Praise for Fundamentals of WiMAX

142 Chapter 4 • Orthogonal Frequency Division Multiplexing4.5.4.2 Signal MappingSignal-mapping techniques share in common that some redundant information is added to thetransmitted signal in a manner that reduces the PAR. This class includes coding techniques,selected mapping (SLM), and partial transmit sequence (PTS).The main idea behind the various coding schemes is to select a low PAR codeword based onthe desired transmit symbols [22, 36]. However, most of the decoding techniques for these codesrequire an exhaustive search and so are feasible only for a small number of subcarriers. Moreover,it is difficult to maintain a reasonable coding rate in OFDM when the number of subcarriersgrows large. The implementation prospects for the coding-based techniques appear dim.In selected mapping, one OFDM symbol is used to generate multiple representations thathave the same information as the original symbol [30]. The basic objective is to select the onewith minimum PAR; the gain in PAR reduction is proportional to the number of the candidatesymbols, but so is the complexity.PTS is similar to SLM; however, the symbol in the frequency domain is partitioned intosmaller disjoint subblocks. The objective is to design an optimal phase for the subblock set thatminimizes the PAR. The phase can then be corrected at the receiver. The PAR-reduction gaindepends on the number of subblocks and the partitioning method. However, PTS has exponentialsearch complexity with the number of subblocks.SLM and PTS are quite flexible and effective, but their principal drawbacks are that thereceiver structure must be changed, and transmit overhead (power and symbols) is required to sendthe needed information for decoding. Hence, these techniques, in contrast to peak-cancellationtechniques, would require explicit support by the WiMAX standard.4.6 OFDM’s Computational Complexity AdvantageOne of its principal advantages relative to single-carrier modulation with equalization is thatOFDM requires much lower computational complexity for high-data-rate communication. Inthis section, we compare the computational complexity of an equalizer with that of a standardIFFT/FFT implementation of OFDM.An equalizer operation consists of a series of multiplications with several delayed versionsof the signal. The number of delay taps in an equalizer depends on the symbol rate of the systemand the delay spread in the channel. To be more precise, the number of equalizer taps is proportionalto the bandwidth-delay-spread product T . We have been calling this quantity v,m/ Ts ≈ BTmor the number of ISI channel taps. An equalizer with v taps performs v complex multiply-andaccumulate(CMAC) operations per received symbol. Therefore, the complexity of an equalizeris of the order2Ov ( ⋅ B)= OBT ( m).(4.45)