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Introduction to Synchronization Schemes in OFDM Systems. 2018/08/06. Outline. Introduction. Impact of timing offset (TO). Impact of carrier frequency offset (CFO). TO estimation algorithm CFO estimation algorithm ML Estimation of Time and Frequency Offset in OFDM
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Introduction to Synchronization Schemes in OFDM Systems 2018/08/06
Outline • Introduction. • Impact of timing offset (TO). • Impact of carrier frequency offset (CFO). • TO estimation algorithm • CFO estimation algorithm • ML Estimation of Time and Frequency Offset in OFDM • Robust Frequency and Timing Synchronization for OFDM
Introduction (1/2) • Synchronization issue: • Symbol timing offset (TO): • Due to unknown transmission time. • Carrier frequency offset (CFO): • Oscillator mismatch. • Doppler effect. • Sampling clock offset (SCO): • Mismatch between ADC and DAC. • Phase noise: • Introduced by local oscillators used for up/down-conversion.
Introduction (2/2) • There are two categories in general: • Data-Aided methods. • The drawback of the data-aided scheme is the leakage of the bandwidth efficiency due to redundancy overhead. • Non-Data-Aided methods. • Non-data-aided methods or called blind relying on the cyclo-stationarity, and virtual sub-carriers, etc.. • The blind estimation requires a large amount of computational complexity, therefore, it may be not be available in short-burst wireless communication.
Impact of timing offset • Timing offset: where and are the integer part and fractional part of timing offset, respectively. • For fractional part of timing offset : • For integer part of timing offset : , Appendix-A
Impact of Carrier frequency offset (2/4) Faded signal attenuated and rotated by CFO Inter-Carrier Interference (ICI)
Impact of Carrier frequency offset (3/4) • A simple representation of received signal with only fractional CFO is given by where is the ICI coefficient, Appendix-B
Impact of Carrier frequency offset (4/4) • Fractional CFO • Phase shift in time domain. • Induce the magnitude attenuation and ICI. • Loss of orthogonality. • Integer CFO • Phase shift in time domain. • No effect on the orthogonality. • Index shift.
J.-J. van de Beek, M. Sandell, and P. O. Borjesson, “ML Estimation of Time and Frequency Offset in OFDM Systems,” IEEE Transactions on Signal Processing, vol. 45, no. 7, pp. 1800-1805, Jul. 1997.
Introduction • We present and evaluate the joint maximum likelihood (ML) estimation of the time and carrier-frequency offset in OFDM systems. • Our novel algorithm exploits the cyclic prefix preceding the OFDM symbols, thus reducing the need for pilots. • In the following analysis, we assume that the channel is nondispersive and that the transmitted signal s(k) is only affected by complex additive white Gaussian noise (AWGN) n(k).
System Model • Consider two uncertainties in the receiver of this OFDM symbol: the uncertainty in the arrival time of the OFDM symbol and the uncertainty in carrier frequency. • The first uncertainty is modeled as a delay in the channel impulse response , where is the integer-valued unknown arrival time of a symbol. • The latter is modeled as a complex multiplicative distortion of the received data in the time domain , where denotes the difference in the transmitter and receiver oscillators as a fraction of the intercarrier spacing.
ML Estimation • Assume that we observe 2N+L consecutive samples of r(k), as shown in Fig. 2, and that these samples contain one complete (N+L)-sample OFDM symbol.
ML Estimation • Define the index sets and • Collect the observed samples in the (2N+L) ×1-vector • Notice that the samples in the cyclic prefix and their copies r(k), are pairwise correlated, i.e., while the remaining samples r(k), are mutually uncorrelated.
ML Estimation • Using the correlation properties of the observations r, the log-likelihood function can be written as • Under the assumption that r is a jointly Gaussian vector and omit some factor, we can show that : (1)
ML Estimation • The joint complex gaussian PDF can be expressed as . • Note that utilize AB*+A*B=2Re[AB*], we can easily show and .
ML Estimation • The maximization of the log-likelihood function can be performed in two steps: • The maximum with respect to the frequency offset is obtained when the cosine term in (1) equals one. • This yields the ML estimation ofwhichis • We assume that an acquisition, or rough estimate, of the frequency offset has been performed and that 0, thus u=0. • Since the cosine tern equals to one, the log-likelihood function of θ becomes and the joint ML estimation of θ and ε becomes
T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing Synchronization for OFDM,” IEEE Transaction on Communications, vol. 45, no. 12, Dec. 1997.
TO Estimation Algorithm (1/10) • Schmidl’s Method [1]: First of all, we could design a training symbol which contains a PN sequence on the odd frequencies.
TO Estimation Algorithm (2/10) • Due to the property of IDFT, the resulting time domain training symbol would have a repetition form as shown below: • After sampling, the complex samples are denoted as rm. • Ex: Let the multipath channel L = [h0h1], the received sample r0 and rN/2 can be expressed by: (w/o CFO)
TO Estimation Algorithm (3/10) • Received signal without CFO: • Received signal with CFO: Extra phase rotation due to CFO Phase difference, which contains the information about CFO
TO Estimation Algorithm (4/10) • With CFO, if the conjugate of a sample from the first half is multiplied by the corresponding sample from the second half ( T/2 seconds later), there will be an extra phase difference caused by the CFO, as shown below.
TO Estimation Algorithm (5/10) • Let there be N/2complex samples in one-half of the training symbol (excluding the cyclic prefix), and let the sum of the pairs of products be : • Note that d is a time index corresponding to the first sample in a window of N samples. • The received energy for the second half-symbol is defined by • A timing metric can be defined as
TO Estimation Algorithm (6/10) • Delay correlator:
TO Estimation Algorithm (7/10) • If d’ is the correct symbol timing offset: • If d’ falls behind the correct symbol timing offset 1 sample:
TO Estimation Algorithm (9/10) • Drawback: Plateau effect. Since CP is the copy of the last few samples, these two observation windows result in the same correlation(without noise).
Fractional CFO estimation • Fractional CFO estimation can be accomplished when the symbol boundary is detected. where L is the distance between two identical block, R is the block size. • For example: L = N; R = Ncp. L = N/2; R = N/2. N cp N N cp N
Estimation Range • The acquisition range of is , which depends on the repetition interval. • For example: • 802.16e-2005 (L=N/4): • DVB-T (L=N): • Note that , is the subcarrier spacing.
HW • Number of subcarrier N = 128, length of CP NCP =16. • Channel: AWGN. • Pilot : ZC sequence (loaded on the subcarriers 0,2,4,…,N-2) • Time offset = 3 samples. • CFO
HW • Exercise 1: Timing offset estimation. • Plot the timing metric where • Exercise 2: Carrier frequency offset estimation. • Given a CFO estimator • Plot the mean square error of CFO estimation versus SNR.