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  Kavya Vinod, Suma  Sekhar                                                       Sakuntala S. Pillai, Senior Member- IEEE                               Department of Electronics and Communication                                     Department of Electronics and Communication

LBS Institute of Technology for Women,                                         Mar Baselios College of Engineering & Technology Thiruvananthapuram, India                                                                         Thiruvananthapuram, India

[email protected],                                                                            [email protected]

             [email protected]

Abstract— In this paper, a blind carrier frequency offset estimation technique for orthogonal frequency division multiplexing (OFDM) is proposed. For broadband wireless communication systems, this OFDM technique has been selected. OFDM provides large data rate with acceptable robustness to radio channel impairments. The estimation method is based on remodulated received vectors. A cost function is designed which is used to estimate CFO. It can be seen that the proposed estimator can achieve better estimation performance when compared with existing competitors.



The rapid growth in information network lead to the need for new communication technique. Orthogonal frequency-division multiplexing is an attractive modulation technique for high speed wireless data transmission due to its high spectral efficiency and robustness against frequency-selective channel. This OFDM technique is more powerful and is computationally efficient due to the use of FFT technique. In OFDM, a large number of orthogonal overlying narrow band subcarriers transmitted in parallel split the available transmission bandwidth. The main advantages of OFDM includes immunity to delay spread, efficient bandwidth usage, resistance to frequency selective fading. The majore demerits are large peak to average power ratio and synchronization issues.It is the modulation technique used in many broadband communication schemes including digital television, digital audio broadcasting, ADSL, and wireless LANs. It allows reliable and efficient transmission of digital data over a radio channe [8][11].

 OFDM system are sensitive to synchronization errors such as carrier frequency offset. CFO destroys the orthogonality between subcarriers and generates inter-carrier interference.One of the non-idealities in receiver design is CFO.  CFO is caused by Doppler shifts or imbalance in oscillators. When CFO occurs, there will be frequency shift in the received signal.

 CFO can be broadly divided into two: Integer part(IFO) and Fractional part(FFO). Basically for getting better performance, the CFO should be estimated and corrected.  Many methods  for CFO estimation have been proposed. These methods can be divided into two categories: Data aided method and non-data aided method.. This paper focuses on blind CFO estimation [2].

CFO causes the received signal to be shifted in frequency. This shift is illustrated below:


Fig 1.Frequency Offset

There will be a difference between the receiver generated carrier frequency with the one that is generated in the transmitter.. This difference is known as frequency offset.

δF = f-f’ (1)

where f is the carrier frequency in the transmitter and f’ is the carrier frequency in the receiver

The different sources of frequency offset include Doppler shift, frequency shift in transmitter and receiver oscillator, radio propagation and the tolerance of electronic elements  in local oscillator in transmitter and the receiver[2]. Doppler shift is mainly due to the relative motion of transmitter and receiver. As the receiver moves with some velocity relative to the transmitter, there will be changes in the phase shifts of the receiver signal. The Doppler effect defines the Doppler frequency as

    Fd = v.f/c (2)

Where v is the velocity of the moving receiver, c is the speed of light and f is the carrier frequency of transmitter.

Then the normalized CFO is

                     Ɛ = δF/Δf (3)

where  Δf is subcarrier spacing

Fig 2. System model

This normalized CFO has two parts : an integer and a fractional part. Therefore

Ɛ = Ɛi+ Ɛf (4)


CFO estimation and compensation algorithms have been proposed because CFO can produce Inter Carrier Interference which can be much worse than the effect of noise. The CFO estimation algorithms can be broadly classified into two:

1.Training based algorithm

2.Blind algorithm

In training based algorithms training symbols such as pilot tones or preambles are used .This algorithm have low computational complexity. The main demerit of this method is the reduction in data throughput. This method is also called as data aided method [12].

The non-data aided method or blind method uses the statistical properties of the received signal to estimate CFO. When compared with data aided method, blind method have no need of training sequence. So this method has high bandwidth efficiency.

Most of the existing estimators are based on pilot tones, which take place at the expense of bandwidth efficiency [1],[4]. These pilot tone methods are suited for packet oriented applications. Constant modulus constellation allows accurate CFO estimation [5]. A kurtosis type criterion based approach was proposed in [10]. In [9], diagonality based blind estimation was proposed.

In this paper, we propose a new blind CFO estimation method based on remodulation of received signal. This method works for OFDM system with or without virtual subcarriers. When compared with existing method this method has better result

with low complexity.


Consider an OFDM system model as shown in fig 2. Consider an OFDM system with N subcarriers in total. From this N subcarriers V subcarriers are deactivated and allocated to the spectrum to avoid intercarrier interference. Let L be the length of the cyclic prefix (CP). The relationship between data before and after modulation is given by,

where k=0,1,…N-1 and m is the data block.

Then cyclic prefix is added to the above signal and transmitted through the channel. At the receiver, the received signal is converted to parallel form.

Then, the received signal after removing cyclic prefix is given by,

where φ is the offset and w is the noise term.

The resulting signal is remodulated and offset is estimated.

In this paper, we will show how to estimate CFO from received signal in blind form. For blind estimation, there is no need of channel information.


The remodulated signal can be used for blind CFO estimation.

Let the received signal be   r’. Let us consider the remodulated vector:

That is remodulated vector is (N+L)×1 vector formed by the last N entries of (k-1)th  received signal and the first L entries of kth received signal.

Now, consider the following vector:


Based on this equation, we define a cost function and is given below:



where S1={0,1,………,L-1,N,N+1,……..,N+L-1} and K is total number of received block

Then CFO can be estimated using the equation

where φ € (-0.5,0.5]

 Using coarse estimation CFO can be estimated using the equation:

where phase is defined in the region (-Π, Π ].

After finding coarse estimate of CFO, we can find fine estimate of CFO using the equation given below:

where S2 is a subset of S1

Then the actual estimate of CFO is given by the equation,



The OFDM parameters are chosen as follows:



Total length of data


No. of simulated data


Modulation scheme


Offset Randomly selected

(-0.5 0.5]

Channel Noise


Table 1. Parameters and its values

The performance have been  investigated using Matlab R 201a. Here, we assume that the channel does not varies while CFO is estimated. The modulation scheme used is QPSK..

The mean square error MSE is defined as:

The result presented shows the symbol error rate and  mean square error as a function of signal to noise ratio. The symbol error vs SNR plot of the proposed estimator is shown below:


             Fig.3 Symbol error rate vs SNR

The MSE plot of the proposed estimator is

                            Fig 4. MSE vs SNR

The figure below shows the mse plot of the moose method. When compared with the proposed method, mse curve of the proposed method decreases with increase in SNR.        


        Fig 5 MSE vs SNR of moose method

             VI.  CONCLUSION

In this paper, we propose a new blind CFO estimation method. The main  advantage of this proposed method is its low complexity and has better performance.  Cost function minimization leads to an accurate and computationally efficient estimation. This method can be implemented to MIMO-OFDM system. In this paper we present how to empirically evaluate the symbol error rate and mean square error of OFDM system subjected to carrier frequency offset.



[1] M.Moreli and U. Mengali,” An improved frequency offset estimation for OFDM application,” IEEE Commun.LEtt.,vol.3,pp.75-77,Mar.1999

 [2] Saeed Mohseni and Mohammad A.Matin “Study of the estimation techniques for the carrier frequency offset in OFDM systems”, IJCSNS International journal of computer science and network security, vol.12,no:6

 [3] Timo Roman,Samuli Visuri and Visa Koivunen,” Blind frequency synchronization in OFDm via diagonality criterion”, IEEE transcation on signal processing, vol.54,no.8,August 2006

[4]J.Yu and Y.Su,”Pilot –assisted maximum likelihood frequency offset estimation for OFDm systems,” IEEE trans.Commun, vol.52,pp.1997-2008,Nov.2004

[5]M .Ghogho and A.Swami, “Blind frequency-offset estimator for OFDM systems transmitting constsnt modulus symbols,” IEEE Commn.Lett.,vol.6,pp.343-345,Aug.2002

[6] Weiyang u, Yuqing Wang, Xingbo Hu,”Blind joint estimation of carrier frequency offset and I/Q imbalance in OFDM systems” Elsevier signal processing108 2015

[7] Wei-yang XU, Bo LU, Xing-bo HU, Zhi-liang HONG;”Blind carrier frequrency offset estimation for constant modulus signaling based OFDM systems: algorithm,identofiablity and performance analysis”, Journal of Zhejiang Univesrity, ISSN 1869-1951,2010

[8] Andreas F Molish “Wireless communication” second edition

[9] Neha Mukul and Shailendra Singh Pawar,”BER and SER Based Performance Analysis of BPSK and QPSK modulation sechemes with OFDM in Rayleigh Fading Channel”IJETST-vol.01,issue:08,ISSN2348-9480 oct 2014

[10]Y.Yao and G.Giannakis,’’ Blind carrier frequency offset estimation in SISO, MIMO and multiuser OFDM systm,” IEEE Trans. Commun. Vol.53,pp.173-183,jan.2005.

[11] Megha Gupta1, Prof. Rajesh Nema2, Dr. Ravi Shankar Mishra3, Dr. Puran Gour,” Bit Error Rate Performance in OFDM System Using MMSE & MLSE Equalizer Over Rayleigh Fading Channel Through The BPSK, QPSK,4 QAM & 16 QAM Modulation Technique”, IJERA, ISSN: 2248-9622, Vol. 1, Issue 3, pp.1005-1011.

[12] L. H¨aring and A. Czylwik,” Synchronization in MIMO OFDM systems”, Advances in Radio Science (2004) 2: 147–153 © Copernicus GmbH 2004.


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