er fre- quency offset (CFO) caused by the mismatch from the RF local oscillators (fc) and the Doppler shift (fD). Most parts of the algorithms for time synchronization are based on the calcula- tion of correlation metrics that exploit some periodicity of the OFDM signal-that is, due to the cyclic prefix (CP) (Van de Beek, Sandell, and Borjesson 1997, 1800) Channel Impulse Response Doppler Spectrum r(k) e N h(l)-s(k - 0) SRF(t) r'RF(t) Mobile Channel Y-N-1 N-DFT WINDOW OFDM Symbol Figure 3.28 OFDM system model. © 2009 by Taylor & Francis Group, LLC Radio-Interface Physical Layer or to a known training sequence (Schmidl and Cox 1997, 1613). The obtained met- rics also allow for having an estimation of the CFO in the time domain. Morelli, Kuo, and Pun (2007, 1394) present a comprehensive survey on synchronization techniques for OFDM-based systems. The OFDM system model follows the scheme described in Figure 3.28. The received signal, r(k), is affected by a CFO, E (namely, the frequency offset relative to the subcarrier spacing, Af); an uncertainty on the beginning of the OFDM sym- bols denoted as O; and multipath propagation due to a channel impulse response, h(t), with length L. The time and frequency synchronization consists of the esti- mation of O and E, respectively. Timing errors result in intersymbolic interference (ISI), whereas imperfect estimations of CFO lead to intercarrier interference (ICI), degrading the system performance. The problem of time synchronization (Figure 3.29) in an OFDM-based system is focused on finding the instant at which the OFDM symbol starts, whose estima- tion is denoted as O. The portion of the cyclic prefix corrupted by ISI depends on the length of the channel response, but, in general, a valid range of values exists for acquiring time synchronization inside the ISI free zone. If the value of O is located within this region, data subcarriers, Xk will not be affected by ISI, but rather by a phase shift proportional to k index and AO. This phase shift causes a rotation of the rece