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

Synchronization 153Transmitted 2 ref. symbols in frequencyTransmitted first ref. symb. in time- PN1 in even sub-carriers - PN1 in even sub-carriers- zero in odd sub-carriers - PN2 in odd sub-carriers1/2 OFDM symb. 1/2 OFDM symb.1. Ref. symb.2. Ref. symb. 1. Ref. symb.Frequency processingFFTPhasecorrec.Time processingr(k)frequencyoffset2z/T sB(z)2. Ref. symb. Ref. symb.diff. demod.of PN1DelayN cPowerestim.1. Ref. symb.Phaseestim.[ . ]*1/2 OFDM Ref. symb.DelayN c /2Powerestim.1/2 OFDM Ref. symb.Figure 4-18Schmidl and Cox frequency offset estimation using two OFDM symbolshave a special construction that allows a frequency offset estimation greater than severalsub-carrier spacings. The first OFDM training symbol in the time domain consists oftwo identical symbols generated in the frequency domain by a PN sequence on the evensub-carriers and zeros on the odd sub-carriers. The second training symbol contains adifferentially modulated PN sequence on the odd sub-carriers and another PN sequenceon the even sub-carriers. Note that the selection of a particular PN sequence has littleeffect on the performance of the synchronization.In Equation (4.38), the second term can be estimated in a similar way to the Mooseapproach [60] by employing the two halves of the first training symbols, ˆφ = angle[M(d)](see Equation (4.35)). These two training symbols are frequency-corrected by ˆφ/(πT s ).Let their FFT be x 1,k and x 2,k , the differentially modulated PN sequence on the evenfrequencies of the second training symbol be v k ,andX be the set of indices for the evensub-carriers. For the estimation of the integer sub-carrier offset given by z, the followingmetric is calculated:∑∣ x1,k+2z ∗ v∗ k x 22,k+2z∣k∈XB(z) = ( ) ∑2. (4.39)2 |x 2,k | 2k∈XThe estimate of z is obtained by taking the maximum value of the above metric B(z).The main advantage of this method is its simplicity, which may be adequate for bursttransmission. Furthermore, it allows a joint estimation of timing and frequency offset (seeSection 4.2.4.1).4.2.5.2 Fine Frequency SynchronizationUnder the assumption that the frequency offset is less than half of the sub-carrier spacing,there is a one-to-one correspondence between the phase rotation and the frequency offset.