Praise for Fundamentals of WiMAX

4.4 Timing and Frequency Synchronization 125Table 4.1 Summary of OFDM ParametersSymbol Description RelationB* Nominal bandwidth B=1/T sExample WiMAXvalue10MHzL *G *L d*Number of subcarriers Size of IFFT/FFT 1024Guard fraction % of L for CP 1/8Data subcarriers L–pilot/null subcarriers 768T sSample time T =1/ B1 µ secsN gGuard symbols N GL128g =T gGuard timeT = T Ng s g12.8 µ secT OFDM symbol time T = T ( L+ N ) 115.2 µ secsgB scSubcarrier bandwidth B = scB / L9.76 KHz* Denotes WiMAX-specified parameters; the other OFDM parameters can all be derived from these values.Figure 4.9 shows an OFDM symbol in time (a) and frequency (b). In the time domain, theIFFT effectively modulates each data symbol onto a unique carrier frequency. In Figure 4.9, onlytwo of the carriers are shown: The transmitted signal is the superposition of all the individual carriers.Since the time window is T =1µ sec and a rectangular window is used, the frequencyresponse of each subcarrier becomes a “sinc” function with zero crossings every 1/ T = 1MHz.This can be confirmed using the Fourier transform F{}⋅ , sinceF{ cos(2 πf ) ⋅rect( t/ T)} = F{ cos(2 πf )} ∗F{ rect(2 t/ T)}c= sinc T(f − f c),(4.14)(4.15)where rect( x) = 1, x∈− ( 0.5,0.5) , and zero elsewhere. This frequency response is shown forL =8 subcarriers in Figure 4.9b.The challenge of timing and frequency synchronization can be appreciated by inspectingthese two figures. If the timing window is slid to the left or the right, a unique phase change willbe introduced to each of the subcarriers. In the frequency domain, if the carrier frequency synchronizationis perfect, the receiver samples at the peak of each subcarrier, where the desiredsubcarrier amplitude is maximized, and the intercarrier interference (ICI) are zero. However, ifc( )