Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Synchronization 149the timing error d is defined asM(d) =M−1 ∑m=0M−1∑m=0r ∗ d+m r d+m+M|r d+m+M | 2 . (4.35)Finally, the estimate of the timing error is derived by taking the maximum quadraticvalue of the above function, i.e. max |M(d)| 2 . The main drawback of this metric is its‘plateau’, which may lead to some uncertainties.Guard time exploitationEach OFDM symbol is extended by a cyclic repetition of the transmitted data (seeFigure 4-15). As the guard interval is just a duplication of a useful part of the OFDMsymbol, a correlation of the part containing the cyclic extension (guard interval) with thegiven OFDM symbol enables a fast time synchronization [78]. The sampling rate canalso be estimated based on this correlation method. The presence of strong noise or longechoes may prevent accurate symbol timing. However, the noise effect can be reducedby integration (filtering) on several peaks obtained from subsequent estimates. As far asechoes are concerned, if the guard time is chosen long enough to absorb all echoes, thistechnique can still be reliable.4.2.4.2 Fine Symbol TimingFor fine time synchronization, several methods based on transmitted reference symbols canbe used [14]. One straightforward solution applies the estimation of the channel impulseresponse. The received signal without noise r(t) = s(t) ⊗ h(t) is the convolution of thetransmit signal s(t) and the channel impulse response h(t). In the frequency domainafter FFT processing we obtain R(f ) = S(f)H(f). By transmitting special referencesymbols (e.g. CAZAC sequences [63]), S(f) is apriori known by the receiver. Hence,OFDM symbolwith guard timeCorrelation with lastpart of OFDM symbolCyclic extension= same informationCorrelation peak= start of an OFDMsymbolCyclic extension= same informationGuardtimeFigure 4-15Time synchronization based on guard time correlation properties