sc-cdma

© MASTERSERIES

Abstract:Single carrier frequency

division multiple access (SC-FDMA), a modified form of Orthogo-

nal FDMA (OFDMA), is a promisingtechnique for high data rate uplink communi-

cations in future cellular systems. SC-FDMA hassimilar throughput performance and essentially the

same overall complexity as OFDMA. A principaladvantage of SC-FDMA is the peak-to-average powerratio (PAPR), which is lower than that of OFDMA. SC-FDMA is currently a strong candidate for the uplink multi-ple access scheme in the Long Term Evolution of cellularsystems under consideration by the Third Generation Part-nership Project (3GPP). In this paper, we give an overviewof SC-FDMA. We also analyze the effects of subcarriermapping on throughput and PAPR. Among the possiblesubcarrier mapping approaches, we find that localizedFDMA (LFDMA) with channel-dependent scheduling(CDS) results in higher throughput than interleavedFDMA (IFDMA). However, the PAPR performance

of IFDMA is better than that of LFDMA. As inother communications systems there are

complex tradeoffs between designparameters and performance in

an SC-FDMA system.

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Single Carrier FDMA for Uplink Wireless Transmission

Hyung G. Myung, Junsung Lim, and David J. Goodman, Polytechnic University

Over the past fifteen years, the bit rates achieved incellular and local area wireless communicationssystems have increased steadily. The earliest digi-tal cellular systems, North American TDMA and

GSM employed time division multiple access. Second gen-eration CDMA systems and the two third generation cellu-lar systems all use direct sequence spread spectrum formultiplexing and multiple access [1]. The highest bitrates in commercially deployed wireless systems areachieved by means of Orthogonal Frequency DivisionMultiplexing (OFDM) in wireless LANs based on the IEEE802.11a and IEEE 802.11g standards. The next advance incellular systems, under investigation by the Third Gener-ation Partnership Project (3GPP), also anticipates theadoption of OFDMA to achieve higher bit rates.

1.1 Frequency Division Multiple AccessIn cellular applications, a big advantage of OFDMA is itsrobustness in the presence of multipath signal propaga-tion [2]. The immunity to multipath derives from the factthat an OFDMA system transmits information on Morthogonal frequency carriers, each operating at 1/Mtimes the bit rate of the information signal. On the otherhand, the OFDMA waveform exhibits very pronouncedenvelope fluctuations resulting in a high peak-to-averagepower ratio (PAPR). Signals with a high PAPR requirehighly linear power amplifiers to avoid excessive inter-modulation distortion. To achieve this linearity, the ampli-fiers have to operate with a large backoff from their peakpower. The result is low power efficiency (measured bythe ratio of transmitted power to dc power dissipated),

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which places a significant burden on portable wireless ter-minals. Another problem with OFDMA in cellular uplinktransmissions derives from the inevitable offset in fre-quency references among the different terminals thattransmit simultaneously. Frequency offset destroys theorthogonality of the transmissions, thus introducing multi-ple access interference.

To overcome these disadvantages, 3GPP is investigat-ing a modified form of OFDMA for uplink transmissions inthe “long-term evolution (LTE)” of cellular systems[3]–[5]. The modified version of OFDMA, referred to assingle carrier FDMA (SC-FDMA), is the subject of thispaper. As in OFDMA, the transmitters in an SC-FDMA sys-tem use different orthogonal frequencies (subcarriers) totransmit information symbols. However, they transmitthe subcarriers sequentially, rather than in parallel. Rela-tive to OFDMA, this arrangement reduces considerablythe envelope fluctuations in the transmitted waveform.Therefore, SC-FDMA signals have inherently lower PAPRthan OFDMA signals. However, in cellular systems withsevere multipath propagation, the SC-FDMA signals arriveat a base station with substantial intersymbol interfer-ence. The base station employs adaptive frequencydomain equalization to cancel this interference. Thisarrangement makes sense in a cellular system because itreduces the burden of linear amplification in portableterminals at the cost of complex signal processing (fre-quency domain equalization) at the base station.

1.2 Performance MeasuresWhile PAPR is a major concern in portable terminals,information throughput is an even more important indica-tor of system performance. As in OFDMA, throughput inSC-FDMA depends on the way in which information sym-bols are applied to subcarriers. There are two approach-es to apportioning subcarriers among terminals. Inlocalized SC-FDMA (LFDMA), each terminal uses a set ofadjacent subcarriers to transmit its symbols. Thus thebandwidth of an LFDMA transmission is confined to afraction of the system bandwidth. The alternative toLFDMA is distributed SC-FDMA in which the subcarriersused by a terminal are spread over the entire signal band.One realization of distributed SC-FDMA is interleavedFDMA (IFDMA) where occupied subcarriers are equidis-tant from each other [6]. Figure 1 showsthe two arrangements in the frequencydomain. There are three terminals, eachtransmitting symbols on four subcarriersin a system with a total of 12 subcarriers.In the distributed arrangement, terminal 1uses subcarriers 0, 3, 6, and 9; withLFDMA it uses subcarriers 0, 1, 2, and 3.

With respect to immunity to transmis-sion errors (which determines through-put), distributed SC-FDMA is robust

against frequency selective fading because its informa-tion is spread across the entire signal band. Therefore itoffers the advantage of frequency diversity. On the otherhand, LFDMA can potentially achieve multi-user diversityin the presence of frequency selective fading if it assignseach user to subcarriers in a portion of the signal bandwhere that user has favorable transmission characteris-tics (high channel gain). Multi-user diversity relies onindependent fading among dispersed transmitters. It alsorequires channel-dependent scheduling (CDS) of subcarri-ers. CDS requires the system to monitor the channelquality as a function of frequency for each terminal, andadapt subcarrier assignments to changes in the channelfrequency responses of all the terminals.

In this paper, we present the results of our studies ofsome of the important issues in the design of a SC-FDMAsystem. In particular, we compare LFDMA and IFDMAwith respect to the two major performance indicators,system throughput and PAPR. For each configuration, wepresent throughput measures with static subcarrierassignments and with channel dependent scheduling. Wefind that as in other engineering systems there are com-plex tradeoffs between design parameters and perfor-mance. Configurations with the lowest PAPR tend to havelower throughput. Therefore equipment designers andsystem operators can use their judgment to find the besttradeoff to meet their specific needs. For example, we findthat a system with many users each transmitting at amoderate bit rate is better off with IFDMA, while LFDMAworks better in a system with a few high-bit-rate users.

This article is organized as follows. We describe thesignal processing operations in SC-FDMA and OFDMAsystems in the next section. The third section containsthe results of our analysis of PAPR. We show that IFDMAhas inherently lower PAPR than LFDMA and that both ofthem are better than OFDMA with respect to PAPR. How-ever, much of the advantage of IFDMA is eroded by thepulse shaping that is necessary to curtail out-of-bandspectrum components prior to radio transmission. Thefourth section analyzes system throughput, with respectto two performance measures: an upper bound onachievable bit rate given by Shannon’s capacity formula,and outage defined as the probability that the signal-to-interference ratio falls below a certain threshold. The

FIGURE 1 Subcarrier allocation methods for multiple users (3 users, 12 subcarriers,and 4 subcarriers allocated per user).

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analysis considers static subcarrier assignments andchannel dependent scheduling for LFDMA and IFDMA. Itdemonstrates that LFDMA with channel-dependentscheduling has the potential for considerably highercapacity in terms of number of users than IFDMA. Thefinal section summarizes our major findings anddescribes work in progress.

2. System Configuration of Single Carrier FDMA

The transmitter of an SC-FDMA system converts a binaryinput signal to a sequence of modulated subcarriers. Todo so, it performs the signal processing operationsshown in Figure 2. Signal processing is repetitive in a fewdifferent time intervals. Resource assignment takes placein transmit time intervals (TTIs). In 3GPP LTE, a typicalTTI is 0.5 ms. The TTI is further divided into time inter-vals referred to as blocks. A block is the time used totransmit all of subcarriers once. At the input to the trans-mitter, a baseband modulator transforms the binaryinput to a multilevel sequence of complex numbers xn inone of several possible modulation formats includingbinary phase shift keying (BPSK), quaternary PSK (QPSK),16 level quadrature amplitude modulation (16-QAM) and64-QAM. The system adapts the modulation format, andthereby the transmission bit rate, to match the currentchannel conditions of each terminal.

The transmitter next groups the modulation symbols,xn into blocks each containing N symbols. The first stepin modulating the SC-FDMA subcarriers is to perform anN -point discrete Fourier transform (DFT), to produce a

frequency domain representation Xk of the input sym-bols. It then maps each of the N DFT outputs to one ofthe M(> N) orthogonal subcarriers that can be transmit-ted. As in OFDMA, a typical value of M is 256 subcarriersand N = M/Q is an integer submultiple of M . Q is thebandwidth expansion factor of the symbol sequence. Ifall terminals transmit N symbols per block, the systemcan handle Q simultaneous transmissions without co-channel interference. The result of the subcarrier map-ping is the set X̃l (l = 0, 1, 2, . . . , M − 1) of complexsubcarrier amplitudes, where N of the amplitudes arenon-zero. As in OFDMA, an M -point inverse DFT (IDFT)transforms the subcarrier amplitudes to a complex timedomain signal X̃m. Each X̃m then modulates a single fre-quency carrier and all the modulated symbols are trans-mitted sequentially.

The transmitter performs two other signal processingoperations prior to transmission. It inserts a set of sym-bols referred to as a cyclic prefix (CP) in order to provide aguard time to prevent inter-block interference (IBI) due tomultipath propagation. The transmitter also performs alinear filtering operation referred to as pulse shaping inorder to reduce out-of-band signal energy. In general, CP isa copy of the last part of the block, which is added at thestart of each block for a couple of reasons. First, CP actsas a guard time between successive blocks. If the length ofthe CP is longer than the maximum delay spread of thechannel, or roughly, the length of the channel impulseresponse, then, there is no IBI. Second, since CP is a copyof the last part of the block, it converts a discrete time lin-

ear convolution into a discretetime circular convolution. Thustransmitted data propagatingthrough the channel can bemodeled as a circular convolu-tion between the channelimpulse response and the trans-mitted data block, which in thefrequency domain is a point-wise multiplication of the DFTfrequency samples. Then, toremove the channel distortion,the DFT of the received signalcan simply be divided by theDFT of the channel impulseresponse point-wise or a moresophisticated frequency domainequalization technique can beimplemented, as described atthe end of this section.

Figure 2 includes a block dia-gram of an OFDMA transmitterand receiver. It has much incommon with SC-FDMA. Theonly difference is the presenceFIGURE 2 Transmitter and receiver structure of SC-FDMA and OFDMA systems.

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of the DFT in the SC-FDMA transmitter and the IDFT in theSC-FDMA receiver. For this reason SC-FDMA is sometimesreferred to as DFT-spread OFDMA.

Several approaches to mapping transmission symbolsXk to SC-FDMA subcarriers are currently under consider-ation. They are divided into two categories; distributedand localized as shown in Figure 1. In the distributed sub-carrier mapping mode, DFT outputs of the input data areallocated over the entire bandwidth with zeros occupyingthe unused subcarriers resulting in a non-continuouscomb-shaped spectrum. As mentioned earlier, interleavedSC-FDMA (IFDMA) is an important special case of distrib-uted SC-FDMA. In contrast with IFDMA, consecutive sub-carriers are occupied by the DFT outputs of the inputdata in the localized subcarrier mapping mode resultingin a continuous spectrum that occupies a fraction of thetotal available bandwidth. Subcarrier mapping methodsare further divided into static and channel dependentscheduling (CDS) methods. CDS assigns subcarriers tousers according to the channel frequency response ofeach user. For both scheduling methods, distributed sub-carrier mapping provides frequency diversity becausethe transmitted signal is spread over the entire band-width. With distributed mapping, CDS incrementallyimproves performance. By contrast CDS is of great bene-fit with localized subcarrier mapping because it providessignificant multi-user diversity as discussed in the firstsection of this paper.

Until now, we have referred in general to mappings ofthe N symbols in each block onto the M > N transmis-sion subcarriers. However, with M = 256 in a practicalsystem the number of possible mappings is far too largefor practical scheduling algorithms to consider. Toreduce the complexity of the mapping, subcarriers aregrouped into chunks and all of the subcarriers in a chunkare assigned together. In our research we have studied256 subcarriers grouped in 32 chunks of 8 subcarriersper chunk or 16 chunks with 16 subcarriers per chunk.Figure 3 shows an example of SC-FDMA transmit symbolsin the frequency domain for N = 4, Q = 3 and M = 12.After subcarrier mapping, the frequency data is trans-formed back to the time domain by applying M -pointinverse DFT (IDFT). As in Figure 1, different users occupydifferent orthogonal subcarriers.

For IFDMA, time symbols are simply a repetition ofthe original input symbols with a systematic phaserotation applied to each symbol in the time domain [6].Therefore, the PAPR of IFDMA signal is the same as inthe case of a conventional single carrier signal. In thecase of LFDMA, the time signal has exact copies ofinput time symbols in N sample positions. The otherM -N time samples are weighted sums of all the sym-bols in the input block [7]. Figure 4 shows an exampleof IFDMA and LFDMA signals that occupy the chunkthat includes subcarrier zero.

The receiver transforms the received signal into thefrequency domain via DFT, de-maps the subcarriers, andthen performs frequency domain equalization. BecauseSC-FDMA uses single carrier modulation, it suffers fromintersymbol interference (ISI) and thus equalization isnecessary to combat the ISI. Practical considerationsfavor minimum mean square error (MMSE) frequencydomain equalization. MMSE is generally preferred overzero forcing (ZF) due to the robustness against noise. Theequalized symbols are transformed back to the timedomain via IDFT, and detection and decoding take placein the time domain.

Relative to OFDMA, there is a fundamental differencein the SC-FDMA receiver equalization and detectionprocesses. Since each data symbol is conveyed on indi-vidual subcarriers in OFDMA, channel equalization or

FIGURE 3 An example of SC-FDMA transmit symbols in the fre-quency domain for N = 4 subcarriers per user, Q = 3 users, andM = 12 subcarriers in the system. X̃l,Distributed denotes transmitsymbols for distributed subcarrier mapping scheme and X̃l,Localized

denotes transmit symbols for localized subcarrier mapping scheme.

FIGURE 4 An example of SC-FDMA transmit symbols in the timedomain for N = 4, Q = 3, and M = 12.



inversion is performed individually on each subcarrierand data detection is also carried out on each subcarrier.Thus, a null in the channel spectrum severely degradesthe system performance since there is essentially no wayto recover the data that is affected by the null. To protectindividual subcarriers from frequency nulls in the chan-nel, channel coding or power/rate adaptation is requiredfor OFDMA. In the case of SC-FDMA, channel equalizationis done similarly in the frequency domain but data detec-tion is performed after the frequency domain equalizeddata is reverted back to time domain by IDFT. Hence, it ismore robust to spectral nulls compared to OFDMA sincethe noise is averaged out over the entire bandwidth.Additional disadvantages of OFDMA compared to SC-FDMA are the strong sensitivity to carrier frequency off-set and strong sensitivity to nonlinear distortion in thepower amplifier due to the high PAPR, both properties ofthe multicarrier nature of OFDMA [8], [9].

The next two sections of this paper demonstrate that thedetails of the subcarrier mapping have a strong effect on thetwo main performance measures: PAPR and throughput. Wealso describe how the pulse shaping influences PAPR.

3. PAPR analysis of SC-FDMA

In this section, we analyze the PAPR of the SC-FDMA sig-nal. We use the notation in Figure 3 and assume that thetotal number of subcarriers is M = Q · N , where N is thenumber of subcarriers per block. The integer Q is themaximum number of terminals that can transmit simulta-neously. For distributed subcarrier mapping, we considerthe case of IFDMA with subcarriers equally spaced overthe system bandwidth.

The PAPR is defined as the ratio of peak power to aver-age power of the transmitted signal in a given transmis-sion block. Without pulse shaping, that is, usingrectangular pulse shaping, symbol rate sampling will givethe same PAPR as the continuous time domain case sincean SC-FDMA signal is modulated over a single carrier.

To evaluate PAPR of individual system configurations,we have simulated the transmission of 105 blocks of sym-bols. After calculating PAPR for each block, we presentthe data as an empirical CCDF (Complementary Cumula-tive Distribution Function). The CCDF is the probabilitythat PAPR is higher than a certain PAPR value PAPR0(Pr{PAPR > PAPR0}). Our simulations apply to 256 subcar-riers in a transmission bandwidth of 5 MHz. The data blocksize is N = 64 and the spreading factor is Q = M/N = 4.We used 8 times oversampling to calculate PAPR for eachblock when pulse shaping is considered. To evaluate theeffects of pulse shaping on SC-FDMA, we convolved eachtransmitted symbol waveform with a raised cosine pulsetruncated from −6T to +6T , where T seconds is the sym-bol duration. No pulse shaping was applied in the caseOFDMA. The impulse response of a raised cosine filter is,

r(t ) = sinc(

πtT

)cos

(παtT

)

1 − 4α2t2

T2

(1)

where the parameter α(0 ≤ α ≤ 1) is referred to as therolloff factor. Lower values of α introduce more pulseshaping and more suppression of out-of-band- signalcomponents.

Figure 5 contains plots of the distribution (CCDF) ofPAPR for IFDMA, LFDMA, and OFDMA. For each example,

FIGURE 5 Comparison of CCDF of PAPR for IFDMA, LFDMA, and OFDMA with M = 256 system subcarriers, N = 64 subcarriers per user,and a = 0.5 rolloff factor; (a) QPSK; (b) 16-QAM.



we observe the PAPR0 value that is exceeded with proba-bility less than 0.1% (Pr{PAPR > PAPR0} = 10−3), or 99.9-percentile PAPR. First, in the case of no pulse shaping,the PAPR of IFDMA is 10.5 dB lower than the PAPR ofOFDMA for QPSK modulation. The difference is 7 dB for16-QAM. The PAPR of LFDMA is lower than the PAPR ofOFDMA by 3 dB for QPSK. The difference is 2 dB for 16-QAM. Therefore LFDMA has 7.5 dB higher PAPR thanIFDMA with QPSK and 5 dB higher PAPR for 16-QAM. Withraised-cosine pulse shaping with rolloff factor of 0.5,PAPR increases significantly for IFDMA whereas PAPR ofLFDMA hardly increases.

Figure 6 also shows that raised-cosine pulse shaping ismore harmful in terms of PAPR for IFDMA than it is forLFDMA. As the rolloff factor α increases from 0 to 1 (pro-gressively less rolloff), PAPR decreases significantly forIFDMA. This implies that there is a tradeoff between PAPRperformance and out-of-band radiation since out-of-bandradiation increases with increasing rolloff factor.

We also relate the PAPR to RF transmit poweramplifier efficiency. In an ideal linear power amplifierwhere linear amplification is achieved up to the satu-ration point, maximum power efficiency is achievedwhen the amplifier is operating at the saturation point.To prevent distortion in the presence of PAPR, trans-mit power backoff is needed to operate the poweramplifier in the linear region.

Together, Figures 5 and 6 show that SC-FDMA signalsindeed have lower PAPR than OFDMA signals. Also,LFDMA incurs higher PAPR compared to IFDMA but,compared to OFDMA, it is lower, though not significant-ly. Another noticeable fact is that pulse shaping signifi-cantly increases the PAPR of IFDMA. A pulse shapingfilter should be designed carefully in order to limit the

PAPR without degrading the system performance. Ingeneral, IFDMA is more desirable than LFDMA in termsof PAPR and power efficiency. However, in terms of sys-tem throughput, we will show in the next section thatLFDMA is clearly superior when channel-dependentscheduling is utilized [10].

4. Channel-Dependent Scheduling (CDS)

for Uplink SC-FDMA

In this section, we investigate channel-dependentresource scheduling for an SC-FDMA system in uplinkcommunications. A key question of CDS is how we shouldallocate time and frequency resources fairly among userswhile achieving multi-user diversity and frequency selec-tive diversity. To do so, we introduce utility-based sched-uling where utility is an economic concept representinglevel of satisfaction. The choice of a utility measure influ-ences the tradeoff between overall efficiency and fairnessamong users. In our studies, we consider two differentutility functions: aggregate user throughput for maximiz-ing system capacity and aggregate logarithmic userthroughput for maximizing proportional fairness [11],[12]. The objective is to find an optimum chunk assign-ment for all users in order to maximize the sum of userutility at each transmit time interval (TTI). If the userthroughput is regarded as the utility function, the

FIGURE 6 Comparison of CCDF of PAPR for IFDMA and LFDMA with M = 256 system subcarriers, N = 64 subcarriers per user, and rollofffactor α of 0, 0.2, 0.4, 0.6, 0.8, and 1; (a) QPSK; (b) 16-QAM.


A KEY QUESTION OF CHANNEL DEPENDENTSCHEDULING IS HOW WE SHOULD ALLOCATE TIMEAND FREQUENCY RESOURCES FAIRLY AMONGUSERS WHILE ACHIEVING MULTI-USER DIVERSITYAND FREQUENCY SELECTIVE DIVERSITY.


resource allocation maximizes rate-sum capacity ignoringfairness among users. Therefore, only the users near thebase station who have the best channel conditions occu-py most of the resources. On the other hand, setting thelogarithmic user data rate as the utility function providesproportional fairness.

In considering the optimization problem of CDS formulticarrier multiple access, it is theoretically possible toassume that the scheduler can assign subcarriers individ-ually. Allocating individual subcarriers is, however, a pro-hibitively complex combinatorial optimization problem insystems with 256 subcarriers and on the order of ten ter-minals transmitting simultaneously. Moreover, assigningsubcarriers individually would introduce unacceptablecontrol signaling overhead. In practice, the units ofresource allocation are chunks, which are disjoint sets of

subcarriers. As a practical matter chunk-based transmis-sion is desirable since the input data symbols aregrouped into a block for DFT operation before subcarriermapping. We will consider only chunk-based schedulingin the remainder of this section. With regards to chunkstructure, there is a restriction on chunk selection forIFDMA such that all assigned subcarriers should beequidistant in order to maintain the lowest PAPR [13].

Even with subcarriers assigned in chunks, optimumscheduling is extremely complex for two reasons: 1) Theobjective function is complicated, consisting of nonlinearand discrete constraints dependent on the combined chan-nel gains of the assigned subcarriers; and 2) there is a totaltransmit power constraint for each user. Furthermore, theoptimum solution entails combinatorial comparisons withhigh complexity. Instead of directly solving the optimiza-

tion problem, a sub-optimalchunk allocation schemecan be used for both IFDMAand LFDMA to obtain mostof the benefits of CDS. ForLFDMA, a greedy chunkselection method can beapplied where each chunkis assigned to the user whocan maximize the marginalutility when occupying thespecific chunk. For IFDMA,the benefit of multi-userdiversity can be achievedby selecting users in orderof the estimated marginalutility based on the averagechannel condition over theentire set of subcarriers.The users with higher chan-nel gains may occupy alarger number of chunksthan users with lower chan-nel gains [10].

Our throughput mea-sure in this study is thesum of the upper boundon user throughputs givenby Shannon’s formula,C = B log(1 + S N R) whereB is the effective band-width depending on thenumber of occupied sub-carriers and SNR is signal-to-noise ratio of a block.

Figures 7, 8, and 9 arethe results of computer sim-ulations of SC-FDMA with256 subcarriers spread over

FIGURE 7 Comparison of rate-sum capacity with M = 256 system subcarriers, N = 8 subcarriers peruser, bandwidth = 5 MHz, and noise power per Hz = −160 dBm; (a) utility function: sum of userthroughputs; (b) utility function: sum of the logarithm of user throughputs.

FIGURE 8 Average user data rate as a function of user distances with M = 256 system subcarriers,N = 8 subcarriers per user, bandwidth = 5 MHz, and noise power per Hz = −60 dBm; (a) utility function:sum of user throughputs; (b) utility function: sum of the logarithm of user throughputs.



a 5 MHz band. They compare the effects of channel depen-dent subcarrier allocation (S) with static (round-robin)scheduling (R) for localized FDMA (L-FDMA) and inter-leaved FDMA (I-FDMA). In all of the examples, the schedul-ing took place with chunks containing 8 subcarriers.

Figure 7 shows two effects of applying different utilityfunctions in the scheduling algorithm. In the two graphsin Figure 7, the utility functions are the sum of userthroughputs and the sum of the logarithm of userthroughputs, respectively. Each graph shows the aggre-gate throughput as a function of the number of simultane-ous transmissions. Figure 8 shows the expected userthroughput at each distance from the base station for thesame utility functions. The simulation results in the fig-ures use the following abbreviations: R-LFDMA (staticround robin scheduling of LFDMA), S-LFDMA (CDS ofLFDMA), R-IFDMA (static round robin scheduling ofIFDMA), and S-IFDMA (CDS of IFDMA).

Figure 7 shows that for throughput maximization(utility=bit rate), the advantage of channel dependentscheduling over round robin scheduling increases as thenumber of users increases. This is because the sched-uler selects the closer users who can transmit at higherdata rate. If there are more users, the possibility oflocating users at closer distance to the base stationincreases. As a result, the CDS achieves significantimprovements for both IFDMA and LFDMA. In the caseof logarithmic rate utility, the CDS gain stops increasingbeyond approximately 32 users. With 32 users, maximiz-ing logarithmic rate utility can increase system capacityby a factor of 1.8 for LFDMA and 1.26 for IFDMA relativeto static scheduling.

Figure 8 shows that the CDS scheme based on the loga-rithm of user throughput as a utility function providesproportional fairness whose gains are shared among allusers, whereas the CDS gains are concentrated to theusers near the base station when the user throughput isconsidered as the utility function.

Figure 9 shows the outage probability which isdefined as the probability that the average user through-put is lower than the minimum required data rate after100 msec. Considering user capacity at 1% outage prob-ability and minimum required rate of 144 Kbps, roundrobin scheduling supports less than 20 users but CDSschemes can support 24 users forIFDMA and 48 users for LFDMA. TableI compares round robin schedulingand utility-based scheduling with log-arithmic user data rate with respectto system capacity and fairness.

For static subcarrier assignment(round robin scheduling), a systemwith users each transmitting at amoderate data rate is better off withIFDMA while LFDMA works better in

a system with a few high date rate users. Due to theadvantages of lower outage probability and lowerPAPR, IFDMA is an attractive approach to static subcar-rier scheduling. For channel-dependent scheduling,LFDMA has the potential for considerably higher datarate. The results show that CDS increases systemthroughput by up to 80% relative to static schedulingfor LFDMA but the increase is only 26% for IFDMA. Thescheduling gains in LFDMA can be exploited to reducepower consumption and PAPR by using power controlto establish a power margin instead of increasing sys-tem capacity.

FIGURE 9 Outage probability (utility: logarithmic user data rate,minimum required data rate = 144 Kbps, M = 256, system subcar-riers, N = 8 subcarriers per user, bandwidth = 5 MHz, and noisepower per Hz = −160 dBm).

Type S-LFDMA R-LFDMA S-IFDMA R-IFDMA

Rate-sum capacity 18 Mbps 10 Mbps 12 Mbps 9.55 Mbps(32 users)

Fairness (32 users) 0.417 0.334 0.352 0.334User capacity 48 users Less than 20 24 users Less than 20

Fairness = average user data rate of users at the cell boundary (900 m – 1 km)/average user data rate.

User capacity: Number of users achieving 1% outage probability when the minimum rate equals to 144 Kbps.

TABLE 1 Comparisons between utility-based schedulingand round-robin scheduling (logarithmic rate utility).


RESULTS SHOW THAT CHANNEL DEPENDENTSCHEDULING INCREASES SYSTEM THROUGHPUT BYUP TO 80% RELATIVE TO STATIC SCHEDULING FORLOCALISED FDMA BUT THE INCREASE IS ONLY26% FOR INTERLEAVED FDMA.


5. Conclusions

SC-FDMA is a promising technique for high data rateuplink communication in future cellular systems. Within aspecific SC-FDMA system configuration, there are manydesign and operational choices that affect performance ina complex manner. In this paper, we have focused on theeffects of subcarrier mapping on throughput and peak-to-average power ratio (PAPR). Among the possible subcar-rier mapping approaches, we find that localized FDMA(LFDMA) with channel-dependent scheduling (CDS)results in higher throughput than interleaved FDMA(IFDMA). However, the PAPR performance of IFDMA isbetter by 4 to 7 dB than that of LFDMA. When we consid-er the pulse shaping necessary to control adjacent chan-nel interference, we find a narrower difference betweenLFDMA and IFDMA in terms of PAPR performance.

Our work in progress is an investigation of the impactof channel estimation error on the throughput perfor-mance of SC-FDMA. Effective scheduling depends onaccurate information about the frequency response of theradio channels linking terminals to an SC-FDMA base sta-tion. Channel estimation errors are caused by noisy esti-mation and changes in channel properties. The errorsdegrade the performance of CDS by causing incorrectadaptation of the modulation technique and incorrectassignment of subcarriers to users. Our research aims toquantify the effects of these errors.

Author Information

Hyung G. Myung received the B.S. and M.S. degrees in EEfrom Seoul National University, South Korea, and the M.S.degree in applied mathematics from Santa Clara Universi-ty. He is currently working towards his Ph.D. degree atPolytechnic University, Brooklyn. From 1997 to 1999, hewas with Republic of Korea Air Force Academy as an aca-demic instructor. From 2001 to 2003, he was with Array-Comm as a software engineer. In summer of 2005, he wasan intern at Samsung Advanced Institute of Technologyand from February to August of 2006, he was an intern atInterDigital. His research interests include DSP for com-munications and wireless communications. For moreinformation, visit http://hgmyung.googlepages.com/.

Junsung Lim received the B.S. degree in electricalengineering from Hallym University, South Korea, in 1999,the M.S. degree in electrical engineering from Sogang Uni-versity, South Korea, in 2002, and the Ph.D. degree at theElectrical and Computer Engineering Department of Poly-

technic University, Brooklyn, NY in 2006.He was a summer intern in System Archi-tecture Group of InterDigital Communica-tion Corporation, Melville, NY, in 2005,and has a pending patent resulting fromthe works. He is currently with SamsungElectronics. His current research inter-ests are single-carrier frequency division

multiple access, resource management, and system per-formance for wireless communications.

David J. Goodman (M’67-SM’86-F’88) is currently aProgram Director at the National Science Foundation onleave from his position as Professor of Electrical andComputer Engineering at Polytechnic University, Brooklyn, New York. At Poly, he was Director of WICAT,the Wireless Internet Center of Advanced Technology, aNational Science Foundation Industry/University Cooper-ative Research Center. Prior to joining Poly in 1999, hewas at Rutgers University where he was founding directorof WINLAB, the Wireless Information Network Laboratory.Until 1988, he was a Department Head in CommunicationsSystems Research at AT&T Bell Laboratories. Dr. Goodman was recently elected to the National Academyof Engineering in recognition of his contributions to digi-tal signal processing and wireless communications.

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13. R. Dinis, D. Falconer, C.T. Lam, and M. Sabbaghian, “A Multiple Access Schemefor the Uplink of Broadband Wireless Systems,” Proc. IEEE GLOBECOM ’04, vol.6, Dallas, TX, pp. 3808–3812, Dec. 2004.


RESULTS SHOW THAT SINGLE CARRIER FREQUENCY DIVISIONMULTIPLE ACCESS (SCFDMA) IS A PROMISING TECHNIQUE FORHIGH DATA RATE UPLINK COMMUNICATIONS IN FUTURE CELLULARSYSTEMS, THOUGH THERE ARE MANY DESIGN AND OPERATIONALASPECTS THAT AFFECT PERFORMANCE.


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