Research on Synchronization Algorithms of OFDM

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Systems Engineering Procedia 00 (2011) 000–000 Systems Engineering Procedia 2 (2011) 278 – 286

Systems Engineering Procedia www.elsevier.com/locate/procedia

Research on Synchronization Algorithms of OFDM Reliability Engineering Xiaomin Lia, Hui Yanga, Xin Ninga, Guangchun Fua, Tao Xua * a

Henan Institute of Science and Technology, Xinxiang,453003, China

Abstract Orthogonal frequency division multiplexing is an efficient modulation technology, its basic idea is to distribute the serial highspeed data stream to the quadrature sub-carriers, and to transmit parallel. The synchronization is the key problem in OFDM reliability engineering. In this paper, OFDM reliability engineering model is provided, the synchronization problem is analyzed in details, the description of the algorithms of carrier frequency synchronization and timing synchronization is presented, and the simulation based on CP synchronization algorithm is also made. The simulation results show that OFDM reliability engineering has good frequency acquisition ability and smaller errors.

© 2011 Published by Elsevier B.V. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of Desheng Dash Wu Keywords: OFDM; synchronization; algorithm; simulation; reliability engineering

1. Introduction 1.1. OFDM OFDM technology has the history of nearly 50 years. In 1966, Chang described the concepts of parallel data transmission and FDM, and proposed the first OFDM mode. In 1980, Hirosaki proposed the equalization algorithm, which is used to suppress the crosstalk and interference between sub-carriers caused by channel pulse influence or time errors and frequency errors. In the same year, Peled proposed a simplified OFDM modulation tool. At the same time, Hirosaki brought up DFT-based Saltzberg O-QAM OFDM system. Soon after that, Kalet published the exploratory experimental achievements about the performance analysis of the application of OFDM to wireless communication channel. From then on, OFDM was widely used in mobile communications. In 1980s, OFDM technology was used in a variety of high-speed modem of telephone network. In 1990s, OFDM was first widely used in broadband data communication fields of broadcast channel, such as DAB (digital audio broadcasting), HDTV (high-definition digital television), and ADSL system. In 1995, the DAB standard proposed by ETSI (European Telecommunications Standards Institute) is the first OFDM-based wireless standards of digital audio

* Xiaomin Li. Tel.:15237307524. E-mail address: [email protected].

2211-3819 © 2011 Published by Elsevier B.V. doi:10.1016/j.sepro.2011.10.039

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broadcasting [1]. In OFDM system, data are distributed to many sub-carriers, which are orthogonal and with small bandwidth, and simultaneously transmitted in parallel. The data volume transmitted on each sub-carrier is relatively small; therefore different modulations can be used. By reducing the bit rate and increasing the symbol cycle on each sub-carrier, the inter-symbol interference (ISI) caused by radio channel time dispersion can reduce greatly. From the perspective of frequency domain, each sub-channel bandwidth is small, much smaller than the certain channel width; so the frequency response on each sub-channel is relatively flat. The decrease of ISI can also reduce the complexity of the equalizer in receiver. In OFDM system, the method of inserting cyclic prefix instead of the equalizer can also be used to eliminate the effect of ISI. In traditional frequency-division multiplexing system, the total signal bandwidth is divided into N sub-channels with their frequency domains do not overlap each other; and the guard band between each sub-channel will be reserved, at the receiver a set of filters can be used to separate each sub-channel. In OFDM system, the space between each sub-carrier is very small, they overlap in frequency domain. But because sub-carriers are orthogonal, certain technologies can be used to distinguish them at the receiver. Comparing with traditional frequency-division multiplexing system, OFDM system can use the spectrum resources more efficiently, as shown in Figure 1.

Fig. 1. OFDM Multi-carrier modulation

1.2. OFDM System Theory Diagram

Fig. 2. The OFDM system theory diagram

The OFDM system theory diagram is shown as Figure 2. The bits stream of 0 and 1 emitted by information source maps as QPSK or QAM signals in groups after M-ray modulation, and the bit stream of 0 and 1 is set equally distributed. After the conversion between series connection and parallel connection, the bit stream turns into a number of parallel signals. Then after inserting pilot, all the parallel frequency domain signals turn into time domain signals through IFFT conversion. Inserting guard interval (CP), we can get:

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 N g ,  N g  1, , 1  x ( N  n) n  xg ( n )   n 0,1, , N  1  x ( n) 

(1)

In formula (1), N is the number of sub-carriers, Ngis the sampling points contained in guard interval (i.e.CP). Then emitting the signals through multi-path fading channel with AWGN frequency selectivity, when they reach at the receiving end, converting them with FFT, then the frequency domain sequence Y(k) can be obtained. 2. OFDM reliability engineering model and the mathematical expression 2.1. OFDM Multiple modulation and demodulation Figure 3 shows an OFDM multiple modulation and demodulation reliability engineering. It contains multiple phase shift keying (PSK) or quadrature amplitude modulation (QAM) sub-carriers.

e j 2f1t

d0

e j 2f1t

~

积分

d1 e

j 2f 2 t

e

S/P

＋ e

S(t)

d0 ~

 j 2f 2 t

积分

d1

积分

d N 1

P/S

信道

j 2f N 1t

e

 j 2f N 1t

~

d N 1

Fig. 3. OFDM Reliability Engineering Block Model

In Figure 2, N s represents the number of sub-carriers; Ts represents the duration (period) of OFDM symbol;

d i represents data symbols assigned to each sub-channel; f i is the carrier frequency of the i th sub-carrier; retc  (t ) 1, | t | T2 , then the OFDM symbol beginning from t  t s can be expressed as formula (2) :   N 1  Re  di retc t  ts  T 2 exp  j 2 fi (t  ts ) s(t )    i 0  0 





t s  t  ts  T t  ts  t  T  t s

(2)

After demodulation at the receiver, the symbol of each sub-carrier is formula (3) : 

d ( m)

nm

N 1 NT j 2 t 1 NTs N 1 1 s j 2  f n t  j 2 f m t NTs  d n e e dt d n e dt  d ( m) ( ) ( )   0 NTs 0 n 0 NTs n 0

(3)

After the demodulation of the m-th sub-carrier, it will recover the expected symbol d(m) as for other sub-carriers, because the frequency deviation is integral multiple of in integration interval, the integration result is 0. The role of series-parallel conversion is converting the serial bit stream into OFDM symbols, which can be

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transmitted. Because OFDM belongs to parallel data transmission system, in OFDM reliability engineering, a number of symbols are transmitted at the same time; while in general serial data stream, the symbols are transmitted continuously, each data symbol spectrum can occupy the entire available bandwidth. In OFDM reliability engineering, because each sub-carrier’s modulation has adaptive control, the sub-carrier’s modulation is changeable, the number of bits can be transmitted is also changeable, the assigned data segment lengths of each sub-carrier are different during series-parallel conversion. When series-parallel conversion is made at the receiving end, the data sent from each sub-carrier are converted into original serial data. To further improve the performance of OFDM, data scrambling is added into series-parallel conversion. Specifically, each serial data bit is randomly assigned to each sub-carrier. By using data scrambling, not only the original data bit sequence can be restored at the receiving end, but also the series of bit errors caused by channel fading can be spread, they can be spread approximately evenly distributed in time. Thus the system performance is improved. In OFDM practice, due to carrier frequency offset, timing deviation, and channel frequency selective fading and other effects, the signal will be damaged, this will lead to phase shift and amplitude change[4]. In order to restore the signal accurately, we can use two methods of signal detection at the receiver: differential detection and coherent detection, then we have non-coherent (differential) OFDM reliability engineering and coherent OFDM reliability engineering. In the non-coherent (differential) OFDM reliability engineering, after transmitter’s differential coding of the symbols on the corresponding sub-carrier in continuous transmitted OFDM code words, the IFFT process is made and cyclic prefix CP is added. The receiver obtains the estimation of transmitted symbols by differential demodulation. The biggest advantage of this approach is that, it does not need channel state information, the receiver is relatively simple. But in order to improve the spectral utilization of the system, OFDM reliability engineering requires non-constant amplitude modulation. In this case, the receiver needs to know the channel state information and makes coherent demodulation. In fact, even for QPSK (quadrature phase shift keying) with so constant amplitude, by using channel state information to make coherent demodulation is much better than by using differential demodulation to improve the system performance, so the coherent demodulation is better than noncoherent demodulation overall. Because of this, the coherent demodulation is used widely in OFDM receiver system. The core idea of the coherent demodulation is by using channel estimation to gain the absolute reference phase and amplitude of OFDM symbol sub-carrier. 2.2. OFDM synchronization In OFDM reliability engineering, according to the function of synchronization, it can be divided into: carrier synchronization, bit synchronization, and group synchronization. The so-called synchronization means the sender and receiver have the same pace in terms of time, so it is also known as timing. Carrier synchronization refers to the receiver needs to provide a coherent carrier with the same frequency and the same phase as the receiving signal’s modulation carrier when coherent modulating. The acquisition of the carrier is called carrier extraction or carrier synchronization. During simulation modulation or digital modulation process, in order to achieve coherent demodulation, there must be coherent carrier. Therefore carrier synchronization is a prerequisite to achieve coherent demodulation. Bit synchronization is also called symbol synchronization. In digital communication systems, any message is sent through a series of symbol sequence, so when receiving, it needs to know the starting and ending time of each symbol, so as to make sample sentence at the right moment. For example, in the best receiver structure, it needs to make sample sentence for the output of integrator or matched filter, the sample sentence moment should be aligned with the ending time of each receiving symbol. So it requires that the receiver provides a bit timing pulse sequence; the repetition frequency of the sequence is same as the symbol rate, and the phase is consistent with the best sample sentence moment. We call the process of extracting timing pulse sequence bit synchronization. Group synchronization includes: word synchronization, sentence synchronization, shunt synchronization, sometimes frame synchronization is also called. 3. OFDM synchronization algorithm

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At present, the research on OFDM synchronization algorithm from data perspective main follows the following two ways: data-assisted type, which is based on pilot symbols. The advantages of this kind of algorithm are fast capture, high precision, so it is suitable for packet data communication. The specific method is at the head of packet data adding OFDM training symbols designed to make timing and frequency offset estimation. Non-data assisted type, that is blind estimation, which uses OFDM signal structure, for example, by adding cyclic prefix to make the front-end and back-end of OFDM have certain relevance, by using virtual sub-carrier, and by using data cyclostationarity through shaping filter, etc. to make estimation. Training symbol-based synchronization algorithm is adding known information to waiting to be sent OFDM symbol in time domain. It is usually placed before OFDM symbol or the frame consisted of a number of OFDM symbols. The adding of training symbol can complete synchronization and channel estimation at the same time. The research on training symbol-based synchronization algorithm main includes the following two parts: the structure of training symbols and the pattern of training symbols. The synchronization of OFDM symbol can also take advantage of its own characteristics; the so-called non-dataassisted synchronization is based on this way. Because there is cyclic prefix CP between OFDM symbols, we can examine the correlation between the two receiver samples at an interval of N. If one of the two sample points belongs to prefix, the other one belongs to the copy information within the same OFDM symbol; the two sample points have close correlation. If one of them belongs to CP, the other one belongs to the irrelevant information, the two have smaller correlation. The CP-based synchronization algorithm is based on this method. In practice, the typical algorithm is the Maximum Likelihood (ML). In terms of data-assisted synchronization algorithm, frequency offset estimation is got by using pilot symbol or training sequences, thus the system transmission efficiency is damaged. But its estimation accuracy is much higher than that of non-data assisted synchronization algorithm. 3.1. Maximum likelihood estimation frequency offset estimation In a word, maximum likelihood is according to the probability density function (PDF) of receiving signal to see which symbol of constellation symbols can make the value of PDF the largest, then that symbol will be sentenced. The known receiving signal is y, the channel estimation is H, and then we estimate x:

xˆ

2

y  Hx exp(  ) p ( y H , x) arg max  arg max 2 K /2 (2 n ) 2 n 2 x AK x AK 1

arg min x A

y  Hx

(4)

2

K

From formula (4), we can see that we are supposed to try all the symbols to find the exact symbol which can make the formula get the smallest value. It will take great effort to do the computing, so we should look for a simple sub-optimal program. Supposing after IFFT, OFDM can be represented as follows:

s(k ) 

1

N 1

X N n 0

n

exp( j

j 2kn ) N k=0,1,…,N-1

(5)

In formula (5), X n is data symbol, N is the number of sub-carriers. The impulse response of multi-path can be represented as the following formula:

h( , t ) 

L p 1

 h (t ) (   l 0

l

l

) (6)

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In formula (6), hl (t ) is the equivalent low-pass impulse response of No.1 path;  l is the delay time of No.1 path; Lp is the number of distinguished multi-path, after the receiver making samples of the received signal, the base band signal can be obtained, which can be represented as: L p 1

r (k )  exp( j 2f 0 dTs ) exp( j 2f 0 kTs )  hl ((k  d )Ts ) s (k  nl )  w(k ) l 0

(7)

nl [ d   l / Ts ] ； f 0 is the frequency offset; d is the timing offset; Ts is the sampling In formula (7),  period. Defining

  f 0 NTs  2 l   F

as the relative frequency offset, and

 l and  F

are respectively the

integer multiple of the offset and the small multiple of the offset of the sub-carriers interval. P.Moose assumed under the condition of the channel without multi-path or noise, and under the condition of ideal timing, sending two same OFDM symbols successively to derive the small multiple offset estimation of the maximum likelihood sub-carriers’ interval, then the sequence of 2N points the receiver receives is:

r (k )  s (k ) exp( j 2k / N )  n(k ) k=0,1,…,N-1

(8)

In formula (8), the No.n element of N’s FFT can be expressed as follows: N 1

R1n   r (k ) exp( j k 0

 2kn  ), n 0,1, , N - 1 . N

(9)

In the latter part of the receiving sequence, the No.n element of N’s FFT can be expressed as follows:

R2 n 



2 N 1

 r (k ) exp( j

kN

N 1

 r (k  N ) exp( j k 0

 2kn ) N

2 kn ) N n=0,1,…,N-1

(10)

From formula (10) we can get:

r (k  N )  r (k ) exp( j 2 )  R2 n  R1n exp( j 2 )

(11)

From formula (10) we can see that, if noise is not taken into account, the difference between R2 n and R1n is exp( j 2 ) . If we add white noise, namely:

 Y1n R1n  W1n  Y2 n R2 n  W2 n

n=0,1…,N-1

By using probability theory of conditional probability we can get the maximum likelihood estimation of frequency offset:

(12)

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 N *    Im[Y2 nY1n ]    (1 / 2 ) tan 1  n N N    Re[Y2 nY1n * ]    n  N

(13)

From formula (11) we can see that, the cycle of the exponential function is 2, by using this algorithm we can only get the interval of ±1/2 sub-carriers, therefore, in order to enlarge the capture range, it must be modified. One strategy is to shorten FFT time to make the sub-carrier interval wider, by doing this it can make the total phase not exceed ±  . Absolute frequency offset

f 0   / T  f , T  NTs is the symbol period; f is the sub-carrier

interval; assuming the initial frequency offset does not exceed

  max , then the minimum initial sub-carrier interval

can be decided by the following formula, the corresponding FFT length can also be determined [3].

f initial  2 max

(14)

If the average power of the shortened symbols is unchanged, then the variance of the estimation frequency offset is larger than that of original symbol because of less energy, that is, increasing the capture range is at the expense of synchronization accuracy. The maximum likelihood algorithm: the probability density function of the received signal: 2

y  Hx  p( y H , x ) exp(  ) 2 K /2 (2 n ) 2 n 2 1

(15)

3.2. Sampling clock synchronization algorithm Sampling clock synchronization means the receiver and transmitter maintain the same sampling clock frequency. The sampling clock frequency offset will lead to ICI, and it also will effect synchronization, but we assume the sampling clock synchronization is under ideal condition; generally the study of timing recovery algorithm is based on this assumption, which helps simplify the problem and can let us pay more attention to the core algorithm. Timing offset will cause phase rotation of sub-carrier, and the phase rotation angle is relevant to sub-carrier frequency, the higher the frequency the larger the phase rotation angle. This can be explained in terms of Fourier transform: the offset in time domain is corresponding to phase rotation of frequency domain. If the length sum of timing offset and the maximum delay spread is smaller than the length of cyclic prefix, the orthogonality between sub-carriers is still valid. Without ISI or ICI, the effect on demodulated data symbol is only phase rotation. If the length sum of timing offset and the maximum delay spread is larger than the length of cyclic prefix, then part of the data is lost, and the most serious is the orthogonality between sub-carriers is destroyed. This brought about ISI and ICI, which is one of the key issues that affect system performance. In terms of timing recovery process, it is generally divided into coarse synchronization (capture) and fine synchronization (tracking). For timing recovery, the first step is coarse synchronization the second step is fine synchronization [3]. The carrier frequency offset will destroy the orthogonality between sub-carriers and cause ICI, the symbol timing error will cause FFT demodulation window error, and cause ISI; the sampling clock frequency offset will also cause ICI, and its cumulative results can cause OFDM symbol timing drift. Sampling clock synchronization aims at maintaining the sampling clock of the receiving end has the same

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frequency as the sampling clock of the transmitter end. As the sampling clock of the receiving end and that of transmitter end do not match, there is always a certain clock frequency offset and phase offset. One is timing offset which can cause time-varying, and it will result in receiver must track the phase change of time-varying. The other one is sample frequency offset, that is, FFT cycle offset. After sampling, there is no orthogonality between subcarriers, resulting in ICI. The effect of sample offset on system is small. Clock frequency offset combines the characteristics of symbol timing offset and carrier frequency offset, its main representation is the phase rotation of modulation data and the phase rotation of direct ratio sub-carriers. Therefore, it can belongs to symbol timing offset, its synchronization method is similar to symbol timing synchronization. 4. Simulation There are a lot of orthogonal sub-carriers in OFDM reliability engineering, it is multi-carrier system. The output signals are the superposition of multiple sub-channel signals. Since the sub-channels coverage with each other, the carrier frequency offset will be interfered. So there must be strict orthogonality between them. The frequency synchronization algorithm by using CP can effectively reduce the offset error, and in order to reduce ICI, it must be made feedback to the time domain to correct frequency. We take OFDM using CP synchronization algorithm as an example to make simulink simulations of frequency synchronization algorithm and time synchronization algorithm respectively.

Fig. 4. The time synchronization algorithm using CP

Fig. 5. Frequency synchronization algorithm using CP

From the simulation waveform we can see that, the error of frequency synchronization algorithm using CP represents the trend of gradually decreasing, the capture probability of time synchronization algorithm using CP represents the trend of increasing. Therefore, CP synchronization algorithm can achieve frequency synchronization and time synchronization greatly. 5. Conclusion The synchronization of OFDM reliability engineering is one of the key issues which affect its performance. Through the analysis of synchronization algorithm, this paper provides the principles and application environment of different synchronization algorithms, especially analyzed the frequency synchronization algorithm and time synchronization algorithm based on maximum likelihood. In carrier frequency synchronization aspect, this paper mainly discussed the impact of frequency offset on the system, and provided the expression of frequency synchronization algorithm based in the maximum likelihood, and made MATLAB simulation. In time synchronization aspect, this paper made simulation of OFDM reliability engineering by using CP

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synchronization algorithm. Simulation results show that CP algorithm has a good ability of capture and smaller errors. CP synchronization algorithm can achieve frequency synchronization and time synchronization greatly. 6. Copyright All authors must sign the Transfer of Copyright agreement before the article can be published. This transfer agreement enables Elsevier to protect the copyrighted material for the authors, but does not relinquish the authors' proprietary rights. The copyright transfer covers the exclusive rights to reproduce and distribute the article, including reprints, photographic reproductions, microfilm or any other reproductions of similar nature and translations. Authors are responsible for obtaining from the copyright holder permission to reproduce any figures for which copyright exists. References 1. Y. Tian, W. Zhang, Z. Tan, Joint Synchronization Algorithm for OFDM in Vehicular Wireless Channel. Journal of System Simulation. 4 (2011) 729-734． 2. C. Qing, Y. Tangi, G. Cha, Coarse Timing Synchronization for OFDM Based on Cooperation of Distributed Antennas. Modern Electronics Technique.5(2011) 1-4． 3 D. Hu, F. Shi, E. Zhang, Non-data-aided Symbol Synchronization Algorithm for OFDM Systems. Journal of Electronics & Information Technology. 3(2011) 739-743． 4. J. H. Park, Adaptive synchronization of a unified chaotic systems with an uncertain parameter. International Journal of Nonlinear Sciences and Numerical Simulation. 2(2005) 201-206. 5. L. Ge, Y. Zhao, M. Fu, Joint PAPR Reduction and Residual CFO Synchronization for MQAM-OFDM Systems. Acta Electronica Sinica. 1(2011) 168-171. 6. Z. Jiao and L. An, Passive control and synchronization of hyperchaotic Chen system. Chinese Physics B. 2(2008) 492-497 7. P. Liu, A Novel Timing-and-Frequency Synchronization Algorithm Based on Cyclic Pref ix in OFDM System. Information Security and Communications Privacy. 11(2010) 31-35. 8. K. Kemih, Control of nuclear spin generator system based on passive control. Chaos, Solitons and Fractals. 4(2009) 1897-1901. 9. O. M. Kwon and J. H. Park, LMI.: optimization approach to stabilization of time-delay chaotic systems. Chaos, Solitons and Fractals. 2(2005) 445-450. 10. M. B. Dias, TraderBots : a new paradigm for robust and efficient multirobot coordination in dynamic environments. Pitt sburgh : Robotics Institute , Carnegie Mellon University , 2004. 11. S. Tang, C. Wu, X. Wang, Improvement of Frequency Offset Estimation of ML Algorithm in OFDM. Radio Communications Technology.5(2010) 62-64. 12. K. Kemih, S. Filali, M. Benslama, and M. Kimouche, Passivity-based control of chaotic Lu system. International Journal of Innovative Computing. 2(2006) 331-337. 13. G. Gong, W. Ge, Synchronization algorithm for TDS-OFDM systems using frequency offset compensation. Systems Engineering and Electronics.12(2010)2511-2515. 14. Z. Yao, M. Sheng, Timing synchronization algorithm for MIMO-OFDM systems with distributed antennas. Chinese Journal of Radio Science.4(2010) 717-723. 15. C. K. AHN, Generalized passivity-based chaos synchronization. Applied Mathematics and Mechanics. 5(2010) 1010-1017.