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 (OFDM) systems are very sensitive to carrier frequency offset (CFO), caused by either frequency differences between transmitter and receiver local oscillators or by frequency selective channels. The CFO disturbs the orthogonality among subcarriers of OFDM system and results intercarrier interference (ICI), which degrades the bit error rate (BER) performance of the system. This paper presents a new blind CFO estimation scheme for single-input single-output (SISO) OFDM systems. The presented scheme is based on the assumption that the channel frequency response changes slowly in frequency domain. In this scheme an excellent tradeoff between complexity and performance, as compared to existing estimation schemes, is obtained. The improved performance of the present scheme is confirmed through extensive simulations.
The computational complexity of the scheme is approximately same as that of kurtosis type scheme. The CFO estimation scheme of [9] can be used only with constant modulus signaling like M-ary PSK, but it is not applicable for M-ary QAM (for M>4). In this paper, we present a novel CFO estimation scheme that overcomes the limitation of [9]. The scheme presented in this paper is similar to scheme of [9] but not limited to constant modulus signaling. The proposed scheme assumes that the channel frequency changes slowly in the frequency domain. The effect of this assumption is that the channel behaves nearly same for the two neighboring subcarriers. We exploit this slowly changing property of channel, in frequency domain, to derive the cost function. It is shown in [9] that the minimization of the cost function gives a unique estimate of CFO. It is shown that the performance of the proposed scheme is better than that of kurtosis type (and similar to scheme of [9]) but its computational complexity is somewhat more than that of [9]. In the present scheme it is assumed that the channel frequency response changes slowly in frequency domain as was the case in [8] and [9]. The organization of rest of the paper is as follows: Section II presents the SISO-OFDM system model under consideration. The proposed scheme for SISO-OFDM systems is described in section III. Simulation results are discussed in section IV. Finally, the paper concludes the overall findings of the study.
Index Terms— OFDM systems, carrier frequency offset (CFO), intercarrier interference (ICI).
I. INTRODUCTION Orthogonal frequency division multiplexing has been adopted as a modulation scheme in various digital communication systems, such as digital audio/video broadcasting (DAB/DVB) and several wireless local area networks (WLANs). OFDM is very sensitive to frequency errors caused by frequency difference between the local oscillator in the transmitter and the receiver or by frequency selective channels [1]. This frequency offset causes a number of impairments including attenuation and phase rotation of each subcarrier and ICI between subcarriers. Therefore, OFDM system requires accurate frequency offset estimation and correction [2], [3]. Most of the CFO estimation methods, presented in the literature, rely on periodically transmitted pilots [3], [4]. The pilot-assisted methods are less useful for continuous transmission OFDM based systems such as DAB and DVB and they also reduce the spectral efficiency of the system. Blind CFO estimation is proposed to improve the spectral efficiency of CFO estimation methods in OFDM systems [5], [6]. In [7], the kurtosis metric is considered to construct a kurtosis type cost function for fine CFO estimation. This scheme gives a closed form CFO estimation using curve fitting but its estimation accuracy requires a large number of OFDM symbols. A blind carrier frequency offset estimation scheme with constant modulus (CM) signaling is presented in [9]. This scheme outperforms the kurtosis-type scheme of [8] in terms of BER.
II. SYSTEM MODEL In SISO-OFDM, the wide transmission spectrum is divided into narrower bands and data is transmitted in parallel on these narrow bands. Let us assume a SISOOFDM system with N orthogonal subcarriers. This multicarrier transmitter partitions the data stream into a block of N data symbols that are transmitted in parallel by modulating the N orthogonal subcarriers. Thus if ts is the input data symbol duration, the OFDM symbol duration T becomes Nts . In the mth OFDM symbol duration, a vector of N symbols, namely, X m = [ X m ,0 , X m ,1 ,... X m , N −1 ]T
transmitted simultaneously on N orthogonal subcarriers. Assuming multipath fading channel frequency response changes slowly during one OFDM symbol duration, thus can be represented for mth OFDM symbol duration as H m = diag ([ H m ,0 , H m ,1 ,..., H m , N −1 ]T ) . 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
is
ACEEE Int. J. on Network Security, Vol. 01, No. 03, Dec 2010
Δf . At the receiver, the received noisy (1/ T ) signal is mixed with a local oscillator signal having frequency Δf above the correct frequency. Then, the N time domain samples in the mth received OFDM symbol duration, namely, y m = [ ym ,0 , ym,1 ,..., ym , N −1 ]T can be
1 1 5 9 {K } = [1,5, ,9, , , ] . Thus, based on the above 5 9 9 5 assumption, we propose a cost function, which minimizes the difference of the signal power for each pair of consecutive subcarriers as
CFO as ε =
ε% = a r g
expressed as ( j 2πε / N [( m −1) N + mLcp ]) ym = e C(ε ) WH m X m + w m (1) where m = 1, 2,..., M , Lcp denotes the length of cyclic
J (εˆ ) =
j 2π
j 2πε
× ( N −1)
∑∑Y
m =0 n =0
[( m −1) N + mLcp ]
M −1 N −1
(εˆ ) = ( K i ) 2 ∑ ∑ Ym,(( n +1)) N (εˆ)
(5)
4
m=0 n=0
M −1 N −1
∑ ∑[
m=0 n =0
( Ki )2 + 1 Ym , n (εˆ ) ( Ki )2
4
(6)
2 2 K +1 Ym , n (εˆ) Ym ,(( n +1))N (εˆ ) ] − i Ki
IV. SIMULATION RESULTS In order to examine the performance of the proposed scheme, simulations of the proposed scheme, blind carrier frequency offset estimation of [9] are presented in this section. To compare the performance of various schemes BER is computed. The OFDM system with 64 subcarrier and 16QAM signal constellations is considered for the study. In our simulations, we assume CFO is uniformly distributed in the range [−0.5 0.5) . The multipath fading channel is frequency selective fading channel and has six independent Rayleigh fading paths with exponentially decaying powers as in [8]. It is assumed that the channel and CFO dose not change while estimation of CFO is performed. The cost function for the kurtosis-type and the proposed scheme are plotted in Fig1. and Fig.2, respectively. The Fig. 3-Fig. 4 represents the BER comparison of the proposed scheme with the kurtosis-type scheme over frequency selective fading channel. We observed from these figures that the BER of the proposed scheme is better than the kurtosis type scheme. In terms of complexity, both the schemes have somewhat the same complexity. The scheme presented in [9] is applicable to CM signal constellations only, whereas the proposed scheme is 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 terms of BER. However, the computational complexity of the proposed scheme is somewhat poorer than that of [9].
Ym , n (εˆ | εˆ = ε ) = H m X m . 2
In the case of slowing fading channel, the channel frequency response on two consecutive subcarriers is approximately the same. Therefore, we would have (4)
where (( a )) N denotes a modulo N , and K i ∈ {K } where K represents a set of constants for a given signal constellation, e.g., in case of 16-QAM 51 ©2010 ACEEE DOI: 01.IJNS.01.03.234
m,n
J (εˆ ) =
This section presents the proposed scheme for SISOOFDM systems. If the CFO is completely compensated before DFT stage, i.e., εˆ = ε , the DFT output will be without ICI. Therefore, in the noise free conditions, the DFT output will be represented as Ym (εˆ | εˆ = ε ) = H m X m (3) The squared amplitude of the DFT outputs would be
2
(εˆ ) − K i Ym ,(( n +1)) N (εˆ ) }) 2
the above cost function can be simplified as
III. PROPOSED SCHEME
2
2
2
m, n
4
M −1 N −1
where W H and (•)* represent the Hermitian transpose and conjugate operation, respectively.
Ym , n (εˆ | εˆ = ε ) ≈ K i Ym ,(( n +1)) N (εˆ | εˆ = ε )
∑ ∑ (∏ { Y
Since we have
C(ε ) = diag ([1, e N ,..., e N ]T ) and e N where the latter expression represents the common phase error resulting from the CFO. Therefore, it is clear from (1) that the intercarrier interference (ICI) introduces in the received signal because of CFO. At the receiver, CFO is estimated first and then the signal is compensated in the time domain by using this estimated CFO denoted by εˆ . After compensation, the samples of time domain signal are passed through the discrete Fourier transform (DFT) stage. The output of the DFT stage can be represented as Ym (εˆ ) = W H C * (εˆ)y m (2)
2
M −1 N −1
m = 0 n = 0 min, i
independent zero mean white Gaussian noise samples with variance σ n2 . The effect of CFO on the received samples of OFDM signal is represented by ×1
J ( εˆ )
0 .5 )
where
prefix (CP) which is assumed to be longer than the maximum channel delay spread, W is the N × N 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
j 2π
m in
εˆ ∈ [ − 0 . 5
m in i
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 kurtosistype 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
[1] R. Van Nee and R. Prasad, OFDM for Wireless Multimedia Communications (London: Artech House Publishers, 2000). [2] T.Pollet, M.Van Bladel, and M. Moeneciaey, “BER sensitivity of OFDM system to carrier frequency offset and Wiener phase noise,” IEEE Trans. Commun., vol.43, pp. 191-193, Feb.1993. [3] P.Moose, “A Technique for orthogonal frequency division multiplexing offset correction,” IEEE Trans. Commun., vol. 42, pp. 2908-2914, Oct.1994. [4] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol. 55, pp. 1613-1621, Dec 1997. [5] M. Ghogho, A. Swami, “Blind frequency offset estimator for OFDM systems transmitting constant-modulus symbols,” IEEE Commun. Letter, vol. 6, pp. 343-345, Aug. 2002. [6] X. Ma, M. K. Oh, G. B. Giannakis , and S. Barbarossa, “Non-data-aided carrier offset estimators for OFDM with null-subcarriers: Identifiability, algorithms, and performance,” IEEE J. Select Areas Commun., vol. 19, pp. 2504-2515, Dec. 2001. [7] Y. Yao and G. B. Giannakis, “Blind carrier frequency offset estimation in SISO, MIMO, and multiuser OFDM systems,” IEEE Trans. Commun., vol. 53, pp. 173-183, 2005. [8] T. Roman and V. Koivunen, “Subspace method for blind CFO estimation for OFDM systems with constant modulus constellations,” in Proc. IEEE Vehicular Technology Conf., May 2005, vol. 42, pp. 1253-1257. [9] Xiang N. Z. and Ali Ghrayeb, “A blind carrier frequency offset estimation scheme for OFDM systems with constant modulus signaling,” IEEE Trans. Commun., vol. 56, no. 7, pp. 1032-1037, July 2008.
Fig. 3 BER comparison at ε = 0.05
Fig. 4 BER comparison at ε = 0.1
Fig. 1. Plot of cost function for Kurtosis type scheme
52 ©2010 ACEEE DOI: 01.IJNS.01.03.234