Physical Layer Simulation of a Simplified LTE-OFDM System · Simulation Method: An OFDM block of 7...

THE UNIVERSITY OF TEXAS AT DALLAS

DEPARTMENT OF ELECTRICAL ENGINEERING

EESC 6390 – Introduction to Wireless Communication

Spring 2015

Final Project

Physical Layer Simulation of a Simplified

LTE-OFDM System

Submitted By:

Name Contribution

Krishna Prasad Sreenivassa Rao

[email protected]

50 %

Manjunath Swamy

[email protected]

50 %

mailto:[email protected]

mailto:[email protected]

1. Introduction:

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple sub-carriers. Sub carrier frequencies are chosen so that they are orthogonal to each other

to eliminate cross talk. Long Term Evolution (LTE) uses 12 sub-carriers with each subcarrier

separated from each other by a bandwidth of 15 kHz. LTE standard defines several parameters

like channel bandwidth, FFT size etc. all of which have been mentioned in the subsequent

sections.

The signals are modulated using QPSK, 16 or 64-QAM. Data is assembled in the frequency

domain, modulated and then converted to time domain using inverse fast Fourier transform at the

transmitter and a fast Fourier transform at the receiver to retrieve the original coefficients. Cyclic

prefixes are added to the signal and then transmitted. At the receiver the extra bits are removed,

Fourier transformed and demodulated to retrieve the sent data. The basic block diagram of

OFDM transmitter and receiver is shown below:

Fig

Figure: Block diagram of OFDM transmitter

Figure: Block diagram of OFDM receiver

2. Specifications:

a. Group Number : 2

b. Channel bandwidth: 3 MHz (According to UTD IDs)

c. Modulation Types: QPSK, 16-QAM

d. FFT size (Nfft): 308

e. CP length (Ncp): 18

f. No. of used sub-carriers (Nused): 12 (per resource block for 15 resource blocks)

g. No. of data subcarriers per symbol (Ndata): 180

h. No. of null subcarriers (Nleft, Ndc, and Nright): 128

i. Channel Impulse response model: Channel B (indoor & outdoor)

3. Simulation Method:

An OFDM block of 7 symbols is constructed, with each symbol comprising of 308 bits.

Out of the 308 bits, 180 bits carry the data to be transmitted, while the remaining are null

sub-carriers. No pilot bits, in particular, are used for this simulation. If required, pilot bits

can be accommodated as a part of data bits (Ndata).

According to LTE standard, for 3 MHz channel bandwidth, each sub-carrier occupies 15

kHz and 12 such sub-carriers are required for the transmission of each OFDM symbol,

thus occupying 180 kHz. At a time instant, 15 resource blocks are transmitted, thereby

sending 15 OFDM symbols, thus occupying 2.7 MHz (180 kHz * 15). The remaining 0.3

MHz (10 % of the channel bandwidth) is occupied by guard bands.

Figure: The Basic LTE Downlink Physical Resource seen as a time-frequency grid

OFDM symbols are sent across AWGN and Rayleigh Channels. For Rayleigh channels,

two models have been specified (Channel A and Channel B) for indoor and outdoor

environments. For our group number (2), we have taken values for Channel B. The

impulse response of the channel is known to the receiver, thus facilitating easy decoding

of transmitted signals. In both AWGN and Rayleigh channel cases, the noise is added to

the signal according to the given SNR values and the variation of Bit Error Rate (BER) is

observed with SNR.

Again using the channel impulse response models and a given target Bit Error rate, target

SNRs for the given constellation sizes are determined. LTE specifies only limited

constellation sizes, namely 4, 16 and 64. Since the SNR of the received signal changes

due to channel impulse response (for indoor and outdoor), the target SNR is compared

with the received SNR, following which, the allowable constellation size (for LTE

standard)is determined which in turn is used to find the number of bits to be transmitted

(Spectral Efficiency) corresponding to each target SNR, which is then plotted.

All plots are generated over several Monte-Carlo iterations.

4. Simulations:

i. AWGN Channel, QPSK Modulation

%Program to compute BER vs SNR for LTE-OFDM (QPSK modulation) in an AWGN

%Channel

clc;

clear all;

close all;

%LTE Specifications

N = 308; %FFT Size

Nfft = 308;

Ndata = 180; %% Data points

Ncp = 18; %% Cylic Prefix

NLeft = 63; %%

NRight = 64; %%

SNR = 3:2:11; %% Given SNR Range

monte_carlo_limit = 50;

T = 7;

for s = 1:length(SNR) % SNR loop

for monte_carlo_index = 1:monte_carlo_limit %Monte carlo loop

nooferrors = 0;

for i=1:1:15

raw_data = randi([0 1],1,2*1260);%% Data bits generated

raw_data_combine(1,i*2*1260-2*1260+1:i*2*1260) = raw_data; %Storing data-bits for 15

resource blocks

reshaped = reshape(raw_data,2,1260)'; %%reshaping data-bits for modulation

bin_to_gray = (bin2gray(bi2de(reshaped,'left-msb'),'psk',4))';%% Binary to gray

mapping

modulated = pskmod(bin_to_gray,4,0,'gray');%% QPSK Modulation

ofdm_symbol_data = reshape(modulated,180,T)';%% Isolating data bits for each symbols

for t = 1:T

ofdm_sequence(t,:) = [0 ofdm_symbol_data(t,91:180) zeros(1,NLeft+NRight)

ofdm_symbol_data(t,1:90)]; %Constructing transmission sequence

ofdm_ifft(t,:) = sqrt(N)*ifft(ofdm_sequence(t,:));%% Time domain conversion, for

transmission

tx(t,:) = [ofdm_ifft(t,308-Ncp+1:308) ofdm_ifft(t,:)];%% Adding CPs

end

tx_combine(t+(i-1)*7-6:t+(i-1)*7,:)=tx; % Storing modulated data-bits (time domain)

for 15-resource blocks

end

rx_combine = awgn(tx_combine,SNR(s),'measured'); % Signal received at the receiver (after

travelling through AWGN channel)

for t=1:1:105

rx_ofdm_symbol(t,:) = rx_combine(t,Ncp+1:326); %Removing Cyclic Prefix

rx_sequence(t,:) = fft(rx_ofdm_symbol(t,:))/sqrt(N); % Time-to-Frequency domain

conversion

rx_raw_data(t,:) = [rx_sequence(t,219:308) rx_sequence(t,2:91)]; %Extracting data

bits

end

rx_symbol_data= reshape(rx_raw_data',1,180*105);%% Isolating data bits corresponding to

15 resource blocks (containing 180 data bits per symbol)

demodulated = pskdemod(rx_symbol_data,4,0,'gray');%% QPSK Demodulation

gray_to_binary = (de2bi(gray2bin(demodulated,'psk',4),'left-msb'))';%% Binary Conversion

from Gray

final_data = reshape(gray_to_binary,1,180*2*105); % reshaping after demodulation

nooferrors = nooferrors + sum(xor(final_data,raw_data_combine));%% Comparison of received

& transmitted data for bit errors

BER(monte_carlo_index) = nooferrors/(180*2*105);%% Bit errors averaged over monte-carlo

iterations

end

BER_avg(s)=mean(BER);%% Mean bit error for every SNR

end

% Plotting BER vs SNR

figure

semilogy(SNR,BER_avg);

title('LTE-OFDM QPSK Modulation for AWGN');

ylabel('BIT ERROR RATE');

xlabel('SNR (dB)');

Published with MATLAB® R2014a

ii. AWGN Channel, 16-QAM Modulation

%Program to compute BER vs SNR for LTE-OFDM (16-QAM modulation) in an AWGN

%Channel

clc;

clear all;

close all;

%LTE Specifications

N = 308; %FFT Size

http://www.mathworks.com/products/matlab

Nfft = N;



NLeft = 63; %%

NRight = 64; %%



T = 7;


for monte_carlo_index=1:monte_carlo_limit %Monte carlo loop

nooferrors = 0;

for i=1:1:15


raw_data_combine(1,i*4*1260-4*1260+1:i*4*1260)=raw_data; %Storing data-bits for 15

resource blocks

reshaped = reshape(raw_data,4,1260)';%%reshaping data-bits for modulation

bin_to_gray = (bin2gray(bi2de(reshaped,'left-msb'),'psk',16))';%%Binary to gray

mapping

modulated = qammod(bin_to_gray,16,0,'gray');%% 16 QAM Modulation


for t = 1:T




transmission


end

tx_combine(t+(i-1)*7-6:t+(i-1)*7,:) = tx;% Storing modulated data-bits (time domain)


end

rx_combine=awgn(tx_combine,SNR(s),'measured');% Signal received at the receiver (after

travelling through AWGN channel)

for t=1:1:105


rx_sequence(t,:) = fft(rx_ofdm_symbol(t,:))/sqrt(N); % Time-to-Frequency domain

conversion


bits

end

rx_symbol_data= reshape(rx_raw_data',1,180*105); %% Isolating data bits corresponding to


demodulated = qamdemod(rx_symbol_data,16,0,'gray');%% 16-QAM Demodulation


from Gray

final_data = reshape(gray_to_binary,1,180*4*105); % reshaping after demodulation




iterations

end


end


figure


title('LTE-OFDM 16-QAM Modulation for AWGN Channel');


xlabel('SNR (dB)');


iii. Rayleigh Channel (Indoor – Channel B), QPSK Modulation

%Program to compute BER vs SNR for LTE-OFDM (QPSK modulation) in an

%Rayleigh Channel

clc;


clear all;

close all;

%LTE Specifications

N = 308; %%FFT Size

Nfft = N;



NLeft = 63; %%

NRight = 64; %%



% Indoor Channel Response (Channel B)

delay = [0 100 200 300 500 700]; %Array with tap delay times

powerDB = [0 -3.6 -7.2 -10.8 -18.0 -25.2]; %Array with power distribution

tap_no = ceil(max(delay)*(10^(-9))*3*10^6); %No. of taps (Max delay / Sampling time)

h_indoor = zeros(1,tap_no+1); %Initializing Rayleigh channel response matrix

L = length(delay);

powerRatio = 10.^(powerDB/10); %Power from DB to ratio form

temp = randn(1,L)+j*randn(1,L);

%Populating Rayleigh channel response matrix

for k=1:L

h_indoor(k)=sqrt(powerRatio(k)/2).*real(temp(k))+j*sqrt(powerRatio(k)/2).*imag(temp(k));

end

T = 7;


for monte_carlo_index=1:monte_carlo_limit % Monte-carlo loop

nooferrors = 0;

for i=1:1:15



resource blocks



mapping

modulated = pskmod(bin_to_gray,4,0,'gray');%%QPSK Modulation


for t = 1:T




transmission


end

tx_combine(t+(i-1)*7-6:t+(i-1)*7,:) = tx; % Storing modulated data-bits (time domain)


end

%Convolving transmitted signal with channel impulse response

for u=1:1:105

convDataVeh(u,:) = conv(tx_combine(u,:),h_indoor);

end

%Adding noise to the system (after passing through Rayleigh channel)

rx_combine=awgn(convDataVeh,SNR(s),'measured');

for t=1:1:105


hf = fft(h_indoor,308);% Time-to-Frequency domain conversion of impulse response

recf(t,:) = fft(rx_ofdm_symbol(t,:),308); %F-domain conversion of the received signal

rec(t,:) = ifft(recf(t,:)./hf); %Eliminating the effect of Rayleigh channel fading

rx_sequence(t,:) = fft(rec(t,:))/sqrt(N); % FFT of the received signal without

fading


bits

end





from Gray

final_data = reshape(gray_to_binary,1,180*2*105);% reshaping after demodulation




iterations

end


end


figure


title('LTE-OFDM QPSK Modulation - Indoor Rayleigh Channel');


xlabel('SNR (dB)');


iv. Rayleigh Channel (Outdoor – Channel B), QPSK Modulation

%Program to compute BER vs SNR for LTE-OFDM (QPSK modulation) in an

%Rayleigh Channel

clc;

clear all;

close all;

%LTE Specifications

N = 308; %%FFT Size

Nfft = N;



NLeft = 63; %%

NRight = 64; %%



% Outdoor Channel Response (Channel B)


delay = [0 5 30 45 75 90 105 140 210 230 250 270 275 475 595 690]; %Array with tap delay times

powerDB = [-1.5 -10.2 -16.6 -19.2 -20.9 -20.6 -16.6 -16.6 -23.9 -12 -23.9 -21 -17.7 -24.6 -22 -

29.2]; %Array with power distribution



L = length(delay);




for k=1:L


end

T = 7;



nooferrors = 0;

for i=1:1:15



resource blocks



mapping

modulated = pskmod(bin_to_gray,4,0,'gray');%%QPSK Modulation


for t = 1:T




transmission


end



end


for u=1:1:105


end



for t=1:1:105






fading


bits

end





from Gray





iterations

end


end


figure


title('LTE-OFDM QPSK Modulation - Outdoor Rayleigh Channel');


xlabel('SNR (dB)');


v. Rayleigh Channel (Indoor – Channel B), 16 QAM Modulation

%Program to compute BER vs SNR for LTE-OFDM (16QAM modulation) in an

%Rayleigh Channel

clc;

clear all;

close all;

%LTE Specifications

N = 308; %%FFT Size

Nfft = N;



NLeft = 63; %%

NRight = 64; %%









L = length(delay);




for k=1:L


end

T = 7;



nooferrors = 0;

for i=1:1:15



resource blocks



mapping

modulated = qammod(bin_to_gray,16,0,'gray');%%16QAM Modulation


for t = 1:T




transmission


end



end


for u=1:1:105


end



for t=1:1:105






fading


bits

end



demodulated = qamdemod(rx_symbol_data,16,0,'gray');%% 16QAM Demodulation


from Gray





iterations

end


end


figure


title('LTE-OFDM 16QAM Modulation - Indoor Rayleigh');


xlabel('SNR (dB)');


vi. Rayleigh Channel (Outdoor – Channel B), 16 QAM Modulation

%Program to compute BER vs SNR for LTE-OFDM (16QAM modulation) in an

%Rayleigh Channel

clc;

clear all;

close all;

%LTE Specifications

N = 308; %%FFT Size

Nfft = N;



NLeft = 63; %%

NRight = 64; %%




delay = [0 5 30 45 75 90 105 140 210 230 250 270 275 475 595 690]; %Array with tap delay times


powerDB = [-1.5 -10.2 -16.6 -19.2 -20.9 -20.6 -16.6 -16.6 -23.9 -12 -23.9 -21 -17.7 -24.6 -22 -

29.2]; %Array with power distribution


h_outdoor = zeros(1,tap_no+1); %Initializing Rayleigh channel response matrix

L = length(delay);




for k=1:L

h_outdoor(k)=sqrt(powerRatio(k)/2).*real(temp(k))+j*sqrt(powerRatio(k)/2).*imag(temp(k));

end

T = 7;



nooferrors = 0;

for i=1:1:15



resource blocks



mapping

modulated = qammod(bin_to_gray,16,0,'gray');%%16QAM Modulation


for t = 1:T




transmission


end



end


for u=1:1:105

convDataVeh(u,:) = conv(tx_combine(u,:),h_outdoor);

end



for t=1:1:105


hf = fft(h_outdoor,308);% Time-to-Frequency domain conversion of impulse response




fading


bits

end



demodulated = qamdemod(rx_symbol_data,16,0,'gray');%% 16QAM Demodulation


from Gray





iterations

end


end


figure


title('LTE-OFDM 16QAM Modulation - Outdoor Rayleigh');


xlabel('SNR (dB)');


vii. Adaptive Modulation

%Program to plot Spectral Efficiency vs SNR for Adaptive Modulation

clc;

clear all;

close all;

N =308; %No.of bits per OFDM symbol

bandwidth = 3*10^6;

SNR = 10:1:30; % SNR Range

targetBER = 10^(-3);

%Allowed Constellation sizes according to LTE Specifications

M=[4 16 64];

%Determining target SNR for each constellation size

for i=1:length(M)

targetSNR(i)=((M(i)-1)*log(5*targetBER))/(-1.5);

end



for montecarloindex = 1:1:monte_carlo_limit






L = length(delay);




for k=1:L


end

%Frequency domain translation of channel impulse response

H_indoor = fft(h_indoor,308);

%Constellation restriction according to received SNR

for s = 1:length(SNR)

rxSNR = abs(H_indoor.*SNR(s));

for i=1:length(rxSNR)

if rxSNR(i) < targetSNR(1)

constellation(i) = 1; %If received SNR is below Threshold SNR, no transmission is

done.

elseif ((rxSNR(i) > targetSNR(1)) && (rxSNR(i) < targetSNR(2)))

constellation(i) = 4;

elseif ((rxSNR(i) > targetSNR(2)) && (rxSNR(i) < targetSNR(3)))


else


end

end

%Bits = log2(M)

indoor_efficiency(s) = mean(log2(constellation));

end

%Storing spectral efficiencies for every iteration

temp1(montecarloindex,:) = indoor_efficiency;


delay = [0 5 30 45 75 90 105 140 210 230 250 270 275 475 595 690]; %Array with tap delay

times

powerDB = [-1.5 -10.2 -16.6 -19.2 -20.9 -20.6 -16.6 -16.6 -23.9 -12 -23.9 -21 -17.7 -

24.6 -22 -29.2]; %Array with power distribution


h_outdoor = zeros(1,tap_no+1); %Initializing Rayleigh channel response matrix

L = length(delay);




for k=1:L

h_outdoor(k)=sqrt(powerRatio(k)/2).*real(temp(k))+j*sqrt(powerRatio(k)/2).*imag(temp(k));

end

%Frequency domain translation of channel impulse response

H_outdoor = fft(h_outdoor,308);

%Constellation restriction according to received SNR

for s=1:length(SNR)

rxSNR = abs(H_outdoor.*SNR(s));

for i=1:length(rxSNR)

if rxSNR(i) < targetSNR(1)

constellation(i) = 1; %If received SNR is below Threshold SNR, no transmission is

done.

elseif ((rxSNR(i) > targetSNR(1))&&(rxSNR(i) < targetSNR(2)))


elseif ((rxSNR(i) > targetSNR(2))&&(rxSNR(i) < targetSNR(3)))


else


end

end

%Bits = log2(M)

outdoor_efficiency(s) = mean((log2(constellation)));

end

%Storing spectral efficiencies for every iteration

temp2(montecarloindex,:) = outdoor_efficiency;

end

%Calculating the mean spectral efficiency from every Monte Carlo iteration

for k=1:1:21

indoor(:,k) = mean(temp1(:,k));

outdoor(:,k) = mean(temp2(:,k));

end

plot(SNR, indoor,'r');

hold on;

plot(SNR, outdoor,'b');

grid on;

title('Adaptive Modulation');

xlabel('SNR (db)');

ylabel('Spectral efficiency in bits/Hz');

legend('Indoor','Outdoor');


5. Conclusion:

The generated information bits were successfully encoded with OFDM modulation according to

LTE standards and the Bit Error Rate vs SNR for every case – like AWGN and Rayleigh (for

indoor and outdoor) were plotted. Adaptive modulation was also simulated where the spectral

efficiency vs SNR was plotted.

6. References: 1. http://www.tsiwireless.com/docs/whitepapers/LTE%20in%20a%20Nutshell%20-

%20Protocol%20Architecture.pdf

2. http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-

evolution/lte-ofdm-ofdma-scfdma.php

3. http://www.tutorialspoint.com/lte/lte_ofdm_technology.htm

4. http://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

5. http://lteworld.org/presentation/long-term-evolution-lte-basics

6. http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-

evolution/3g-lte-basics.php


http://www.tsiwireless.com/docs/whitepapers/LTE%20in%20a%20Nutshell%20-%20Protocol%20Architecture.pdf

http://www.tsiwireless.com/docs/whitepapers/LTE%20in%20a%20Nutshell%20-%20Protocol%20Architecture.pdf

http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-evolution/lte-ofdm-ofdma-scfdma.php

http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-evolution/lte-ofdm-ofdma-scfdma.php

http://www.tutorialspoint.com/lte/lte_ofdm_technology.htm

http://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

http://lteworld.org/presentation/long-term-evolution-lte-basics

http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-evolution/3g-lte-basics.php

http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-evolution/3g-lte-basics.php

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