Maximum Likelihood CFO Estimation in OFDM Based Communication Systems

Maximum Likelihood CFO Estimation in OFDM Based Communication Systems Yetera B. Bereket, K. Langat, and Edward K. Ndungu 1 Abstract - Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for the next generation (3G/4G and beyond) wireless communication systems. These systems are very sensitive to the carrier frequency offset (CFO) that destroys the orthogonality property of the OFDM sub-carriers and introduces inter-carrier interference (ICI) which degrades the bit error rate (BER) performance. However, Inter Symbol Interference (ISI) that occurs during transmission can be totally averted by adding cyclic prefix (CP) to the OFDM symbol. Also adding CP reduces the level of CFO introduced during transmission. Nonetheless adding CP cannot protect ICI from occurring and distorting the transmitted symbol data at the receiver side. In this paper, we set the CP to vary in length depending on the channel conditions and obtained a better performance. We have also proposed a novel bandwidth efficient ML estimation technique that has a better bit error rate compared to that of conjugate cancellation method. We have also simulated and discussed bit-error-rate (BER) of the system against SNR under different channel conditions and compared it with other existing ICI mitigation techniques and found it better. Key words: Orthogonal Frequency Division Multiplexing (OFDM), Inter-Symbol-Interference (ISI), Inter-Carrier-Interference (ICI), Carrier Frequency Offset (CFO), Cyclic Prefix (CP), Maximum Likelihood (ML), Bit-Error-Rate (BER), Signal-To-Noise Ratio (SNR). I. INTRODUCTION During the last two decades, the wireless communication systems (3G/4G) have experienced a huge growth in both capacity and variety. This growth is going to shrink the world to a small village in which users with different requirements are efficiently accommodated anywhere and at any time. This will be resulted in an increased demand for new services that provide higher bit rate and higher capacity. One of the major themes in today's broadband systems is the use of the orthogonal frequency division multiplexing (OFDM)[1]. OFDM is a modulation scheme suitable for frequency selective channels (time dispersive) and for providing high speed data transmission, which makes it one of the promising solutions for the next generation wireless Yetera Bereket, Department of Electrical Engineering, Pan African University of Science Technology and Innovation(Correspondence: berryboyy@yahoo.com) K. Langat, Deparment of Telecommunication and Information Systems,Jomo Kenyatta University of Agriculture and Technology Edward K. Ndungu,Deparment of Telecommunication and Information Systems, Jomo Kenyatta University of Agriculture and Technology communications [2]. However, there is a need for more developments of OFDM systems in terms of complexity reduction and adaptation, therefore reconfigurable solutions are needed to achieve the user requirements. This is necessary because the end users require lightweight, compact size and power efficient devices besides the high bit rate capabilities. Furthermore, combining the communication systems with the new techniques such as multiple-input-multiple-output (MIMO) or cooperative communication can also enhance the capacity and the bit rate of the emerging systems [3]. Also Multiple-input multiple-output (MIMO) transmissions have been extensively studied as a means to improve spectral efficiency in wireless networks. While MIMO techniques offer tremendous advantages, its performance strongly depends on the number of antenna elements, spatial fading correlations between antennas, the presence of line of sight component, etc. Especially, multiple antennas at small handsets/cellular phones are unattractive for the achievement of transmit/receive diversity due to the limitation on size, power, hardware and price [4]. The advantages of MIMO techniques can be achieved via cooperative communication [5]. OFDM is a modulation technique that allows achieving high data rates over multipath fading channels. OFDM can also be seen as a multiplexing technique in the form of OFDMA, which allows many users to share the orthogonal bands [6]. OFDM mitigates the effects of multipath channel by essentially dividing the source spectrum into many narrow sub-bands that are transmitted simultaneously. The bandwidths of the sub-bands are designed to be narrow enough so that the channel exhibits a flat fading over each sub-band. The data bearing symbol stream for transmission is divided into a number of small chunks and modulated unto the subcarriers for parallel transmission. To achieve this, a number of oscillators are required in the transmitter side to modulate the small chunks into the respective subcarriers. However, using a number of oscillators in the transmitter side will make the transmitter big in size and introduce noises. DSP is now mature enough to implement the OFDM using IFFT/FFT with low cost and reduced computational complexity. Though OFDM is a very powerful technology in achieving better performance under worst wireless channel conditions, it has a major setback compared to the conventional FDM [1]. Self interference, or the corruption of desired signal by itself, is the major setback of any OFDM based system. Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) are the two self interferences manifested in ISSN 2079-6226 285

any OFDM based wireless communication systems. ISI, which is the interference of echoes of the transmitted signal with the original transmitted signal, can be completely averted by using Cyclic Prefix (CP). CP is a redundant part of the transmitted symbol appended either as a prefix or postfix to the original symbol and has no meaning except for protection. Another common self-interference in OFDM systems is the Inter-Carrier-Interference (ICI), which occurs when the subcarriers loss their orthogonality and it is referred to as Carrier Frequency Offset (CFO) [1]. CFO is caused by the synchronization error of the transmitter and receiver oscillators and by Doppler Shift. Inter Carrier Interference (ICI) is the power leakage among different sub-carriers that degrades the performance of both symbol detection and channel estimation. Hence, ICI is a major problem in multi carrier transmission systems which need a serious attention and extensive research. for n = 0,,N 1, xx(nn) = 1 1 HH(kk) kk=0 ddddee jj 2ππππ +ΔΔΔΔ.TTTT nn + z[n].(3) where H(k) is the channel frequency response corresponding to subcarrier k, z(n) is additive complex Gaussian noise, and Ts= T/N is the symbol interval with T being the IDFT interval (or OFDM symbol interval, excluding the guard time, as often termed in the literature).here the initial phase due to frequency offset is assumed to be zero (equivalently, the initial phase can be absorbed into H(k)).Notice if we define φ = Δω Ts, then φ and the frequency offset Δω differ only by a constant scalar, hence estimation of Δω is equivalent to estimation of the normalized phase shift φ. III. SYSTEM MODEL In this paper, we developed an OFDM system with ML estimator and set the CP to vary in length depending on the channel side information. The results we obtained disclosed that the ML estimator has a better performance compared to the self-cancellation, conjugate self-cancellation and symmetric conjugate self-cancellation estimators. II. SIGNAL MODEL In OFDM system with N subcarriers, N information symbols are used to construct one OFDM symbol. Each of the N symbols is used to modulate a subcarrier and the N modulated subcarriers are added together to form an OFDM symbol. Orthogonality among subcarriers is achieved by carefully selecting the carrier frequencies such that each OFDM symbol interval contains integer number of periods for all subcarriers. Using discrete-time baseband signal model, one of the most commonly used schemes is the IDFT-DFT based OFDM systems [2]. Guard time, which is cyclically extended to maintain inter-carrier orthogonality, is inserted that is assumed longer than the maximum delay spread to totally eliminate inter-symbol-interference [7].In the presence of virtual carriers, only M out of N carriers are used to modulate information symbols. Without loss of generality, we assume that the first M carriers are used to modulate information symbol, while the last N M carriers are virtual carriers. With symbol rate sampling, the discrete time OFDM model is s(n) =1/ 1 kk=0 dddd ee jj2ππππππ/..(1) where each dkis used to modulate the subcarrier ej2πk/n. Written in matrix form, we have s= Wd..(2) where W consists of the first M columns of the IDFT matrix U as defined in (1) and d = [d0,, dm 1]T is the symbol vector. In the presence of time dispersive channel, additive noise, and carrier frequency offset, the OFDM signal at the receiver is now, Figure 1 The overall developed OFDM system The overall system diagram is shown in figure 1 above. Up on receiving the bit stream to be transmitted the system performs modulation. Hence the bit stream will be converted into symbols. Then the system performs serial to parallel conversion. The number of parallel symbols should coincide with the number of available subcarriers. After the conversion IFFT is performed to obtain OFDM symbol. The cyclic prefix (CP) is lastly added before transmission to minimize the intersymbol interference (ISI).At the receiver, the process is reversed to obtain the decoded data. The CP is removed to obtain the data in the discrete time domain and then processed using the FFT for data recovery. Since the wireless channel is known to be fading and to introduce Doppler shift, the maximum likelihood (ML) estimator that comes immediately after the FFT block in the system is used to perform CFO estimation. Then using the estimated values of CFO inter carrier interference (ICI) that occurs during transmission will be compensated. Finally the symbols pass through the demapper (demodulation) in order to generate the received bit streams. The system is simulated using matlab simulation software and the system performance was measured by calculating the bit error rate. ISSN 2079-6226 286

IV. Maximum Likelihood (ML) Estimation R1,k= (10) 1, k=0,1,2,,n-1, This method has been presented in several papers in slightly varying forms [8, 9]. The training information required is at least two consecutive repeated symbols. The IEEE 802.11a preamble satisfies this requirement for both the short and long training sequence. Let the transmitted baseband signal be ss nn, then the complex baseband model of the passband signal yy nn is yy nn = ss nn ee jj2ππππππππππππππ,...(4) Where f tx is the transmitter carrier frequency and Ts is the sampling interval. After the receiver down-converts the signal with a carrier frequency f rx, the received complex baseband signal r n is rn= sne j2πftxnts e j2πfrxnts + wn = snee jj2ππ(δδδδ)nnnnnn +wn...(5) Where Δf=ftx frx is the carrier frequency offset and w n is the white Gaussian noise. Let D denote the delay between the identical samples of the two repeated symbols. Then the frequency offset estimator is developed as follows: The cross-correlation of the two consecutive symbols is computed as, 1 c= EE[ nn=0 rr nn rr nn+dd ]...(6) 1 = EE[ nn=0(ss nn ee jj2ππππffffffff + ww nn ) (ss nn+dd ee jj2ππππff(nn+dd)tttt + ww nn+dd ) ] Since w n is an additive white Gaussian noise white mean zero and covariance σ 2, the above equation will reduce to c= 1 ss nn ee jj2ππππffffffff ee jj2ππππff(nn+dd)tttt nn=0 ss nn+dd = ee jj2ππππff(dd)tttt 1 nn=0 ss nn c=ee jj2ππππff(dd)tttt 1 ss nn 2 nn=0 ss nn+dd...(7) Hence, the maximum likelihood estimate gives us the frequency offset estimation as, Δf = aaaaaaaaaa(cc)...(8) 2ππππππππ The ML estimation of frequency offset can also be derived after the discrete Fourier Transform (DFT) processing (i.e., in frequency domain). The received signal during two repeated symbols is (ignoring noise for convenience), rn= 1 kk= XX kk HH kk ee jj2ππππ(kk+ff rr), for n=0,1,..,2n- 1,...(9) where Xk s are the transmitted data symbols, Hk is the channel frequency response for the k th subcarrier, K is the total number of subcarriers, and ff rr is the relative frequency offset to the subcarrier spacing. The DFT of the first symbol and for the k-th subcarrier is And the DFT of the second symbol is derived as R2,k= 2 1 nn= rr nn = 1 +...(11),k=0,1,2,,N-1, But from equation (5) the received signal at the index of n+nr n+n is given as rn+n= 1 kk= XX kk HH kk ee jj2ππ(nn+)(kk+ff rr) = 1 XX kk HH kk ee jj2ππππ(kk+ff rr)... (12) kk= ee jj2ππ(kk+ff rr),k=0,1, N-1 But ee jj2ππ(kk+ff rr) = ee jj2ππππ ee jj2ππff rr, andee jj2ππππ = 1, for all integer values of k. Hence, equation (12) can be rewritten as rn+n= 1 kk= XX kk HH kk ee jj2ππππ(kk+ff rr) ee jj2ππff rr = 1 XX kk HH kk ee jj2ππππ(kk+ff rr) ee jj2ππff rr kk= r n+n =r n ee jj2ππff rr n=0,1,.,2n-1 (13),Substituting equation (13) into equation (11) yields, R2,k = 1 R2,k= ee jj2ππff rr ee jj2ππff rr, (14) ee jj2ππff rr 1, k=0,1,2,.n-1 R2,k = R1,k This, therefore, shows us that every subcarrier experiences the same shift that is proportional to the frequency offset. The cross-correlation of the two subcarriers is obtained as follow: C= kk= RR 1,kk RR 2,kk = kk= RR 1,kk RR 1,kk ee jj2ππff rr = ee jj2ππff rr kk= RR 1,kk RR 1,kk C = ee jj2ππff rr RR 1,kk 2 kk=..(15) Thus, the frequency offset estimator governing equation is ff rr = 1 angle(c),..(16) 2ππ ISSN 2079-6226 287

Δf= ff ssss angle(c),.(17) 2ππ which is quite similar in form to the time domain version of the ML estimation. V. SIMULATION RESULTS, DISCUSSION AND CONCLUSION For simulation, we chose QAM modulation scheme with M=4 and set the total number of subcarriers to 64. For the channel condition which exhibits white Gaussian Noise only the system uses the whole subcarriers to modulate the data symbols, which means there is no need to use CP in the system. Figure 2 shows the transmitted data, received data and figure 3 shows the bit error rate under different SNR values that ranges from 0 to 40dB. Figure4 shows the comparison of an OFDM system with and without CP insertion under fading channel condition. The fading channel is set to have six different paths with a maximum Doppler frequency of 100Hz (which is the worst case) and uniformly distributed delay spread. Literally, figure4shows that OFDM with CP has system performance. Figure 5 shows how the performance of the system degrades as the channel experiences CFO of normalized values of 0.1, 0.2, 0.3, and 0.4. The simulation result shows that how the system performance degrades as the level of CFO introduced by the channel increases. Finally, figure 6 shows how the fading channel and CFO effects mitigated by using ML estimation. An ML estimator based OFDM system developed in this paper has a better bit-error-to noise ration as compared to self-cancellation estimator. This paper also showed how spectral efficiency increased by baring the length of CP depending up on the channel condition. 10 0 10-1 10-2 10-3 10-4 10-5 10-6 10-7 0 2 4 6 8 10 12 14 SNR Figure3 bit error rate against signal to noise ratio for different SNR values BER 10 0 10-1 10-2 10-3 10-4 BER OFDM system performance for variable SNR OFDM IN Rayleigh Fading Channel With and Without CP Inclusion OFDM without CP OFDM with CP 10-5 0 5 10 15 20 25 30 35 40 SNR (db) Figure 4 OFDM system performance of fading channel with and without inclusion of CP Figure 2 transmitted and received OFDM signals Figure 5 OFDM without estimator Figure 6 OFDM system with ML estimator REFERENCES [1] J. Armstrong Analysis of New and Existing Methods of Reducing Intercarrier Interference Due to Carrier Frequency Offset in OFDM, IEEE Trans. Commun., vol.47, pp. 365-369 2010 [2] Weinstein, S. and Ebert, P. Data Transmission By Frequency-Division Multiplexing Using the Discrete Fourier Transform IEEE Trans. on Commun. vol. 19 Issue: 5, pp.628 634, 1971 ISSN 2079-6226 288

[3] Qienfei Huang and MounirGhogho Practical timing and frequency synchronization for OFDM-based cooperative systems IEEETransactions on signal processing. Vol58 :1-11 2010 [4] Kwnar.R, S. Malarvizhi and S. Jayashri Time-Domain Equalization Technique for Intercarrier Interference Suppression in OFDM Systems IEEE Trans. Commun., vol.4, pp. 78-86 2011 [5] O.Shin and Albert.M.2007 Design of an OFDM Cooperative Space- Time Diversity System IEEE. vol56: 2203-2214, 2007 [6] R. Prasad, OFDM for Wireless Communication Systems,Boston London: ArtechHouse, 2004. [7] Ali Ramadan M.Ali. Channel Estimation and ICI Cancelation for Adaptive OFDM Systems in Doubly Selective Channel Otto-Von Guerickle University, 2010. [8] P. H. Moose, A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction, IEEE Trans. on Communications, Vol. 42, No. 10,pp. 2908-2914, October 1994. [9] J-J. van de Beek, M. Sandell, and P. O. Börjesson, ML Estimation of Time and Frequency Offset in OFDM Systems, IEEE Trans. on Signal Processing, Vol.45, No. 7, pp. 1800-1805, July 1997. [10] Ali Ramadan M.Ali. Channel Estimation and ICI Cancelation for Adaptive OFDM Systems in Doubly Selective Channel Otto-Von Guerickle University, 2010. [11] P. H. Moose, A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction, IEEE Trans. on Communications, Vol. 42, No. 10,pp. 2908-2914, October 1994. [12] J-J. van de Beek, M. Sandell, and P. O. Börjesson, ML Estimation of Time and Frequency Offset in OFDM Systems, IEEE Trans. on Signal Processing, Vol.45, No. 7, pp. 1800-1805, July 1997. ISSN 2079-6226 289