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

150 Implementation Issuesafter dividing R(f ) by S(f) and IFFT processing, the channel impulse response h(t) isobtained and an accurate timing information can be derived.If the FFT window is not properly positioned, the received signal becomeswhich turns intor(t) = s(t − t 0 ) ⊗ h(t), (4.36)R(f ) = S(f)H(f) e −j2πf t 0(4.37)after the FFT operation. After division of R(f ) by S(f) and again performing an IFFT, thereceiver obtains h(t − t 0 ) and with that t 0 . Finally, the fine time synchronization processconsists of delaying the FFT window so that t 0 becomes quasi zero (see Figure 4-16).In case of multi-path propagation, the channel impulse response is made up of multipleDirac pulses. Let C p be the power of each constructive echo path and I p be the power ofa destructive path. An optimal time synchronization process is to maximize the C/I, theratio of the total constructive path power to the total destructive path power. However,for ease of implementation a sub-optimal algorithm might be considered, where the FFTwindow positioning signal uses the first significant echo, i.e. the first echo above a fixedthreshold. The threshold can be chosen from experience, but a reasonable starting valuecan be derived from the minimum carrier-to-noise ratio required.4.2.4.3 Sampling Clock AdjustmentAs we have seen, the received analogue signal is first sampled at instants determined bythe receiver clock before FFT operation. The effect of a clock frequency offset is twofold:the useful signal component is rotated and attenuated and, furthermore, ICI is introduced.The sampling clock could be considered to be close to its theoretical value so it mayhave no effect on the result of the FFT. However, if the oscillator generating this clockis left free-running, the window opened for FFT may gently slide and will not match theuseful interval of the symbols.GuardtimeSymbol timeSignal constellationFFT window properlypositionedf = 0FFT window with t 0time differencet 0tf = 2pft 0Time domain processingFrequency domain processingFigure 4-16Fine time synchronization based on channel impulse response estimation