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Non Binary SC-FDMA for 3GPP LTE Uplink

Mohammad Rakibul Islam1, Mohammad Irfan, Nadim Ullah, Shafi Ullah, Shaikh Mohammad Fahim, Ishtiza Ibne Azad

Dept. of Electrical and Electronic Engineering, Islamic University of Technology

Board Bazar, Gazipur-1704, Dhaka, BangladeshE-mail: rakibultowhid@yahoo.com

1Corresponding author

Abstract- Single Carrier Frequency Division Multiple Access

(SC-FDMA) is a multiple access scheme that uses DFT spreading

prior to OFDM modulation to map the signal from each user to a

subset of the available subcarriers. That has similar performance

and almost the same overall structure as those of an OFDMA

system. Its advantage over OFDMA is that the SC-FDMA signal

has lower peak-to-average power ratio (PAPR). SC-FDMA has

drawn great attention as an attractive alternative to OFDMA,

especially in the uplink communications where lower PAPR

greatly benefits the mobile terminal in terms of transmitted

power efficiency. In this paper, we have given the proposal of

Non Binary SC-FDMA, replacing binary number by octal

number system. The most prominent result that we have

obtained using non-binary SC-FDMA, compared to binary case

is further reduction of BER and peak power of SC-FDMA signalswhich have been shown by mathematical analysis, and are

simulated for different channels using Interleaved FDMA

(IFDMA), and localized FDMA (LFDMA).

Keywords SC-FDMA, LFDMA, DFDMA, IFDMA, LTE

I. INTRODUCTION

Demands for media rich wireless data services havebrought much attention to high-speed broadband mobile

wireless techniques in recent years. Orthogonal frequencydivision multiplexing (OFDM), which is a multicarrier

communication technique, has become widely acceptedprimarily because of its robustness against frequency selective

fading channels which are common in broadband mobilewireless communication

Broadband wireless communication systems mustachieve high data rates in a spectrally efficiency manner. Forthis reason, Orthogonal Frequency Division Multiplexing

(OFDM) [1, 2] has been widely employed in systems such asthe IEEE 802.11a/g standards. Orthogonal Frequency Division

Multiple Access (OFDMA) is multiple access schemes forOFDM that works by assigning each user a unique set ofsubcarriers. OFDMA is currently employed in the IEEE802.16

standard. One major drawback of OFDM and OFDMA is thehigh peak-to-average power ratio (PAPR) that results from a

multicarrier signal [2]. High-PAPR transmit signals requiresignificant back off in the power amplifier and this reduces

their power efficiency and mean power output. This can beproblematic, particularly on the uplink where battery poweredterminals struggle to match the data rate and range of the

downlink. Since in OFDMA the bandwidth of a subcarrier isdesigned to be smaller than the coherence Bandwidth each

sub-channel is seen as flat fading channel, which simplifiesthe channel equalization process In the time domain, bysplitting a high-rate data streams into a number of lower rate

data streams that are transmitted in parallel, OFDM resolvesthe problem of ISI in wide band communications [3]. But

OFDM has its disadvantages High peak-to-average powerratio (PAPR), high sensitivity to frequency offset, and a needfor an adaptive or coded scheme to overcome spectral nulls in

the channel [3],[4]. In this paper, we give an in-depthoverview of a single carrier FDMA (SC-FDMA) system,

which is a newly developed multiple access scheme adopted inthe uplink of 3GPP Long Term Evolution (LTE), and show

some research results on its PAPR characteristics and resource

scheduling. At the same time we have given a proposal fornon-binary SC-FDMA and have shown its effect on bit errorrate. The remainder of this paper is organized as follows.

Section II comprises of an over view of SC-FDMA. Section

III describes subcarrier mapping in SC-FDMA. Section IVgives an overview of non-binary SC-FDMA and subcarriersmapping using non-binary case include numerical analysis forthe PAPR using IFDMA and LFDMA mapping schemes.

Section V concludes with BER analysis along with itssimulated results.

II. OVERVIEW OF SC-FDMA

By comparing both OFDMA and SC-FDMA as shown infigure.1; both have quite similar characteristics. The SC-FDMA uses extra DFT block after baseband Modulation asshown by yellow rectangle. So, the SC-FDMA can be

considered as a modified version of OFDMA and can becalled as DFT spread OFDMA where time domain data

symbols are transformed to frequency domain by DFT beforegoing through OFDMA modulation [5]. The orthogonality ofthe users stems from the fact that each user occupies different

subcarriers in the frequency domain, similar to the case ofOFDMA. Because the overall transmit signal is a single

carrier signal PAPR is inherently low compared to the case ofOFDMA, which produces a multicarrier signal [6]. The

transmitter of an SC-FDMA system first groups the

modulation symbols into blocks each containing N symbols.Next, it performs an N-point DFT to produce a frequency

domain representation of the input symbols. It then maps eachof the N-DFT outputs to one of the (M > N) orthogonal

subcarriers that can be transmitted. If N = M/Q and allterminals transmitNsymbols per block, the system can handleQ simultaneous transmissions without co-channel interference.

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Q is the bandwidth expansion factor of the symbol sequence.

CP is a copy of the last part of the block, which is added at thestart of each block. The mathematical notation used in this

paper follows that reported in [6]. M represents the total

number of available subcarriers, whereM=Q.N, Q denotes thespreading factor and N represents the number of sub carriers

assigned to each user. We further assume that each user

occupies the same number of subcarriers, so in this case Qalso represents the number of users. Each userp,p = 0,..., Q -1, generates a block ofNcomplex-valued symbols, xn ,n =0,...,

N-1. By applying anN-point DFT to, the xn frequency domain

Fig.1 Block diagram of SC-FDMA

Symbols, xn can be described as

The frequency domain symbols are then mapped onto a set of

user-dependent subcarriers

Fig. 2 Time and frequency domain symbols of different subcarrier mapping

III.SUBCARRIER MAPPING

Once we get the symbols in frequency domain the nextstep is to allocate subcarrier to each symbol, such that each

user is provided with separate bandwidth avoiding inter-

symbol interference. And at the same time maximum numberof user can communicate. There are two methods to choose

the subcarriers for transmission distributedsubcarrier mappingand localizedsubcarrier mapping. In the distributed subcarrier

mapping mode, DFT outputs in the distributed subcarriermapping of the input data are allocated over the entire

bandwidth with zeros occupying the unused subcarriers,

whereas consecutive subcarriers are occupied by the DFToutputs, of the input data in the localized subcarrier mapping

mode. The case ofM = QN for the distributed mode withequidistance between occupied subcarriers is called

Interleaved FDMA (IFDMA) [6], [7]. Figure 2 shows thetime and frequency symbols for different subcarrier mapping

schemes. The signal for each subcarrier mapping forM= 12,N = 4, Q IFDMA = 3, and Q DFDMA = 2 without pulse

shaping.

IV. PROPOSED NON-BINARY SC-FDMA

Non Binary SC-FDMA is the proposed scheme, wherenon-Binary octal number system is used instead of

conventional binary system. The Fig. 3 shows the blockdiagram of non -binary SC-FDMA transmitter and receiver. Inthe first block, we encoded our baseband signal. Before going

to baseband modulation, we have to convert our basebandsignal into its non binary equivalent numbers using binary tonon binary converter; in our case we have used non binary

octal digits. As each octal digit corresponds to three binary

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digits as shown in Fig. 4, the equivalent octal digit is then

assigned to each group. The transmitter of non binary SC-FDMA system first groups the modulation symbols into

blocks each containing N symbols. Next, it performs an N-

point DFT to produce a frequency domain representation ofthe input symbols. It then maps each of the N-DFT outputs to

one of the (M > N) orthogonal subcarriers that can betransmitted. If N = M/Q and all terminals transmit N symbols

per block, the system can handle Q simultaneoustransmissions without co-channel interference. As in SC-

FDMA an M-point IDFT transforms the subcarrier amplitudes

to a complex time domain signal is then modulated theremaining portion is almost same to the binary case. The

receiver transforms the received signal into the frequencydomain via DFT, De-maps the subcarriers, and then performsfrequency domain equalization. At the receiver side aftertaking the N-point IDFT, the non binary signal is

demodulated, and by the use of non binary to binary converterit is converted back to is binary form. The decoder then

decodes the signal in binary.

A. Subcarrier Mapping in Non-Binary SC-FDMAThe Fig. 5 is almost similar to Fig. 2. The input binary is first

converted to its equivalent non-binary and is then grouped intoblock of N size. Here our block size becomes N = 4 which isequivalent to N = 12 in binary case. The results show that,

using non binary (octal) SCFDMA, our block size (N) isreduced by three times. In the similar manner the bandwidth

expansion factor Q, which determines the number of users in agiven instant can be increased and hence increase the user

availability as Q = M/N. Therefore, more users cancommunicate at the same time without any inter symbolinterference. The subcarrier mapping follows the same

techniques used for binary SC-FDMA. Only change is thereduction of block size N. The different schemes for subcarrier

mapping are shown in Fig. 5 which is similar to that of abinary case.

Fig.3. Block Diagram of Non binary SC-FDMA

Fig.4 Binary to Non Binary Conversion

Fig.5.Time Symbols of Different Subcarrier Mapping

B. PAPR of Non-Binary SC-FDMA signalsCurrently, a lot researches have been done in reducing the

PAPR, especially in uplink side of LTE, the most prominentresults been shown by Binary SC-FDMA. But, still there is a

need for research in the area of coding theory and channelmodeling to design codesfor channels, that are power limitedand or bandwidth limited. One of the major steps in allocating

maximum users to the available bandwidth is done byintroducing Non Binary SCFDMA

C. Numerical AnalysisIn this section, we analyze the PAPR of the SC-FDMA

signal for each subcarrier-mapping scheme. For distributed

subcarrier mapping mode, we will consider the case ofIFDMA. In the subsequent derivations, we assume that M =

Q*N, Also Q = M/N, Where, N shows number of symbols perblock allocated per user. M is the total number of subcarriers

and Q shows the bandwidth expansion factor which is alsoknown as the number of users.

In our simulation we take M = 384 And N = 12. Hence,

in binary case the number of users are Q = 32, While in non-binary (octal) case the N block length reduces by three timesso N = 4, and Q = 96 for non-binary (octal) case.

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Let {xn be the time

domain data symbols to be modulated. Then, TheXkfrequencydomain symbols after DFT will be {xk: k= 0,1,2,..N/3 -1}

the frequency domain symbols after subcarrier mapping willbe { Xl

: l = 0,1,2.M - 1} and {Xm : m = 0,1,2,.M -

1} are time symbols after IDFT. The complex pass bandtransmit signal of SC-FDMA x(t) for a block of data isrepresented by

where wc is carrier frequency and r(t) is the baseband pulse.

1) Time domain symbols of IFDMA:For IFDMA, the frequency samples after subcarrier mapping

{Xl} can be described as follows

The time symbol { } can be obtained by taking the

IDFT of . Let m = .q+n, where ,and , then

=

An example of IFDMA has shown in fig.7.

2) Time domain symbols of LFDMA:

For LFDMA, the frequency samples after subcarrier mapping{Xl} can be described as follows

Let m = Q*n+q Where, and ,

If q =0;

An example of LFDMA has shown in Fig. 7.

D. BER Simulation and results for Non-Binary SC-FDMAIn this portion we present the effects on average bit error

rate of different channels by using our proposed non binarySC-FDMA. For our analysis we have taken different channels

and have simulated their bit error rate performance accordingto the respective SNR values. We have also shown our results

for different subcarrier mapping schemes emphasising onIFDMA and LFDMA. For simplicity we have analysed each

channel as separate entity and have then simulated

accordingly.

1) BER analysis for Ideal Channel:Probability of a bit error for particular values of SNR for idealchannel is shown in Fig. 6. In our research we have shown

binary and non-binary (octal) for both interleaved andlocalized subcarrier mapping schemes. The simulation result

of binary case is only shown for localized subcarrier mapping.

For ideal channel, localized and interleaved subcarriermapping has the same BER. Form Fig. 6, it is clear that for

SNR values below 7 dB, the probability of bit error is less inthe case of non binary SC-FDMA.

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0 5 10 1510

-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

B

ER

I ideal channel (Non binary)

L ideal channel (Non binary)

L ideal channel (binary)

Fig.6, BER comparison between binary and Non binary for localized and

interleaved subcarrier mapping using Ideal channel for, M = 384.,N = 12,

using BPSK modulation for binary case and 8-QAM for Non Binary case

2) BER Analysis for PedA Channels:

A PedA channel is a tap-delay line multi-path channel

according to the 3GPP specification. For this type of channel,we have shown BER versus SNR curve in Fig. 7. The non-

binary SC-FDMA shows better BER results for localized

subcarrier mapping for lower values of SNR. In non-binarycase, probability of bit error is less than the probability of bit

error in binary case of SC-FDMA for particular lower value ofSNR.

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BER

I pedA channel (Nonbinary)

L pedA channel (Nonbinary)I pedA channel (binary)

L pedA channel (binary)

Fig. 7 BER comparison between binary and Non binary for localized and

interleaved subcarrier mapping using PedA channel for, M = 384, N = 12,

using BPSK modulation for binary case and 8-QAM for Non Binary case

3) BER Analysis for VehA channels:

Fig 8 shows a similar comparison in VehA channel. For this

type of channel both the interleaved and localized subcarriermapping schemes shows better results in non-binary SC-

FDMA for any SNR value.

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

10

0

SNR (dB)

BER

L vehA channel (binary)

I vehA channel (binary)

I vehA channel (nonbinary)

L vehA channel (nonbinary)

Fig. 8 BER comparison between binary and Non binary for localized and

interleaved subcarrier mapping using VehA channel For M = 384, N = 12,using BPSK modulation for binary case and 8-QAM for Non Binary case

4) Analytic power calculation for Non-binary SC-FDMA:

In this portion we have analytically determined the peak

power and average power of IDFT signals without using pulse

shaping filter. For our simulation we have taken block sizeN=12, which then reduces to N=4 for non-Binary SC-FDMA

and M- point DFT size = 384, hence the rolling factor Q=32.

The data has been simulated for 10^5 numbers of runs.

We have obtained results for BPSK and 8-QAM modulation

schemes for both binary and non binary cases, which is shownin table 1

TABLE 1

PEAK AND AVERAGE POWER VALUES OF SC-FDMA SIGNAL

Peak Power(watt)

AveragePower (watt)

Modulationscheme used

Non-

Binary

0.0011 6.5047*10- 4 8 - QAM

Binary 0.0010 0.0010 BPSK

Binary 0.0098 0.0098 8 - QAM

The peak power of the SC-FDMA signal is almost thesame for Binary and Non-binary case but the average power is

different. The average power of non-binary SC-FDMA signalis less than that of Binary case SC-FDMA signal.

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E. Effect of Non-Binary SC-FDMA on total number ofusers at a time:

The maximum number of users in a cell that can access the

network at a time equals Q = M / N; where M is the totalnumber of subcarriers and N is the number of subcarriers

allocated for each user in other words input block size. Inour research here we are using M=512 and N=128. For Non-

Binary case M remains the same and N reduces for differentM-ary systems. As (M-ary)i = 2i

, where (i=1,2,3,4,5,6,7) N

block size becomes N/=N/i, so Q=M / N

/, As N

/reduces Q

increases which shows that the total number of usersincreases. In our research we are taking i=1, 2,, 7; the

result is shown in fig 9.

2 4 8 16 32 64 1280

5

10

15

20

25

30

M-ary

N

um

berofusers

Fig.9 Effect of Non-binary SC-FDMA on number of users

V. CONCLUSIONS

In this paper, we have given a proposal of non-binary SC-FDMA for 3GPP LTE uplink. Our simulation results have

shown that introducing non-binary SCFDMA into the LTEuplink performs better than binary SC-FDMA in certain cases.Such as the number of users increases by three times using

Non-Binary (octal) SC-FDMA, By considering different

channels simulation results shows that BER is decreased inmost of the cases as compared to binary SC-FDMA, for both

LFDMA and IFDMA subcarrier mapping schemes and themost prominent results are obtained in the case of VehAchannel. Moreover, the average power of SC-FDMA signals

reduced in case of non-binary SCFDMA.Our future work is based on finding Non-binary

algorithms for MIMO SC-FDMA. And the effect of Non-binary SC-FDMA on throughput and latency

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