Synchronization for OFDM Modulation

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Copyright © IF AC Programmable Devices and Systems, Ostrava, Czech Republic, 2003

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SYNCHRONIZA TION FOR OFDM MODULATION Marcin Szebeszczyk Institute of Electronics, Silesian University of Technology, Gliwice, Poland

Abstract: This article focuses on frame synchronization for orthogonal frequency division multiplexing modulation. At the beginning of the article general principles of this modulation are explained. Then influence of inaccurate synchronization in receiver is described. Overview of practical synchronization methods is enclosed in the next part. Algorithm utilizing autocorrelation function of received signal is described in details. Copyright © 2003 IFAC Keywords: OFDM modulation, Frame synchronization, Synchronization errors.

1.

INTRODUCTION

of the synchronization algorithm to disperssive and noisy transmission channel must be assured.

OFDM (Orthogonal Frequency Division Multiplexing) modulation is a kind of multi-carrier modulation (Bingham, 1990). The whole bandwidth used by the OFDM system for transmission is divided into equidistant channels. Carriers with different frequencies are utilized simultaneously. The spectrum of particular carrier overlap with the spectrum of all other carriers utilized. Carrier separation in the receiver is achieved by maintaining orthogonality among carriers. Thus, there is no need for band-pass separating filters in the receiver. Transmitting data in parallel over many channels causes that a bit rate in each channel decreases proportionally to the number of channels. This contributes to very important advantage of the OFDM modulation - high immunity to dispersive nature of the transmission medium. Therefore this modulation is nowadays commonly used in systems utilizing dispersive channels: Asymmetrical Digital Subscriber Line (ADSL), Digital Audio Broadcast (DAB), Wireless Local Area Networks (WLAN), Power Line Communication (PLC). Additional important advantage of OFDM modulation is that all digital transmitter and receiver operations can be efficiently and easy implemented on DSP processor. Description of DSP based OFDM modem was presented in (Izydorczyk and Szebeszczyk 2002). Proper synchronization with received OFDM signal is a very important task for the receiver. Robustness

2.

OFDM MODULATION SCHEME

Consecutive steps performed by OFDM transmitter and receiver are briefly described below. 2.1 Transmitter operations.

Block diagram of the transmitter is presented in figure 1. During the first step, stream of input data consisting of M bits is split into groups of R bits. Thus, L=MIR numbers from the range 0 ... 2R - I are obtained. These numbers are in the next step coded by means of PSK or QAM constellation. Each number is replaced by real and imaginary part of responding symbol. Number of symbols in utilized constellation must be equal 2R. This operation is equivalent to modulating each carrier by means of PSK or QAM modulation. Phase and amplitude of PSK (or QAM) symbol changes when it is transmitted over the channel. This problem can be simply resolved for PSK constellation. Differential phase coding DPSK should be used. Then, each carrier (pSK symbol) in the formed OFDM symbol is coded in respect to the same carrier in the previous OFDM symbol. Information is encoded in the phase difference on each carrier between consecutive OFDM symbols. After coding, L complex values (PSK symbols) are obtained: X(k), k=I .. .L. During 433

(4)

Guard Interval remove

M PIS bits

Last step performed in the transmitter is shifting the base-band signal into high frequency range by means of analog mixer. This signal is sent over the transmission channel to the receiver.

SIP

2.1 Receiver operations.

Fig.l OFDM transmitter block diagram.

Fig.2 OFDM receiver block diagram.

Guard Interval adding,

M

bit~ SIP

The first operation in the receiver is shifting received analog high frequency signal into baseband frequency . Then, the signal is filtered by antialiasing filter and sampled in AID converter. First G samples of OFDM symbol are removed, they refer to guard interval. On remaining N samples FFf is performed. That way, frequency spectrum of OFDM symbol is received:

PIS

N- l

X(N-k)=X*(k)

n=O

When N point IFFf is performed, maximum number of carriers is equal to:

(2)

3.

A value X(k)=O means that corresponding k-th carrier is switched off. The n-th time domain sample of the OFDM symbol is given as: N-l x(n) = LX(k) . exp ( j2;rn.k

k=O

]

(5)

N

In the next step, difference between the phase of k-th carrier in present OFDM symbol and the phase of kth carrier in the previous OFDM symbol are calculated. This operation is performed for each carrier used in the system, and as a result L angles are obtained. Decision algorithm converts the received L angles to numbers corresponding to certain PSK symbols. This numbers are converted into binary form, according to algorithm used in the transmitter. The received bits are concatenated into serial stream.

(I)

N L MAX =--1 2

(

Y(k)=Ly(n) .exp _j2;rn .k]

the next step N - point IFFf is performed on this complex values. That way, time domain samples of OFDM symbol are obtained. Result of IFFf must be real. Therefore, before performing IFFf symbols are complemented according to:

SYNCHRONIZATION ERRORS: REASONS AND RESULTS

When the receiver starts to work, the first thing which has to be done is examining whether the received signal contains a signal from the receiver. When it turns out to be true, the beginning of the first OFDM symbol has to be found. Therefore, certain amount of OFDM symbols are grouped at the transmitter in the frame. Synchronization sequence is added at the beginning of each frame.

(3)

N

In the following step guard interval (cyclic prefix) is appended. Last G samples bf calculated time domain signal are copied and inserted before all other samples. Guard interval is added in order to avoid Inter-Symbol Interference (ISI) and Inter-Channel Interference (ICI) caused by disperssive nature of the channel and synchronization inaccuracy. Guard interval should last longer than channel impulse response. Resulting N+G samples form one complete OFDM symbol. During the next step this samples are converter with frequency fs to analog signal beginning from the guard interval. This analog signal is passed through low-pass reconstruction filter with bandpass frequency k < fs 12. That way, baseband OFDM signal is obtained. Frequency of the k-th carrier in this signal is given as:

3.1 Synchronization error sources

Three sources of the overall synchronization error can be distinguished. Inaccurate frame beginning detection . This causes Inter-Symbol Interferences and phase shift. The phase shift is for certain k-th carrier equal for each OFDM symbol within the frame. When differential coding is used, constant phase shift in consecutive OFDM symbols does not cause any errors. InterSymbol Interference influence can be -greatly reduced

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by guard interval longer than the impulse response of the channel. Frequency deviation of intermediate signals Frequency conversion signals originate from local oscillators, their frequencies differ slightly. As a result spectrum of received signal converted to baseband is shifted in respect to base-band signal in transmitter. This causes spectral leakage orthogonality between carriers is lost. As a result Inter-Channel Interferences arise. Important parameter of the OFDM system is the ratio of frequency deviation to frequency distance between two carriers:

fIT fST = DF

(9)

The same dependence exist for the receiver signals fSR. hR' Under such assumptions it can be derived that

relationship between

£

8 is:

£=N·DF·8

( 10)

For systems with big enough ratio DF of the intermediate frequency fIT to the sampling frequency fST equation (8) can be simplified: (11 )

£=fIR-fIT fe

(6) In this case intermediate frequency deviation contributes to the overall phase error much stronger than sampling frequency deviation. Hence, it can be assumed that the phase error is the same for each carrier within the same OFDM symbol and proportional to the number of OFDM symbol within the frame. Comprehensive description of synchronization problems in OFDM modulation is enclosed in (Langfeld and Dostert, 2000).

Beside ICI intermediate frequency deviation causes phase shift and amplitude change of transmitted PSK symbols. Resulting phase shift is equal for each carrier within the same OFDM symbol and proportional to the number of OFDM symbol within the frame . Difference between sampling clocks frequencies. Both in transmitter and receiver DAC and ADC sampling signals originate from local oscillators. Therefore sampling period between transmitter and receiver differs slightly. Normalised sampling error can be expressed as:

4.

Synchronization sequence added at the beginning of the transmitted frame consists of two identical M point sequences. Receiver, after start, examines the level of received signal and looks for two similar, consecutive M point length sequences. Receiving such sequences means beginning of the frame. In order to determine synchronization sequence for each received sample autocorrelation and normalization factor is calculated. For sample y(n) M point autocorrelation is calculated as:

(7) where TST• TSR are sampling periods respectively in transmitter and receiver. This causes Inter-Channel Interferences, and additionally phase shift and change of amplitude. Phase shift is proportional to the carrier number and to the OFDM symbol number within the frame.

M-I

P(n}= Ly(n+w}.y(n+M+w}

3.2 Estimation of the overal phase error

= 2tr(£-k8}

(12)

w=o

In the overall phase error static and dynamic part can be distinguished. Static error is equal for each OFDM symbol within the frame. Dynamic error is proportional to the number of the OFDM symbol within the frame. When differential coding is used information is encoded in phase difference between two consecutive symbols. Therefore static error doesn't introduce any changes. When ISI and leI are neglected and some additional simplifications are assumed it can be derived that for the k-th carrier overall phase error between two consecutive OFDM symbols is equal to: V'(k)

SYNCHRONIZATION METHOD

In order to avoid synchronization on noise signal, power of received signal has to be controlled. Nonnalization factor responding to signal power is calculated as: M-I

R(n}= Lly(n+M +wt

(13)

w=o The results of autocorrelation are taken into account only when signal power is greater than threshold value. Synchronization error function for n-th sample is calculated as:

(8)

Frequency conversion signal hT and sampling signal fST usually originate from the same oscillator in the

(14) E(n) = 11- p(n)1 R(n) This value is calculated for each received sample y(n). In case of ideal transmission conditions E(n) = 0 for the first sample of synchronization sequence.

transmitter. Dependence between frequency of this two signals can be expressed as:

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Distortions and noises occurring during transmission influence synchronization sequence. Hence in practice, error function doesn't reach zero value. Therefore, a sample with the smallest value of E(n) is treated as the first sample in the frame. Important advantage of the method described above is relatively high resistance to dispersive nature of the channel. Both received M point sequences are distorted during transmiSSIOn in similar way. Therefore recognizing two similar sequences is still possible even when transmission in highly distorted channels takes place. Accuracy and robustness of synchronization procedure depend on proper synchronization sequence choice. Quality of particular synchronization sequence is evaluated basing on the shape of it's E(n) function calculated for ideal case. The stronger is the slope of E(n) in the neighborhood of the frame beginning the greater accuracy and robustness is achieved. The algorithm described above is a simplified version of algorithm presented in (Schmidl and Cox, 1997).

5.

CONCLUSIONS

The paper presents main problems concerning synchronization for OFDM modulation. Sources of synchronization errors and their influence on transmission result were summarized. Efficient and robust frame synchronization algorithm was presented.

REFERENCES Bingham, J.A.e. (1990). Multicarrier modulation for data transmission: an idea whose time has come. IEEE Communication Magazine, May 1990, 514 Izydorczyk, J, Szebeszczyk, M. (2002). Power Line Modem. Periodica Politechnica, Transactions on Automatic Control and Computer Science, 47, 133-138, University of Timisoara, Editura Politechnica, Timisoara, Romania. Langfeld, PJ. and K. Dostert (2000). OFDM System Synchronization for Powerline Communications. Proceedings of the 2000 International Symposium on Power-Line Communications and its Applications, 15-22. University of Limerick, Limerick, Ireland. Schmidl T.M. and D.e. Cox (1997). Robust Frequency and Timing Synchronization. IEEE Transactions on Communications. 45, 16131621.

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