Frequency Synchronization of OFDM.ppt

1、Frequency Synchronization,Why Frequency Offset Correction,The main problem with frequency offset is that it introduces interference among the multiplicity of carriers in the OFDM signal. The degradation is caused by two main phenomena : reduction of amplitude of the desired subcarrier and ICI caused

2、 by neighboring carriers.,Two deleterious effects caused by freq.offset(1/2),Two deleterious effects caused by freq.offset(2/2),The first component experiences an amplitude reduction and phase shift due to the frequency offset. The second term is the ICI caused by the frequency offsset.,OFDM transmi

3、tter and receiver,Classification of Frequency Synchronization Algorithms(1/2),The frequency synchronization algorithms in OFDM systems can preliminary be classified as fellows: Processing domain: time or frequency Observation space: considering cyclic prefix or not Level of data-assistance: preamble

4、-aided or pilot-aided,Classification of Frequency Synchronization Algorithms(2/2),For WLAN applications, pilot 、preamble and cyclic prefix are used. The preamble and pilot allow the receiver to use efficient maximum likelihood algorithms to estimate and correct the frequency offset.,Time Domain Appr

5、oach for Frequency Synchronization(1/4),Reference T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Comm., vol. 45, pp.1613 -1621, Dec. 1997.,Time Domain Approach for Frequency Synchronization(2/4),Let the transmitted signal be sn, then the complex base

6、band model of the passband signal yn is Then the received complex base band signal rn is Where f=ftx-frx is the difference between the transmitter and receiver carrier frequencies.,Time Domain Approach for Frequency Synchronization(3/4),Let D be the delay between the identical samples of the two rep

7、eated symbols. Then the frequency offset estimator is developed as follows, starting with an intermediate variable z,Time Domain Approach for Frequency Synchronization(4/4),previous equation is a sum of complex variables with an angle proportional to the frequency offset, so, the estimator is formed

8、 as,Properties of the Time Domain Frequency Synchronization Algorithms(1/3),The angle of z is unambiguously defined only in the range -,). Thus if the absolute value of the frequency error is large than the following limit the estimate will be incorrect, since z has rotated an angle larger than .,Pr

9、operties of the Time Domain Frequency Synchronization Algorithms(2/3),For the IEEE 802.11a short training symbols, the sample time is 50ns, and the delay D=16, Thus the maximum frequency error that can be estimated is In IEEE 802.11a system, the carrier frequency is approximately 5.3GHz, standard sp

10、ecifies a maximum oscillator error of 20 parts per million ( ppm ). Thus , with opposite signs, the amounts to a frequency error of f = 40*10-6*5.3*109=212kHz. Hence the max possible frequency error is well within the range of the algorithm.,Properties of the Time Domain Frequency Synchronization Al

11、gorithms(3/3),Now consider the long training symbols. The delay D=64 is four times longer. Observe that this is less than the maximum possible error defined in the standard. Thus this estimator would not be reliable if only the long training symbols were used.,Simulation result for Time domain Algor

12、ithm(1/3),Simulation result for Time domain Algorithm(2/3),Simulation result for Time domain Algorithm(3/3),Post DFT Approach to Frequency Error Estimation(1/8),Reference P. H. Moose, “A technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction,” IEEE Trans. Comm., vol.42,

13、 no. 10, pp. 2908-2914, Oct.,1994,Post DFT Approach to Frequency Error Estimation(2/8),Assume rn is the received sequence in the absence of noise i.e. yn = rn + wn,Post DFT Approach to Frequency Error Estimation(3/8),Post DFT Approach to Frequency Error Estimation(4/8),Then ,we can use efficient max

14、imum likelihood algorithms to estimate frequency offset from these repeated symbol as follows,Post DFT Approach to Frequency Error Estimation(5/8),The limits of accurate estimation are |0.5, that is, 1/2 the intercarrier spacing. As 0.5, may , due to noise and the discontinuity of the arctangent, ju

15、mp to -0.5. When this happens, in practice, the estimate becomes useless.,Post DFT Approach to Frequency Error Estimation(6/8),Thus, for frequency offsets exceeding one half the carrier spacing, an initial acquisition strategy must be prescribled. f : intercarrier spacing max : initial frequency off

16、set finitial 2 max,Post DFT Approach to Frequency Error Estimation(7/8),Example for a digital audio broadcasting service,Post DFT Approach to Frequency Error Estimation(8/8),It also can utilize the 4-pilot symbols in the data OFDM symbols to correct or estimation frequency offsets in the data OFDM s

17、ymbols (carrier frequency estimation). The estimation range is limited to half of the subcarrier spacing, in other words ,an ambiguity of multiples of the subcarrier spacing exists even though this limit can be increased by shortening the training symbol duration at the cost of the reduced estimatio

18、n accuracy.,Simulation result for Post DFT Algorithm (1/3),Simulation result for Post DFT Algorithm (2/3),Simulation result for Post DFT Algorithm (3/3),Comments on Frequency Error Estimation Algorithms(1/3),IEEE 802.11a suggests a two-step frequency estimation process with a coarse frequency estima

19、te performed from the short training symbols and a fine frequency synchronization from the long training symbols. The accuracy of the coarse estimate should easily be better than the 156.25kHz range of the estimator during the long training symbols. Hence a second estimation step could be done from

20、the long training symbols to improve the estimate.,Comments on Frequency Error Estimation Algorithms(2/3),Whether the second step is necessary depends on the accuracy of the first estimate. If enough data samples are used to calculate the first estimate from the short symbols, a satisfactory accurac

21、y can usually be reached. Hence the second estimation would be unnecessary.,Comments on Frequency Error Estimation Algorithms(3/3),The main disadvantage of frequency domain estimation is that the DFT has to be calculated for both repeated symbols. Compared to the time domain estimator, the DFT opera

22、tions mean additional computations without any advantages. Thus the time domain method is preferable for a WLAN receiver, which in general has very little time to complete all the necessary synchronization functions during the preamble.,Carrier Phase Tracking(1/3),Frequency estimation is not a perfe

23、ct process, so there is always some residual frequency error. The SNR loss due to the ICI generated should not be a problem if the estimator has been designed to reduce the frequency error below the limit required for a negligible performance loss for the used modulation. The main problem of the residual frequency offset is constellation rotation.,Carrier Phase Tracking(2/3),Carrier Phase Tracking(3