Praise for Fundamentals of WiMAX

4.6 OFDM’s Computational Complexity Advantage 143In an OFDM system, the IFFT and FFT are the principal computational operations. It iswell known that the IFFT and FFT each have a complexity of OL ( log 2L), where L is the FFTblock size. In the case of OFDM, L is the number of subcarriers. As this chapter has shown, fora fixed cyclic prefix overhead, the number of subcarriers L must grow linearly with the bandwidth-delay-spreadproduct v=BT m. Therefore, the computational complexity for each OFDMsymbol is of the order OBT ( . There are OFDM symbols sent each second. Sincemlog2BTm)BL /L ∝ BT m, this means that there are order O(1/ T m) OFDM symbols per second, so the computationalcomplexity in terms of CMACs for OFDM isOBT ( log BT ) O(1/ T) = OB ( log BT).m 2 m m 2 m(4.46)Clearly, the complexity of an equalizer grows as the square of the data rate, since both thesymbol rate and the number of taps increase linearly with the data rate. For an OFDM system,the increase in complexity grows with the data rate only slightly faster than linearly. This differenceis dramatic for very large data rates, as shown in Figure 4.20.1,6001,400Million CMAC per Second1,2001,000800600400200EqualizerOFDM0010 20 30 40Data Rate (Mbps)Figure 4.20 OFDM has an enormous complexity advantage over equalization for broadband datarates. The delay spread is T m=2µ sec, the OFDM symbol period is T =20µ sec, and the consideredequalizer is a DFE.