M transmission CHAPTER 4.4 e-j2nft Actually, due to its specific structure and the selection of (m+1) Tu a subcarrier spacing Af equal to the per-subcarrier symbol rate 1/T, OFDM allows for low-complexity imple- mentation by means of computationally efficient Fast Fourier Transform (FFT) processing. (m+1) Tu To confirm this, consider a time-discrete (sampled) OFDM signal where it is assumed that the sampling rate fs is a multiple of the subcarrier spacing Af, i.e. fs = 1/Ts = N.Af. The parameter N should be chosen SO that the sampling theorem is sufficiently fulfilled. 1 As Nc Af can be seen as the nominal bandwidth of the OFDM signal, this implies that N should exceed No with a sufficient e-j2TTfNc-1t (m+1)T margin. With these assumptions, the time-discrete OFDM aNc-1 signal can be expressed as2 fk=kaf Figure 4.4-5 Basic principle of OFDM demodulation. this is the case despite the fact that the spectrum of (4.4.4) neighbor subcarriers clearly overlap, as can be seen from Figure 4.4-2. Thus the avoidance of interference between where OFDM subcarriers is not simply due to a subcarrier spectrum separation, which is, for example, the case for the kind of straightforward multi-carrier extension (4.4.5) outlined in Figure 4.3-5 in the previous chapter. Rather, the subcarrier orthogonality is due to the specific Thus, the sequence Xn, i.e. the sampled OFDM signal, is frequency-domain structure of each subcarrier in com- the size-N Inverse Discrete Fourier Transform (IDFT) of bination with the specific choice of a subcarrier spacing the block of modulation symbols ao, A1, aNc - 1 ex- Af equal to the per-subcarrier symbol rate 1/Tu. How- tended with zeros to length N. OFDM modulation can ever, this also implies that, in contrast to the kind of thus be implemented by means of IDFT processing multi-carrier transmission outlined in Section 4.3.3.1 of followed by digital-to-analog conversion, as illustrated in the previous chapter, any corruption of the frequency- Figure 4.4-6. Especially, by selecting the IDFT size N domain