CH. 7 Synchronization Techniues for OFDM Systems 1
Contents Introduction Sensitivity to Phase Noise Sensitivity to Freuency Offset Sensitivity to Timing Error Synchronization Using the Cyclic Extension l Time synchronization l Freuency synchronization Synchronization Using Special Training Symbols 2
Introduction [1] An OFDM receiver has to perform two synchronization tasks: l l Time synchronization to find out symbol boundaries and the optimal timing instant to minimize the effects of ISI (Inter-symbol interference) and ICI (Inter-carrier interference) Freuency synchronization to estimate and correct for the carrier freuency offset of a received signal Ø Ø The sub-carriers are perfectly orthogonal only in the case where the transmitter and the receiver both use exactly the same freuency. Therefore, any freuency offset causes ICI in an OFDM receiver. In addition to the freuency offset, the phase noise of an oscillator also degrades the performance of a receiver. In a single carrier system, the phase noise and freuency offset only give a degradation in the SNR. However, the phase noise causes ICI as well as SNR degradation in an OFDM receiver. The sensitivity to phase noise and freuency offset is one of the main disadvantages of OFDM. 3
Sensitivity to Phase Noise [1] Phase Noise: Distortion in the phase of the carrier generated by a local oscillator due mainly to the thermal noise of a transistor. The power spectral density of phase noise is sometimes modeled by Lorentzian spectrum whose single-sided spectrum S s (f) is S s 2 /( p f ) ( f ) = 1 + f / l 2 2 fl and the double-sided spectrum S d (f) is given by S d ( f ) 1/( p f ) = 1 + f - f / f l 2 2 c l f l : - 3dB linewidth of the oscillator signal f c : carrier freuency Phase noise causes two error components in OFDM; the common phase error that is common to all sub-carriers and the random phase error. The common phase error causes ICI, while the random phase error increases noise component. 4
Sensitivity to Phase Noise (cont.) Fig. 7.1 Phase noise power spectral density (PSD) with - 3dB linewidth of 1Hz and a -100dB c /Hz density at 100 khz offset. 5
Sensitivity to Phase Noise (cont.) Degradation in the SNR caused by phase noise is given by b D phase : - 3dB one-sided bandwidth of the power density spectrum T: FFT interval 11 E @ 4 pbt 6ln10 N The SNR degradation due to phase noise is proportional to bt. s o Fig. 7.2 SNR degradation vs. 3dB bandwidth of the phase noise spectrum for (a) 64QAM (E s /N o = 19dB), (b) 16QAM (E s /N o = 14.5dB), (c) QPSK (E s /N o = 10.5dB). 6
Sensitivity to Freuency Offset [1] If there is a freuency offset in OFDM systems, the number of cycles in the FFT interval is no more integer, thereby resulting in ICI. Degradation in SNR caused by a freuency offset is approximated as D fre @ 10 3ln10 ( pdft ) 2 E N s o Fig. 7.3 SNR degradation vs. normalized freuency offset for (a) 64QAM (E s /N o = 19dB), (b) 16QAM (E s /N o = 14.5dB), (c) QPSK (E s /N o = 10.5dB). 7
Sensitivity to Timing Error [1] OFDM is relatively robust to the timing error; if there is no multi-path, the symbol timing offset can vary over a guard interval without causing any ICI or ISI. However, there exists an optimal timing instant for the best possible multipath resistance. Fig. 7.4 Example of an OFDM signal showing the earliest and latest possible timing instants. 8
Sensitivity to Timing Error (cont.) Looking at Fig. 7.4, we can see that as the timing changes, the phases of the sub-carriers change. The relation between the phase i of i-th sub-carrier and the timing offset is given by j = 2p t i fi j For an OFDM system with the FFT size of N and sub-carrier spacing of 1/T, a timing delay of one sampling interval of T/N causes a significant phase shift of 2 p ( N -1) / N between the first and the last sub-carriers. Therefore, in a coherent OFDM receiver, channel estimation should be performed to estimate and correct for these phase shifts. Figure 7.5 shows an example of the QPSK constellation of a received OFDM signal with 48 sub-carriers, an SNR of 30dB, and a timing offset eual to 1/16 of the FFT interval T. The timing offset translates into a phase offset of a multiple of 2p/16 between the sub-carriers. Because of these phase offsets, the QPSK constellation points are rotated to 16 possible points on a circle. t 9
Sensitivity to Timing Error (cont.) Fig. 7.5 Constellation with a timing error of T/16 before (a) and after (b) phase correction. 10
Time Synchronization Using the Cyclic Extension [1] Because of the cyclic prefix, the first T G seconds part of each OFDM symbol is identical to the last part. This property can be exploited for both timing and freuency synchronization, as shown below. Fig. 7.6 Synchronization using the cyclic prefix. The correlation output can be written as T G ò x( t) = r( t + t ) r ( t + T + t ) dt 0 * 11
Time Synchronization Using the Cyclic Extension (cont.) (a) (b) Fig 7.7 Example of correlation outputs for eight OFDM symbols with 192 sub-carriers for Fig. 7.7(a) and 48 sub-carriers for Fig. 7.7(b) both having a 20% guard time. 12
Time Synchronization Using the Cyclic Extension (cont.) Both figures clearly show eight peaks for the eight different symbols. There are different level of undesired correlation side-lobes: l The correlation of two independent random data seuences is random and its standard deviation is related to the number of samples. l Because the number of independent samples is proportional to the number of sub-carriers, Fig. 7.7(a) shows the better correlation characteristic. Therefore, the cyclic extension correlation techniue is only effective when a large number of sub-carriers are used, preferably more than 100. In order to enhance the correlation characteristic, specially designed training symbols can be used. 13
Fre. Synchronization Using the Cyclic Extension [1] The input signal r(t) that consists of an OFDM signal and additive Gaussian noise is given by r( t) = s( t) exp( j2 pd ft) + n( t) where Df is the freuency offset error, the signal power is P and the noise spectral density is N o. The freuency offset estimator multiplies the signal by its delayed and conjugated version such that { p }{ p } * y t r t r t T s t j ft n t s t T j f t T n t T * ( ) = ( ) ( + ) = ( )exp( 2 D ) + ( ) ( + )exp( 2 D ( + )) + ( + ) = s t - j D ft + n t s t + T - j D f t + T 2 * ( ) exp( 2 p ) ( ) ( )exp( 2 p ( )) * * + n ( t + T ) s( t)exp( j2 pd ft) + n( t) n ( t + T ) The first term is the desired output component with a phase eual to the phase drift over a T second interval. The freuency offset is estimated by averaging y( t) over an interval T G and then estimating the phase of y( t). 14
Fre. Synchronization Using the Cyclic Extension (cont.) The maximum-likelihood estimate of the freuency offset is fˆ 1 Im ( ) = tan ç - 2pT è Re y( t) ø æ 1 y t ö - For averaging over K symbols, the standard deviation is given by s f @ 1 1 1 2 pt K( E / N ) T / T s o G s 15
Fre. Synchronization Using the Cyclic Extension (cont.) Fig. 7.8 Freuency estimation error normalized to the sub-carrier spacing. Solid lines are calculated; dotted lines are simulated. (a) T G /T s =1, (b) T G /T s = 0.2, (c) T G /T s = 0.1. 16
Synchronization Using Special Training Symbols [1] The synchronization techniue based on cyclic extension is particularly suited to tracking in a circuit-switched connection, where no special training signals are available. For packet transmission, however, there is a drawback because an accurate synchronization needs an averaging over a large number (>10) of OFDM symbols. Furthermore, for high rate packet transmission, the synchronization time needs to be as short as possible, preferably a few OFDM symbols only. To achieve this, special OFDM training symbols can be used for which data content is known to the receiver. Figure 7.9 shows a block diagram of a matched filter that can be used to correlate the input signal with the known OFDM training signal. From the correlation peaks in the matched filter output signal, both symbol timing and freuency offset can be estimated. Note that the matched filter correlates with the OFDM time signal, before performing an FFT in the receiver. 17
Synchronization Using Special Training Symbols (cont.) T : sampling interval, c i : matched filter coefficients Fig. 7.9 Matched filter for a special OFDM training symbol. 18
Synchronization Using Special Training Symbols (cont.) Unuantized input signal case 7.10 7 19
References 1. R. V. Nee and R. Prasad, OFDM for Wiress Multimedia Communications, Artech House Publishers, 2000. 2. L. Hanjo, M. Munster, B. J. Choi, T. Keller, OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs, and Broadcasting, John and Wiley, 2003. 20