sc_fdma

Ahsanullah University of Science & Technology Department of Computer Science & Engineering

Course No: CSE 4100

Course Title: Project & Thesis - I

Topic: Single Carrier FDMA

Submitted By:

1. Md. Aminul Islam 11.02.04.089

2. Md. Rashedul Islam 11.02.04.090

3. Maruf Nayeem Siddiqui 11.02.04.067

4. Md. Abu Saleh 10.02.04.076

Necessity of Modulation in Electronic Communication

Any communications medium: e.g. free space - radio waves, Air - Sound waves

or radio waves, Optical Fiber - Light, Copper Wires Electrical Energy (with

frequency limits of the copper wire construction) is made for a certain type of

signal. But if the signal we want to send is not compatible with the medium, then

it does not travel well.

Modulation changes the information we want to send from its original form, into

one that is more compatible with the medium we are trying to use.

Modulation Scheme

Modulation is the "message" or the "intelligence" that is impressed on a radio

frequency (RF) carrier. When we transmit a signal, we generate a carrier

frequency, and then we modulate it. We "add" the message or the information we

wish to transmit by modulating the carrier in some way. There are at least a

dozen different modulation schemes ranging from simple to real head scratchers.

They either modify the amplitude, the frequency or the phase of the carrier. Here

we will discuss about Single Carrier FDMA.

OFDMA & SC-FDMA

Single-carrier FDMA (SC-FDMA) is a frequency-division multiple

access scheme. Like other multiple access schemes (TDMA, FDMA, CDMA,

OFDMA), it deals with the assignment of multiple users to a shared

communication resource. SC-FDMA can be interpreted as a linearly

precoded OFDMA scheme, in the sense that it has an additional DFT processing

step preceding the conventional OFDMA processing.

In order to transition from today's 3rd generation (3G) communications systems

to meet the needs of 4th generation (4G) systems, the 3rd Generation Partnership

Project (3GPP) has released the Long Term Evolution (LTE) specification. Among

the numerous differences between these generations are changes in the physical

layer (PHY), specifically in the modulation and multiple access schemes. While

its parent generation relied on variations of Code Division Multiple Access

(CDMA), LTE implements Orthogonal Frequency Division Multiplexing (OFDM)

for its downlink and Single-Carrier Frequency Division Multiple Access (SC-

FDMA) for its uplink. The purpose of this project is to investigate the reasoning

for this discord between uplink and downlink modulation schemes; specifically,

why Orthogonal Frequency Division Multiple-Access (OFDMA) was not used as

the uplink.

The bases used for comparison between OFDMA & SC- FDMA will be capacity,

outrage probability and peak-to-average power ratio (PAPR). While the first two

bases have always been traditionally used in analyses, PAPR is especially

important for the uplink of mobile devices. Amplifiers used in in circuits today

have a linear region in which they must operate so as not to introduce signal

distortion, and it is ideal to run with maximum amplification. However, if there

is a high PAPR, the device is forced to run with lower amplification so the peak

power does not lie in the non-linear gain region. The farther these amplifiers are

operated from the peak, the less power efficient the device become, leading to

increased power consumption and while this might not be very important for the

base station, it will reduce drain batteries on mobile device more quickly.

Therefore it is important to keep a low PAPR on the uplink.

The distinguishing feature of SC-FDMA is that it leads to a single-carrier

transmit signal, in contrast to OFDMA which is a multi-carrier transmission

scheme.

Transmitter and Receiver Structure of LP-OFDMA/SC-FDMA

The transmission processing of SC-FDMA is very similar to that of OFDMA. For

each user, the sequence of bits transmitted is mapped to a complex constellation

of symbols (BPSK, QPSK or M-QAM). Then different transmitters (users) are

assigned different Fourier coefficients. This assignment is carried out in the

mapping and demapping blocks. The receiver side includes one demapping

block, one IDFT block, and one detection block for each user signal to be

received. Just like in OFDM, guard intervals (called cyclic prefixes) with cyclic

repetition are introduced between blocks of symbols in view to efficiently

eliminate inter-symbol interference from time spreading (caused by multi-path

propagation) among the blocks.

In SC-FDMA, multiple access among users is made possible by assigning

different users different sets of non-overlapping Fourier-coefficients (sub-

carriers). This is achieved at the transmitter by inserting (prior to IFFT) silent

Fourier-coefficients (at positions assigned to other users), and removing them on

the receiver side after the FFT.

Subcarrier mapping can be classified into two types: localized mapping and

distributed mapping.

Fig: Localized Mapping and Distributed Mapping

In localized mapping, the DFT outputs are mapped to a subset of consecutive

subcarriers, thereby confining them to only a fraction of the system bandwidth.

In distributed mapping, the DFT outputs of the input data are assigned to

subcarriers over the entire bandwidth non-continuously, resulting in zero

amplitude for the remaining subcarriers. A special case of distributed SC-FDMA

is called interleaved SC-FDMA where the occupied subcarriers are equally

spaced over the entire bandwidth.

Fig: SC-FDMA

A matlab program for OFDMA and SCFDMA is given below:

%///////////SC-FDMA///////

% No. of Subcarriers

NS = 512;

% Input Generation

x = rand(1,NS)>0.5;

fftlength = 512;

nd = 6;

BW = 5e6;

FS = 2*BW; % Sampling Frequency

% Conversion of data from serial to parallel

par2 = series2parallel(x,NS);

% M ary Modulation of PSK and QAM

M = 2;

X = 0;

for count1 = 2:1:7;

if (M==2||M==4||M==16||M==64)

M = M+X

% M-ary modulation for producing y.

if(M

y=modulate(modem.qammod(M),par2);

end

%Apply FFT operation

out_fft = fft(y,fftlength);

%Applying Mapping

q_out = scfdma_mapping(out_fft,fftlength);

% Apply IFFT operation

out_ifft = ifft(q_out);

% Cyclic Prefix Addition

cp(count1,:) = cyclicpad(out_ifft,64);

cplength = length(cp);

% Conversion of data from parallel to serial

out = reshape(cp(count1,:),1,cplength);

% Signal transmits through an AWGN channel.

ynoisy = awgn(out,100,'measured');

% Rayleigh Fading

c = rayleighchan(1/1000,100,[0 2e-5],[0 -9]);

rf = filter(c,ynoisy);

% Conversion of data from serial to parallel

p = series2parallel(rf,cplength);

re_par = real(p);

% Remove cyclic prefix

rcp(count1,:) = decyclicpad(p,64);

len_rcp = length(rcp);

% Applying FFT operation

cpfft = fft(rcp(count1,:),fftlength);

%Applying Demapping

qq_out = scfdma_demapping(cpfft,fftlength);

%Applying IFFT operation

out_fft = ifft(qq_out);

if (M

switch M

end

end

end

M= 2^count1;

end

figure()

% Plot SNR and BER

semilogy(Eb_No,ber(2,:),'*-

r',Eb_No,ber(3,:),'k',Eb_No,ber1(5,:),'b',Eb_No,ber1(7,:),'g');

axis([0 25 0.0001 1]);

xlabel('SNR [dB]')

ylabel('BER')

legend('BPSK','QPSK','16-QAM','64-QAM')

title('SC-FDMA')

figure()

% Plot Error Probability

semilogy(Eb_No,Pe(2,:),'-k',Eb_No,Pe(3,:),'-r',Eb_No,Pe(5,:),'-

b',Eb_No,Pe(7,:),'-c');

axis([0 50 0.0001 1]);

xlabel('SNR [dB]')

ylabel('Probability of Error')

legend('BPSK','QPSK','16-QAM','64-QAM')

title('SC-FDMA')

h = spectrum.periodogram;

figure()

HS = psd(h,out_ifft,'SpectrumType','twosided','NFFT',NS,'FS',FS);

plot(HS)

xlabel('Sampling Frequency (2BW) in MHz')

ylabel('Power Spectral Density [dBm/Hz]')

title('SC-FDMA')

grid off;

Serial to Parallel:

function y = series2parallel(x,NS)

L=length(x);

q=floor(L/NS);

newvec=zeros(NS,q);

for i=1:q

newvec(1:NS,i)=x((1+(i-1)*NS):i*NS);

end

y=newvec;

Cyclic Prefix:

function y=cyclicpad(X,L)

N=length(X(:,1));

N-L+1

Y=[X(N-L+1:N,:);X];

y=Y;

Remove Cyclic Prefix:

function y=decyclicpad(X,L)

N=length(X(:,1));

Y=X(L+1:N,:);

y=Y;

Mapping:

function [iout,qout]=crmapping(idata,qdata,fftlength,nd);

iout=zeros(fftlength,nd);

qout=zeros(fftlength,nd);

iout(2:27,:)=idata(1:26,:);

qout(2:27,:)=qdata(1:26,:);

iout(39:64,:)=idata(27:52,:);

qout(39:64,:)=qdata(27:52,:);

Demapping:

function [iout,qout]=crdemapping(idata,qdata,fftlength,nd);

iout(1:26,:)=idata(2:27,:);

qout(1:26,:)=qdata(2:27,:);

iout(27:52,:)=idata(39:64,:);

qout(27:52,:)=qdata(39:64,:);

PAPR:

BPSK:

function paprSCFDMA()

dataType = 'B-PSK'; % Modulation format.

NS = 512; % Number of total subcarriers.

Symbols = 16; % Data block size.

Q = NS/Symbols; % Bandwidth spreading factor of SC-FDMA.

BW = 5e6; % System bandwidth.

Ts = 1/BW; % sampling rate.

osf = 4; % Oversampling factor.

Nsub = NS;

Fsub = [0:Nsub-1]*BW/Nsub; % Subcarrier spacing of OFDMA.

Runs = 1e3; % Number of iterations.

papr1 = zeros(1,Runs); % Initialize the PAPR results for sc-fdma.

papr3 = zeros(1,Runs); % Initialize the PAPR results for OFDMA

for n = 1:Runs,

% Generate random data.

if dataType == 'B-PSK'

tmp = round(rand(Symbols,2));

tmp = tmp*2 - 1;

data = (tmp(:,1) + j*tmp(:,2))/sqrt(2);

elseif dataType == '16QAM'

dataSet = [-3+3i -1+3i 1+3i 3+3i ...

-3+i -1+i 1+i 3+i ...

-3-i -1-i 1-i 3-i ...

-3-3i -1-3i 1-3i 3-3i];

dataSet = dataSet / sqrt(mean(abs(dataSet).^2));

tmp = ceil(rand(Symbols,1)*16);

for k = 1:Symbols,

if tmp(k) == 0

tmp(k) = 1;

end

data(k) = dataSet(tmp(k));

end

data = data.';

end

% Convert data to frequency domain.

Z1 = fft(data);

Z2 = fft(data);

% Initialize the subcarriers.

Y1 = zeros(NS,1);

Y2 = zeros(NS,1);

% Subcarrier mapping for SC-FDMA

Y1(1:Q:NS) = Z1;

Y2(1:Symbols) = Z2;

% Convert data back to time domain.

y1 = ifft(Y1);

y2 = ifft(Y2);

% OFDMA modulation.

% Time range of the OFDMA symbol.

t = [0:Ts/osf:Nsub*Ts];

y3 = 0;

for k = 1:Symbols,

y3= y3 + data(k)*exp(j*2*pi*Fsub(k)*t);

end

% Calculate PAPR.

papr3(n) = 10*log10(max(abs(y3).^2) / mean(abs(y3).^2));



end

% Plot CCDF.

figure ()

[N,Z3] = hist(papr3, 100);

[N,Z1] = hist(papr1, 100);

[N,Z2] = hist(papr2, 100);

semilogy(Z1,1-cumsum(N)/max(cumsum(N)),'b')

hold on

semilogy(Z3,1-cumsum(N)/max(cumsum(N)),'black')

hold off

title ('PAPR of SC-FDMA and OFDMA for BPSK')

xlabel ('PAPR[dB]')

ylabel ('{PAPR(PAPR>PAPR0)}')

grid off;

% Save data.

save paprSCFDMA

QPSK:

if dataType == 'QPSK'

tmp = round(rand(Symbols,4));

tmp = tmp*2 - 1;

data = (tmp(:,1) + j*tmp(:,2))/sqrt(2);

16-QAM:


dataSet = [-3+3i -1+3i 1+3i 3+3i ...

-3+i -1+i 1+i 3+i ...

-3-i -1-i 1-i 3-i ...

-3-3i -1-3i 1-3i 3-3i];

64-QAM:


dataSet = [-5+5i -1+5i 1+5i 5+5i ...

-5+i -1+i 1+i 5+i ...

-5-i -1-i 1-i 5-i ...

-5-5i -1-5i 1-5i 5-5i];

Reference Link:

1. https://www.youtube.com/watch?v=dr4YQAfifKA

2. http://www.answers.com/Q/What_is_modulation_and_why_is_it_needed

3. http://web.stanford.edu/~nsoltani/ee359project/project.pdf

4. http://www.mathworks.com/matlabcentral/fileexchange/41814-ofdma---sc-fdma-performance-

analysis/content/ofdma.m

5. http://en.wikipedia.org/wiki/Single-carrier_FDMA

sc_fdma

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