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

132 Implementation Issuesh(t)t = lT sexp(−j2pf 0 t)r RF (t)r(t)exp(−j2pf c t)exp(−j2pf 1 t)h(t)...t = lT sP/SDemapperh(t)t = lT sexp(−j2pf Nc−1 t)Figure 4-3Block diagram of a multi-carrier receiverat the optimum sampling time t = lT s , the samples result in r m (lT s ) = d m,l ,ifthetransmitterand the receiver of the multi-carrier transmission system fulfill both the ISI andICI-free Nyquist conditions [70].To fulfill these conditions, different pulse shaping filtering can be used:Rectangular Band-Limited SystemEach sub-carrier has a rectangular band-limited transmission filter with the impulseresponseg(t) =(sin π t )T sπ tT s= sinc(π tT s). (4.5)The spectral efficiency of the system is equal to the optimum value, i.e. the normalizedvalue of 1 bit/s/Hz.Rectangular Time-Limited SystemEach sub-carrier has a rectangular time-limited transmission filter with the impulseresponseg(t) = rect(t) ={1 0 t