Chapter 7SC-FDMA

7.1 Introduction

Single carrier-frequency division multiple access (SC-FDMA) is an OFDMA vari-ant technology that is tailored for uplink transmission. It uses the standard OFDMAtransceiver blocks with different ordering. SC-FDMA (aka DFT-precoded/spreadOFDMA) is the multiuser version of single carrier modulation with frequency do-main equalization (SC/FDE).

The main objective of SC-FDMA is to introduce transmission with lower PAPRthan OFDMA. Since OFDMA shows envelope fluctuations, and signals with highPAPR requires highly linear power amplifiers to reduce the distortion, the design ofmobile terminals are complex and they become power hungry since the linearity inthe amplifier can only be handled with a large backoff from their peak power.

Another objective is to address frequency offset drawback of OFDMA. In up-link, there are multiple simultaneous transmissions from different mobile stations.If there is slight frequency offset, orthogonality of subcarriers in OFDMA can bedestroyed easily.

These issues are addressed in SC-FDMA as follows: unlike OFDMA, which usesparallel transmission, SC-FDMA transmits symbols sequentially so that the PAPRis reduced by spreading a symbol power over subcarriers. Also, SC-FDMA in onemode introduces localized scheduling in which contiguous subcarriers are assignedto a user. This makes mobile station more robust to frequency offset than OFDMA,but of course, the diversity order becomes lower than OFDMA.

Let us first recall OFDMA as explained in detail in the previous chapters andthen differentiate toward SC-FDMA.

7.2 SC-FDMA vs. OFDMA

OFDMA utilizes narrow-band orthogonal subcarriers and creates multiple datastreams. The transmission rate in each subcarrier is inversely proportional to thetotal number of orthogonal subcarriers. Number of subcarriers (M) depends on theM. Ergen, Mobile Broadband: Including WiMAX and LTE, 261DOI: 10.1007/978-0-387-68192-4 7, c© Springer Science+Business Media LLC 2009

262 7 SC-FDMA

N-pointFFT

SubcarrierMapping

M-pointIFFT

Add CP DAC/RF

Channel

N-pointIFFT

SubcarrierDe-Mapping/Equalization

M-pointFFT

RemoveCP

RF/ADCDetect

PtoS

StoP

SC/FDMA SpecificModules in addition to

OFDMA(M>N)

Fig. 7.1 Transmitter and receiver structure for SC-FDMA. CP cyclic prefix, PS pulse shaping,M > N when SC-FDMA specific module is removed, the structure converges to OFDMA trans-mitter and receiver

available bandwidth and could be 512, 1,024, or more. As a result, OFDMA systemtransmits information on M orthogonal subcarriers, each operating bit rate of 1/M-fold bit rate of the original signal. This rate decrease helps to alleviate the multipatheffect of the channel and reduces the equalizer complexity in the receiver. On theother hand, OFDMA suffers from high peak-to-average-power ratio (PAPR). Thisis due to unpredictable envelope fluctuations after IFFT.

SC-FDMA spreads the energy of one subcarrier over all subcarriers before theIFFT. This way spectral nulls in the channel is reduced with averaging. Hence, PAPRis reduced. This subtle idea is performed by introducing additional FFT block beforethe IFFT block of the transmitter as seen in Fig. 7.1.

In OFDMA, first, information bits are converted to complex numbers with mod-ulation. Then, the complex numbers are mapped to IFFT block of length M whereeach number stream is transmitted in a subcarrier out of M. This could be seen as anindependent transmission block, and each block produces a time domain signal thatare transmitted simultaneously. IFFT block performs these steps and converts thesedifferent signal streams from frequency domain into a time domain signal. In uplinkOFDMA, of course, each mobile station only uses n subcarriers out of M and leavesthe rest null in IFFT process.

In SC-FDMA, these complex numbers are first sent to additional N-point FFTblock in order to spread the energy over all the subcarriers. We know that FFT mul-tiplies each complex number with a multiplier and introduces N complex numbers.As a result, output of FFT block is considered as modified complex numbers, andeach output contains a portion of every input number. These new modified numbersare sent to M-point IFFT block as in OFDMA. Note that N < M and as in OFDMA,zeros are sent in the unoccupied subcarriers.

In the receiver side, OFDMA utilizes a simple equalizer per subcarrier afterFFT. But, SC-FDMA utilizes a complex equalizer before sending the resultant toIFFT. IFFT removes the effect of the FFT in the transmitter. Notice that result of theIFFT is again a time domain signal; the time domain signal is sent to a single de-tector to create the bits. These differences in receiver side are illustrated in Fig. 7.2,

7.3 SC-FDMA System 263

.

.

.

.

DFT Equalizer IDFT Detect

DFTSubcarrier

de-mapping

Subcarrierde-mapping

Detect

Equalizer

Equalizer

Equalizer

Detect

Detect

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

OFDMA

SC-FDMA

Fig. 7.2 Equalizer comparison in SC-FDMA and OFDMA

where we can see the equalizer simplicity of OFDMA against SC-FDMA. As youcan see, SC-FDMA receiver is more complex than OFDMA, but in the transmittersimpler power amplifiers can be utilized to reduce the power consumption. Thesefortify the SC-FDMA as an uplink transmission scheme, since power efficiency andcomplexity is important for mobile stations but not in the base station.

7.3 SC-FDMA System

Let us introduce Fig. 7.1 as an uplink SC-FDMA structure to analyze PAPR andresource allocation. Data symbols {bi} are modulated into complex numbers {xi},which are are sent over to N-point FFT system. N-point FFT produces a frequencydomain representation (Xn) of the input. After this, each of the parallel output ofFFT is sent to a subcarrier of IFFT for transmission resulting X̂k. M-point IFFTtransforms X̂m into time domain complex signals x̂m.

N-point to M-point matching is a resource allocation problem, since N < M.Q = M/N is an integer and indicates the number of simultaneous users without anyinterference since number of users can be increased above M/N with expense onco-channel interference.

Before transmission, first the CP is added to x̂m and then it is serialized. Afterthat it is modulated with a single frequency carrier. In the receiver side, the receivedsignal is converted to digital format and CP is removed before converting the signal

264 7 SC-FDMA

X1

X2

X3

X4

X5

X6

X1

X2

X3

X4

X5

X6

X1

X1

X1

X2

X2

X2X3

X3

X3

X4

X4

X4

X5

X5

X5

X6

X1

X2

X3

X4

X5

X6

X1

X2

X3

X4

X5

X6

X6

X6

X1

X2

X3

X4

X5

X6

N-pointFFT

N-pointFFT

Localized N-to-M mapping

User 1

User 2

Distributed N-to-M mapping

Fig. 7.3 Subcarrier mapping: localized and distributed for two users, where N = 6, M = 12

into frequency domain with M-point FFT. After channel estimation and equaliza-tion, the symbols are sent to N-point IFFT block. Output of the block is sent to thedetector to estimate xi.

The N subcarriers of the user into M subcarriers is mapped in either distributedor localized manner. Figure 7.3 shows an example for the distributed and localizedinterleaving techniques for two nonoverlapping users.

Distributed mapping (aka interleaved FDMA or IFDMA) introduces bandwidthspreading factor to introduce a parameter for interleaving the allocated subcarriersof a user. IFDMA time sample x̂m is equal to 1

Q xm̄ with m̄ = m mod N if mappingstarts from the first subcarrier. Otherwise if mapping starts from rth subcarrier, whichis in between 0 to Q, then x̂m is equal to

x̂m =1Q

e j2πz(r)xm̄, (7.1)

where z(r) is an additional phase rotation.Localized mapping (aka localized FDMA or LFDMA) maps subcarriers allo-

cated to user adjacent to each other. LFDMA time samples x̂m for r = 0 is again1Q xm̄, and if r �= 0, then x̂m equals to

x̂m =1

Q.N(1− e j2πy(r))

N−1

∑i=0

xi

1− e j2πw(r,i) , (7.2)

7.3 SC-FDMA System 265

where y(r) and w(r, i) are additional phase and complex-weighting factors respec-tively. Notice that there is a 1

Q factor in all cases, which basically rounds off the peakpower.

IFDMA exploits frequency diversity, since interleaving channel variations canbe averaged out. LFDMA on the other hand can be utilized to exploit multiuserdiversity, since block of subcarriers can be selected per user according to the chan-nel characteristic. Also note that channel-dependent scheduling does not reach asmuch diversity order as in OFDMA, since in OFDMA, best subcarriers are selectedfor a user, but in SC-FDMA, best block of subcarriers is selected, which may notbe best for each individual subcarrier within the block. LFDMA also shows largerpeak fluctuations in the time domain as compared with IFDMA. This is due to thefact that each user’s input may differ from the others and may cause uneven distri-bution of input symbols. However, in IFDMA, distribution is uniform because ofblended inputs. However, frequency synchronization needs to be tighter in IFDMAas compared with LFDMA, thereby LFDMA preserves orthogonality of subcarrierswith less complexity. According to these features, IFDMA suits best for high mobileenvironment, on the other hand LFDMA is good for low mobile environment withchannel-dependent scheduling.

Performance of LFDMA and IFDMA peak power shows1 that IFDMA andLFDMA show lower PAPR than OFDMA. IFDMA is the lowest peak power ob-served as seen in Fig. 7.4a, and roll-off factor of the raised-cosine pulse shapingfilter is inversely proportional to the instantaneous peak power as seen in Fig. 7.4b.The peak power characteristic of LFDMA on the other hand changes with block sizeas as seen in Fig. 7.4c for a given cut-off w.

0 12

100 100 100

10−4 10−4 10−4

OFDM

LFDMAIFDMA

w [dB]

Pr(

|Z|2

> w

)

Pr(

|Z|2

> w

)

Pr(

|Z|2

> w

)

0 12

r/o =0

IFDMA

w [dB]

r/o =0.2

r/o =

0. 4

r/o =

0.6

0 12

N=32

LFDMA

w [dB]

N=

8N=

4

a b c

BPSK QPSK BPSK

Fig. 7.4 PAPR analysis for upper bound CCDF of SC-FDMA: The distribution of |x(t)|2 of signalx(t) is given with a cut-off filter w. Pr{|x(t)|2 ≥ w} is referred as complementary cumulativedistribution function (CCDF) and Z � x(t0, s̄) is a random variable for a given t0 ∈ [0,T ) andx(t0, s̄) is a baseband representation of the signal carrier modulated signal. {si}∞i=−∞ are mutuallyindependent transmitted symbols

1 “Single Carrier Orthogonal Multiple Access Technique for Broadband Wireless Communica-tions” by Myung, submitted to Electrical and Computer Engineering Department of PolytechnicUniversity, NY, for the degree of Doctor of Philosophy.

266 7 SC-FDMA

7.4 Summary

SC-FDMA is a promising OFDMA-based multicarrier digital technology for uplink.SC-FDMA is being considered to simplify the transmitter in the handsets and reducethe power consumption with lower PAPR feature. In the receiver structure, it is morecomplex than OFDMA for similar link performance, but this might not be an issuesince the receiver is in the base station, which does not have power or complexitylimit.

Localized SC-FDMA is considered for LTE uplink against distributed SC-FDMA and OFDMA. Distributed SC-FDMA has not been selected because of itsvulnerability to Doppler and frequency offset and its limitation to pilot design.SC-FDMA pilot is generally time-multiplexed with data and designed for lowPAPR. This restriction on pilot design is more severe in distributed SC-FDMA andmay result in lower flexibility than OFDMA.

SC-FDMA is also proposed to be included to IEEE 802.16m (WiMAX-m) foruplink. But, recent proposals in IEEE 802.16m support OFDMA against SC-FDMAin uplink stating that localized SC-FDMA cannot exploit full advantage of multiuserdiversity as in OFDMA and PAPR advantage of SC-FDMA can be mitigated withadvanced PAPR techniques in OFDMA. Also backward compatibility to WiMAX-eis another concern when selecting SC-FDMA in uplink of WiMAX-m.

MIMO techniques can be used in SC-FDMA to exploit diversity as well as spatialmultiplexing, somewhat similar to MIMO-OFDM, in the frequency domain afterFFT as described in the previous chapter.

References

1. Myung, H. G., Single Carrier Orthogonal Multiple Access Technique for Broadband WirelessCommunications, PhD Dissertation, Polytechnic University, NY, January 2007.

2. Sorger, U., De Broeck, I., Schnell, M., “Interleaved FDMA – A New Spread-SpectrumMultiple-Access Scheme,” Proceedings of IEEE ICC, pp. 1013–1017, 1998.

3. Falconer, D., Ariyavisitakul, S. L., Benyamin-Seeyar, A., Eidson, B., “Frequency DomainEqualization for Single-Carrier Broadband Wireless Systems,” IEEE Communication Maga-zine, vol. 40, no. 4, pp. 58–66, 2002.

4. Goodman, D. J., Lim, J., Myung, H. G., “Single Carrier FDMA (SC-FDMA) for Uplink Wire-less Transmission,” IEEE Vehicular Technology Magazine, 2006.

5. Goodman, D. J., Lim, J., Myung, H. G., “Peak-to-average Power Ratio of Single CarrierFDMA Signals with Pulse Shaping,” IEEE International Symposium on Personal, Indoor andMobile Radio Communications, pp. 1–5, 2006.

6. Goodman, D. J., Lim, J., Myung, H. G., Oh, K., “Channel-Dependent Scheduling of UplinkSingle Carrier FDMA Systems,” Proceedings of IEEE VTC, 2006.

7. Batariere, M. D., Classon, B. K., “Low-Complexity Technique to Increase Capacity of MobileBroadband Systems,” Proceedings of IEEE VTC, vol. 4, pp. 1939–1943, 2000.

8. Cioffi, J. M., Tellado, J., “PAR Reduction in Multicarrier Transmission Systems,” ANSIT1E1.4/97-367, 1997.

References 267

9. Lopez, P., Monnier, R., Tourtier, P. J., “Multicarrier Modem for Digital HDTV TerrestrialBroadcasting,” Signal Processing: Image Communication, vol. 5, no. 6, pp. 379–403, 1998.

10. VDSL Alliance, VDSL Alliance SDMT VDSL Draft Standard Proposal, ANSI ContributionT1E1.4/97-332, 1997.

11. Leung, C., Warner, W. D., “OFDM/FM Frame Synchronization for Mobile Radio Data Com-munication,” IEEE Transactions on Vehicular Technology, vol. 42, no. 3, pp. 302–313, 1993.