O<strong>FDMA</strong>s <strong>SC</strong>-<strong>FDMA</strong> is built over OFDM modulation, let’s first review an OFDM system structure. Atypical OFDM transmitter and receiver structure is shown <strong>in</strong> Figure 2. A transmitter <strong>in</strong>cludesa baseband modulator, subcarrier mapp<strong>in</strong>g, <strong>in</strong>verse Fourier transform, cyclic prefix addition,parallel-serial conversion, and a digital-to-analog converter followed by an I-Q RFmodulator. Unlike other modulation techniques that operate symbol by symbol, OFDMtransmits a block of data symbols simultaneously over one OFDM symbol. An OFDMsymbol is the time used to transmit all of subcarriers that are modulated by the block of<strong>in</strong>put data symbols.The baseband modulator transforms the <strong>in</strong>put b<strong>in</strong>ary bits <strong>in</strong>to a set of multi-level complexnumbers that corresponds to different modulations formats such as BPSK, QPSK, 16- or64-QAM.The type of modulation format used often depends on the signal-to-noise level of thereceived signal and the receiver ability to decode them correctly. These modulated symbolsare then mapped to subcarriers. An <strong>in</strong>verse-FFT (IFFT) is used to transform the modulatedsubcarriers <strong>in</strong> frequency doma<strong>in</strong> to time doma<strong>in</strong> samples.In general, the same modulation format is used <strong>in</strong> all the subcarriers to keep the control<strong>in</strong>formation overhead small. However, it is possible to have different modulation formatsover multiple subcarriers, and it is <strong>in</strong> fact advantageous <strong>in</strong> harsh and time vary<strong>in</strong>g channelconditions. In a broadband system, the channel is frequency selective over its large systembandwidth, mean<strong>in</strong>g the signal fad<strong>in</strong>g on each subcarrier is <strong>in</strong>dependent. The <strong>in</strong>terferencelevel on each subcarrier can also be different and vary uniquely with time. It results <strong>in</strong> a differentsignal-to-impairment level on each of the subcarriers. Hence, hav<strong>in</strong>g an appropriatemodulation format on these subcarriers would help to maximize the overall system throughput.OFDM system <strong>in</strong>herits an adaptation of modulation formats to each of the subcarriersdepend<strong>in</strong>g on channel conditions, and this is called Channel-dependent schedul<strong>in</strong>g.A cyclic prefix block copies a portion of the samples at the end of the time doma<strong>in</strong> samplesblock (at the IFFT output) to the beg<strong>in</strong>n<strong>in</strong>g. S<strong>in</strong>ce the DFT/FFT outputs are periodic <strong>in</strong>theory, copy<strong>in</strong>g the samples to the beg<strong>in</strong>n<strong>in</strong>g will make the signal cont<strong>in</strong>uous. The lengthof the cyclic prefix depends on the channel delay spread, and is preferably longer thanthe length of the channel response. At the receiver, the prefix part of the symbol is thrownaway as it may conta<strong>in</strong> ISI from its previous symbol. Hence, it removes the effect of ISIcaused by the multipath signal propagation. However, the prefix is the overhead <strong>in</strong> anOFDM system, as it does not carry any useful <strong>in</strong>formation.The block of complex samples are then serialized <strong>in</strong> the time doma<strong>in</strong> and convertedto analog signals. The RF section modulates the I-Q samples to f<strong>in</strong>al transmission radiofrequency. A correspond<strong>in</strong>g receiver does the <strong>in</strong>verse operations of the transmitter <strong>in</strong> thereverse order. A typical OFDM receiver <strong>in</strong>cludes an RF section, ADC, parallel-to-serialconverter, cyclic prefix remover, Fourier transformer, sub-carrier demapper, equalizer anddetector.10
OFDM to <strong>SC</strong>-<strong>FDMA</strong>The ma<strong>in</strong> difference between OFDM and <strong>SC</strong>-<strong>FDMA</strong> transmitter is the DFT mapper. Aftermapp<strong>in</strong>g data bits <strong>in</strong>to modulation symbols, the transmitter groups the modulation symbols<strong>in</strong>to a block of N symbols. An N-po<strong>in</strong>t DFT transforms these symbols <strong>in</strong> time doma<strong>in</strong> <strong>in</strong>tofrequency doma<strong>in</strong>. The frequency doma<strong>in</strong> samples are then mapped to a subset of M subcarrierswhere M is typically greater than N. Similar to OFDM, an M-po<strong>in</strong>t IFFT is used togenerate the time-doma<strong>in</strong> samples of these subcarriers, which is followed by cyclic prefix,parallel to serial converter, DAC and RF subsystems.Frequency Spread OFDMEach data symbol is DFT transformed before mapp<strong>in</strong>g to subcarriers, hence the <strong>SC</strong>-<strong>FDMA</strong>is called DFT-precoded OFDM. In a standard OFDM, each data symbol is carried on a separatesubcarrier. In <strong>SC</strong>-<strong>FDMA</strong>, multiple subcarriers carry each data symbol due to mapp<strong>in</strong>gof the symbols’ frequency doma<strong>in</strong> samples to subcarriers. As each data symbol is spreadover multiple subcarriers, <strong>SC</strong>-<strong>FDMA</strong> offers spread<strong>in</strong>g ga<strong>in</strong> or frequency diversity ga<strong>in</strong> <strong>in</strong> afrequency selective channel. Thus, <strong>SC</strong>-<strong>FDMA</strong> can be viewed as frequency-spread OFDM orDFT-spread OFDM.Subcarrier Mapp<strong>in</strong>gDFT output of the data symbols is mapped to a subset of subcarriers, a process calledsubcarrier mapp<strong>in</strong>g. The subcarrier mapp<strong>in</strong>g assigns DFT output complex values as theamplitudes of some of the selected subcarriers. Subcarrier mapp<strong>in</strong>g can be classified <strong>in</strong>totwo types: localized mapp<strong>in</strong>g and distributed mapp<strong>in</strong>g. In localized mapp<strong>in</strong>g, the DFToutputs are mapped to a subset of consecutive sub-carriers thereby conf<strong>in</strong><strong>in</strong>g them to only afraction of the system bandwidth. In distributed mapp<strong>in</strong>g, the DFT outputs of the <strong>in</strong>put dataare assigned to subcarriers over the entire bandwidth non-cont<strong>in</strong>uously, result<strong>in</strong>g <strong>in</strong> zeroamplitude for the rema<strong>in</strong><strong>in</strong>g subcarriers. A special case of distributed <strong>SC</strong>-<strong>FDMA</strong> is called<strong>in</strong>terleaved <strong>SC</strong>-<strong>FDMA</strong>, where the occupied subcarriers are equally spaced over the entirebandwidth. Figure 6 is a general picture of localized and distributed mapp<strong>in</strong>g.11