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

Multi-Carrier Transmission 31Only sub-channels near the band edges contribute to the out-of-band power emission.Therefore, as N c becomes large, the power density spectrum approaches that of singlecarriermodulation with ideal Nyquist filtering.A key advantage of using OFDM is that multi-carrier modulation can be implementedin the discrete domain by using an IDFT, or a more computationally efficient IFFT. Whensampling the complex envelope x(t) of an OFDM symbol with rate 1/T d the samples arex v = 1 N∑c −1N cn=0S n e j2πnv/N c, v = 0,...,N c − 1. (1.35)The sampled sequence x v , v = 0,...,N c − 1, is the IDFT of the source symbol sequenceS n , n = 0,...,N c − 1. The block diagram of a multi-carrier modulator employing OFDMbased on an IDFT and a multi-carrier demodulator employing inverse OFDM based on aDFT is illustrated in Figure 1-6.When the number of sub-carriers increases, the OFDM symbol duration T s becomeslarge compared to the duration of the impulse response τ max of the channel, and theamount of ISI reduces. However, to completely avoid the effects of ISI and thus, tomaintain the orthogonality between the signals on the sub-carriers, i.e. to also avoid ICI,a guard interval of durationT g ≥ τ max (1.36)has to be inserted between adjacent OFDM symbols. The guard interval is a cyclic extensionof each OFDM symbol, which is obtained by extending the duration of an OFDMsymbol toT s ′ = T g + T s . (1.37)OFDMS nserialtoparallelconverterIDFTorIFFTparalleltoserialconverteraddguardintervalx ndigitaltoanalogconverterx(t)multipathpropagationh(t, t)inverse OFDMn(t)R nparalleltoserialconverterDFTorFFTserialtoparallelconverterremoveguardintervaly nanalogtodigitalconvertery(t)Figure 1-6Digital multi-carrier transmission system applying OFDM