Advanced Telecommunications: OFDM System Design and Simulation

This document discusses the simulation of OFDM system design and performance in a flat Rayleigh fading channel. It includes MATLAB code for defining system parameters, simulating through an AWGN channel, and simulating in a frequency-selective Rayleigh fading channel. The BER vs Eb/N0 graph is also plotted to show the decrease in BER rate with increasing Eb/N0.

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Name of the Student
Name of the University
Author Note

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Part 2:
Now, the channel time delay factor and the delayed relative power factor of the channel is
obtained from the channel.mat file and the multipath impulse response of the channel is
calculated along with the RMS delay spread of the channel as given below by the following
MATLAB code.
MATLAB code:
load 'channel.mat'
rms_delay = std(tvec)*(length(tvec)- 1);
fprintf('The rms delay of the channel is %.4f secs',rms_delay)
channel.Seed = 1;
channel.NRxAnts = 2;
channel.DelayProfile = 'EVA';
channel.DopplerFreq = 300;
channel.CarrierFreq = 2e9;
channel.MIMOCorrelation = 'Low';
channel.SamplingRate = 1/10e-9;
channel.InitTime = 0;
nAntIn = 2;

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impulseSpacing = 300;
noImpResponse = 150;
nInputSamples = impulseSpacing * noImpResponse;
in = zeros(nInputSamples, nAntIn);
onesLocations = 1:impulseSpacing:nInputSamples;
in(onesLocations,1) = 1;
out = lteFadingChannel(channel, in);
for antNo = 1:channel.NRxAnts
figure
mesh(squeeze(abs(reshape(out(:,antNo), ...
impulseSpacing,noImpResponse).')))
titleStr = ['Rx Antenna' num2str(antNo)];
title({'Channel Impulse Response',titleStr})
ylabel('number of impulses')
xlabel('Impulse spacing [no of samples]')
zlabel('|H|')
end

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Output:
The rms delay of the channel is 4155.4783 secs
The Coherence bandwidth of the channel is 0.0010 Hz
The coherence bandwidth of a channel is measurement of frequency over which the channel
is ‘flat’. The coherence bandwidth Wc in rad/sec is approximately given by
Bc = 1/D.
Where, D = multipath delay spread.

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OFDM system design and Simulation through Additive White Gaussian Noise channel:
The system parameters of the OFDM channel is defined and simulated thorough awgn
channel with qam modulation.
MATLAB code:
M = 4; % Modulation alphabet
k = log2(M); % Bits/symbol
numSC = 128; % Number of OFDM subcarriers
cpLen = 32; % OFDM cyclic prefix length
maxBitErrors = 100; % Maximum number of bit errors
maxNumBits = 1e7; % Maximum number of bits transmitted

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qpskMod = comm.QPSKModulator('BitInput',true);
qpskDemod = comm.QPSKDemodulator('BitOutput',true);
ofdmMod = comm.OFDMModulator('FFTLength',numSC,'CyclicPrefixLength',cpLen);
ofdmDemod = comm.OFDMDemodulator('FFTLength',numSC,'CyclicPrefixLength',cpLen);
channel = comm.AWGNChannel('NoiseMethod','Variance', ...
'VarianceSource','Input port');
errorRate = comm.ErrorRate('ResetInputPort',true);
ofdmDims = info(ofdmMod)
numDC = ofdmDims.DataInputSize(1)
frameSize = [k*numDC 1];
EbNoVec = (0:10)';
snrVec = EbNoVec + 10*log10(k) + 10*log10(numDC/numSC);
berVec = zeros(length(EbNoVec),3);
errorStats = zeros(1,3);
for m = 1:length(EbNoVec)
snr = snrVec(m);

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while errorStats(2) <= maxBitErrors && errorStats(3) <= maxNumBits
dataIn = randi([0,1],frameSize); % Generate binary data
qpskTx = qpskMod(dataIn); % Apply QPSK modulation
txSig = ofdmMod(qpskTx); % Apply OFDM modulation
powerDB = 10*log10(var(txSig)); % Calculate Tx signal power
noiseVar = 10.^(0.1*(powerDB-snr)); % Calculate the noise variance
rxSig = channel(txSig,noiseVar); % Pass the signal through a noisy channel
qpskRx = ofdmDemod(rxSig); % Apply OFDM demodulation
dataOut = qpskDemod(qpskRx); % Apply QPSK demodulation
errorStats = errorRate(dataIn,dataOut,0); % Collect error statistics
end
berVec(m,:) = errorStats; % Save BER data
errorStats = errorRate(dataIn,dataOut,1); % Reset the error rate calculator
end
berTheory = berawgn(EbNoVec,'psk',M,'nondiff');
figure

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semilogy(EbNoVec,berVec(:,1),'*')
hold on
semilogy(EbNoVec,berTheory)
legend('Simulation','Theory','Location','Best')
xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')
grid on
hold off
Output:
ofdmDims =
struct with fields:
DataInputSize: [117 1]
OutputSize: [160 1]
numDC =
117

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0 1 2 3 4 5 6 7 8 9 10
Eb/No (dB)
10-6
10-5
10-4
10-3
10-2
10-1
Bit Error Rate
Simulation
Theory
It is evident that for the channel as the Eb/No (in db) i.e. the signal to noise ratio per bit is
increased over time the bit error rate of the channel after filtering through awgn channel
decreases or the quantities are inversely proportional.
Part 3:
Now, the performance of OFDM system is simulated in a flat Rayleigh fading channel with
data of impulse response of pvec and tvec vector. The first 4 data points of pvec and tvec are
chosen for 4 tapping channel simulation.
MATLAB code:
clc;
clear all;
close all;

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load 'channel.mat'
N = 128; % No of subcarriers
Ncp = 16; % Cyclic prefix length
Ts = 1e-3; % Sampling period of channel
Fd = 0; % Max Doppler frequency shift
Np = 4; % No of pilot symbols
M = 2; % No of symbols for PSK modulation
Nframes = 10^3; % No of OFDM frames
D = round((M-1)*rand((N-2*Np),Nframes));
const = pskmod([0:M-1],M);
Dmod = pskmod(D,M);
Data = [zeros(Np,Nframes); Dmod ; zeros(Np,Nframes)]; % Pilot Insertion
%% OFDM symbol
IFFT_Data = (128/sqrt(120))*ifft(Data,N);
TxCy = [IFFT_Data((128-Ncp+1):128,:); IFFT_Data]; % Cyclic prefix
[r c] = size(TxCy);
Tx_Data = TxCy;
%% Frequency selective channel with 4 taps
tau = [tvec(1) tvec(2) tvec(3) tvec(4)].*1e-9; % Path delays
pdb = [pvec(1) pvec(2) pvec(3) pvec(4)]; % Avg path power gains

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h = rayleighchan(Ts, Fd, tau, pdb);
h.StoreHistory = 0;
h.StorePathGains = 1;
h.ResetBeforeFiltering = 1;
%% SNR of channel
EbNo = 0:5:30;
EsNo= EbNo + 10*log10(120/128)+ 10*log10(128/144); % symbol to noise ratio
snr= EsNo - 10*log10(128/144);
%% Transmit through channel
berofdm = zeros(1,length(snr));
Rx_Data = zeros((N-2*Np),Nframes);
for i = 1:length(snr)
for j = 1:c % Transmit frame by frame
hx = filter(h,Tx_Data(:,j).'); % Pass through Rayleigh channel
a = h.PathGains;
AM = h.channelFilter.alphaMatrix;
g = a*AM; % Channel coefficients
G(j,:) = fft(g,N); % DFT of channel coefficients
y = awgn(hx,snr(i)); % Add AWGN noise
%% Receiver

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Rx = y(Ncp+1:r); % Removal of cyclic prefix
FFT_Data = (sqrt(120)/128)*fft(Rx,N)./G(j,:); % Frequency Domain Equalization
Rx_Data(:,j) = pskdemod(FFT_Data(5:124),M); % Removal of pilot and
Demodulation
end
berofdm(i) = sum(sum(Rx_Data~=D))/((N-2*Np)*Nframes);
end
%% Plot the BER
figure;
semilogy(EbNo,berofdm,'ro-','linewidth',2);
grid on;
title('OFDM BER vs SNR in Frequency selective Rayleigh fading channel');
xlabel('EbNo');
ylabel('BER');
Plot:

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0 5 10 15 20 25 30
EbNo
10-4
10-3
10-2
10-1
BER
OFDM BER vs SNR in Frequency selective Rayleigh fading channel
It can be seen from the above BER vs Eb/N0 graph that with the increase of Eb/N0 in the
range 0 to 30 dB the BER rate is decreasing, however the negative slope less than the
previous case of simulation through AWGN channel. Also, the decrement can be considered
almost linear.