposed scheme for SISO-OFDM
errors caused by frequency difference between the local systems is described in section III. Simulation results are
oscillator in the transmitter and the receiver or by discussed in section IV. Finally, the paper concludes the
frequency selective channels [1]. This frequency offset overall findings of the study.
causes a number of impairments including attenuation and
phase rotation of each subcarrier and ICI between II. SYSTEM MODEL
subcarriers. Therefore, OFDM system requires accurate
frequency offset estimation and correction [2], [3]. In SISO-OFDM, the wide transmission spectrum is
Most of the CFO estimation methods, presented in the divided into narrower bands and data is transmitted in
literature, rely on periodically transmitted pilots [3], [4]. parallel on these narrow bands. Let us assume a SISO-
The pilot-assisted methods are less useful for continuous OFDM system with N orthogonal subcarriers. This
transmission OFDM based systems such as DAB and DVB multicarrier transmitter partitions the data stream into a
and they also reduce the spectral efficiency of the system. block of N data symbols that are transmitted in parallel by
Blind CFO estimation is proposed to improve the spectral modulating the N orthogonal subcarriers. Thus if ts is the
efficiency of CFO estimation methods in OFDM systems input data symbol duration, the OFDM symbol duration T
[5], [6]. In [7], the kurtosis metric is considered to becomes Nts . In the mth OFDM symbol duration, a vector
construct a kurtosis type cost function for fine CFO of N symbols, namely, X m = [ X m ,0 , X m ,1 ,... X m , N −1 ]T is
estimation. This scheme gives a closed form CFO
estimation using curve fitting but its estimation accuracy transmitted simultaneously on N orthogonal subcarriers.
requires a large number of OFDM symbols. A blind carrier Assuming multipath fading channel frequency response
frequency offset estimation scheme with constant modulus changes slowly during one OFDM symbol duration, thus
(CM) signaling is presented in [9]. This scheme can be represented for mth OFDM symbol duration as
outperforms the kurtosis-type scheme of [8] in terms of H m = diag ([ H m ,0 , H m ,1 ,..., H m , N −1 ]T ) .
BER. Let Δf be the CFO introduced by mismatch between
local and the transmit oscillators and define the normalized
Corresponding author: Arvind Kumar
50
©2010 ACEEE
DOI: 01.IJNS.01.03.234

2. ACEEE Int. J. on Network Security, Vol. 01, No. 03, Dec 2010
Δf 1 1 5 9
CFO as ε = . At the receiver, the received noisy {K } = [1,5, ,9, , , ] . Thus, based on the above
(1/ T ) 5 9 9 5
signal is mixed with a local oscillator signal having assumption, we propose a cost function, which minimizes
frequency Δf above the correct frequency. Then, the N time the difference of the signal power for each pair of
domain samples in the mth received OFDM symbol consecutive subcarriers as
duration, namely, y m = [ ym ,0 , ym,1 ,..., ym , N −1 ]T can be
ε% = a r g m in J ( εˆ )
expressed as m in i εˆ ∈ [ − 0 . 5 0 .5 )
( j 2πε / N [( m −1) N + mLcp ])
ym = e C(ε ) WH m X m + w m (1)
where
where m = 1, 2,..., M , Lcp denotes the length of cyclic
prefix (CP) which is assumed to be longer than the M −1 N −1
∑ ∑ (∏ { Y
2 2
maximum channel delay spread, W is the N × N J (ε ) =
ˆ m, n (ε ) − K i Ym ,(( n +1)) N (ε ) }) 2
ˆ ˆ (5)
m = 0 n = 0 min, i
normalized inverse discrete Fourier transform (IDFT)
matrix, and w m = [w m ,0 , w m ,1 ,..., w m, N -1 ]T is a vector of
Since we have
independent zero mean white Gaussian noise samples with
variance σ n . The effect of CFO on the received samples of
2
M −1 N −1 4 M −1 N −1
∑∑Y (ε ) = ( K i ) 2 ∑ ∑ Ym,(( n +1)) N (ε )
4
OFDM signal is represented by m,n
ˆ ˆ
j 2π j 2π j 2πε m =0 n =0 m=0 n=0
×1 × ( N −1) [( m −1) N + mLcp ]
C(ε ) = diag ([1, e N ,..., e N ]T ) and e N
where the latter expression represents the common phase the above cost function can be simplified as
error resulting from the CFO. Therefore, it is clear from (1) 4
M −1 N −1
( Ki )2 + 1
that the intercarrier interference (ICI) introduces in the
received signal because of CFO.
J (ε ) =
ˆ ∑ ∑[
m=0 n =0 ( Ki )2
Ym , n (ε )
ˆ
(6)
At the receiver, CFO is estimated first and then the K +1 2 2
− i Ym , n (ε ) Ym ,(( n +1))N (ε ) ]
ˆ ˆ
signal is compensated in the time domain by using this Ki
estimated CFO denoted by ε . After compensation, the
ˆ
samples of time domain signal are passed through the IV. SIMULATION RESULTS
discrete Fourier transform (DFT) stage. The output of the
DFT stage can be represented as In order to examine the performance of the proposed
Ym (ε ) = W H C * (ε )y m
ˆ ˆ (2) scheme, simulations of the proposed scheme, blind carrier
frequency offset estimation of [9] are presented in this
where W H and (•)* represent the Hermitian transpose and section.
conjugate operation, respectively. To compare the performance of various schemes BER is
computed. The OFDM system with 64 subcarrier and 16-
III. PROPOSED SCHEME QAM signal constellations is considered for the study. In
our simulations, we assume CFO is uniformly distributed
This section presents the proposed scheme for SISO-
in the range [−0.5 0.5) . The multipath fading channel is
OFDM systems.
If the CFO is completely compensated before DFT frequency selective fading channel and has six independent
stage, i.e., ε = ε , the DFT output will be without ICI.
ˆ Rayleigh fading paths with exponentially decaying powers
Therefore, in the noise free conditions, the DFT output will as in [8]. It is assumed that the channel and CFO dose not
be represented as change while estimation of CFO is performed.
The cost function for the kurtosis-type and the proposed
Ym (ε | ε = ε ) = H m X m
ˆ ˆ (3)
scheme are plotted in Fig1. and Fig.2, respectively. The
The squared amplitude of the DFT outputs would be Fig. 3-Fig. 4 represents the BER comparison of the
proposed scheme with the kurtosis-type scheme over
2
Ym , n (ε | ε = ε ) = H m X m .
2
ˆ ˆ frequency selective fading channel. We observed from
these figures that the BER of the proposed scheme is better
In the case of slowing fading channel, the channel than the kurtosis type scheme. In terms of complexity, both
frequency response on two consecutive subcarriers is the schemes have somewhat the same complexity. The
approximately the same. Therefore, we would have scheme presented in [9] is applicable to CM signal
constellations only, whereas the proposed scheme is
2
ˆ ˆ
2
Ym , n (ε | ε = ε ) ≈ K i Ym ,(( n +1)) N (ε | ε = ε )
ˆ ˆ (4) applicable to all types of signal constellations. So, it can be
concluded that the present scheme significantly
outperforms the kurtosis-type and the scheme of [9] in
where (( a )) N denotes a modulo N , and K i ∈ {K } where terms of BER. However, the computational complexity of
K represents a set of constants for a given signal the proposed scheme is somewhat poorer than that of [9].
constellation, e.g., in case of 16-QAM
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©2010 ACEEE
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3. ACEEE Int. J. on Network Security, Vol. 01, No. 03, Dec 2010
CONCLUSIONS
OFDM is an effective technology for high data rate
transmissions. The frequency offset in mobile radio
channels distorts the orthogonality between subcarriers
resulting in ICI, which seriously degrades the performance
of systems. This paper has presented a novel blind
estimation of CFO that is applicable to all types of signal
constellation in contrast with the scheme of [9]. The
present scheme gives better performance than the kurtosis-
type scheme in terms of BER. However, these benefits are
derived at the cost of slight increase in the system
complexity.
REFERENCES Fig. 2. Plot of cost function for Proposed scheme
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Fig. 1. Plot of cost function for Kurtosis type scheme
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©2010 ACEEE
DOI: 01.IJNS.01.03.234