lab report based on ofdm

1. Lab10 OFDM 1
Lab no 10
Implementation of Orthogonal Frequency Division Multiplexing (OFDM)
in GNU radio and MATLAB
Objectives
a) Implementation of OFDM transceiver in GNU Radio
b) Implementation of OFDM transceiver in MATLAB
c) Simulation of OFDM System (IEEE 802.11) under AWGN channel
OFDM, also called Discrete Multi-Tone (DMT), is a technique for mitigating the effects of poor channels.
Multipath effects, interference, and impulsive noise, for example, characterize mobile communication
channels. These effectscanprevent high-speed communication (severalmegabits per second).In normal FDM
systems, adjacent channels are typically separated by guard spaces - unused frequencies intended to prevent
the channels from interfering with each other. This, obviously, is inefficient in terms of spectral utility.
An alternative to this is to make the adjacent channels orthogonal to one another. Each channel then carries a
relatively low bit rate,and the channel sidebands can overlap and effective signaling can still occur. Although
in a simplistic implementation, the number of carrier generators and coherent demodulators could get quite
large; in fact, when viewed in the Fourier transform domain, the signal can be demodulated by taking the
transform at the receiver. A completely digital implementation of the receiver is then possible by taking the
Fourier transform of the received signal, as the signals at the transmitter are combined by taking the inverse
Fourier transform.
OFDM is a particular type of FDM that can be viewed as a combination of modulation and multiple-access
scheme. Whereas TDMA segments according to time, and CDMA segments according to spreading codes,
like regular FDM, OFDM segments according to frequency as well. The spectrum is divided into a number of
equally spaced bandwidths the centers of which contain carrier tones. A portion of each user's information is
carried on each tone. Whereas regular FDM typically requires there to be frequency guard bands between the
carrier bands so that mutual interference is minimized, OFDM allows the spectrum of each tone to overlap.
The tones in OFDM are orthogonal with each other, and because of this orthogonality, they do not interfere
with each other.
Following figure illustrates the spectral properties of an OFDM system with five channels. This frequency
domain representation of five tones in this case highlights the orthogonal nature of the tones. The peak of each
tone corresponds to a zero level, or null, of every other tone. The result of this is that there is no interference
between tones. When the receiver samples at the tone frequency at the center of the channel, the only energy
present is that of the desired signal, plus of course, whatever other noise happens to be in the channel.

2. Lab10 OFDM 2
Figure 1: OFDM channels {A, B, C, D, E} each carry a relatively slow waveform but the signaling timing is such that they do not
interfere with each other
The original data stream splits into N parallel data streams,each at a rate 1/ N of the original rate. Each stream
is then mapped to a tone at a unique frequency and combined together using the inverse fast Fourier transform
(lFFT) to yield the time-domain waveform to be transmitted. A block diagram indicating the significant
functions in an OFDM transmitter is illustrated in the following figure. The cycle prefix insertion function is
required to provide a guard time between symbols.
Figure 2: OFDM transmitter
By creating slower parallel data streams,the bandwidth of the modulation symbol is effectively decreased by
a factor of 100, or, due to the inverse relationship between bandwidth and symbol duration, the duration of the
modulation symbol is increased by a factor of 100.
Inter Symbol Interference (ISI)canbe essentially eliminated, because typical multipath delay spreadrepresents
a much smaller proportion of the lengthened symbol time.

3. Lab10 OFDM 3
OFDMis also a multiple-access technique. This occurswhen an individual tone or groups of tonesare assigned
to different users.The resultant structure is called Orthogonal Frequency Division Multiple Access(OFDMA).
To ensure orthogonality betweentones, the symbol time must contain one or multiple cycles of eachsinusoidal
tone waveform. This is ensured by making the period of the tone frequencies integer multiples of the symbol
period where the tone spacing is 1/T as shown in the first figure. The following figure shows an example of
three tones over a single symbol period, where each tone has an integer number of cycles during the symbol
period.
Figure 3: The number of sinusoid periods are integer multiples of each other. In this case there are three waveforms in the same
period.

4. Lab10 OFDM 4
In this Lab we will implement the OFDM system following the steps in figure below:

5. Lab10 OFDM 5
a) Open GNU radio and build the following flow graph
And observe the following output

6. Lab10 OFDM 6
Exercise A
1) Change the modulation and observe the output
2) Change FFT length and observe the output

7. Lab10 OFDM 7
B) Implementation OFDM transceiver in MATLAB
% Configuration Parameters
clc
clear all
close all
%% Setting Parameters
Subcarriers = 64;
% total number of subcarrier (IFFT length equal to
Subcarrier)
M = 4;
% number of constellations
numOfSym = 3000;
% number of OFDM Symbols
GI = 1/4;
% Guard Interval or Cyclic Prefix, normaly 25 of the
entire OFDM symbol
snr = 15;
% Signal to noise ratio in dB
BW = 5e6;
% Band width in MHz
Fs = 2*BW;
%% --------------------- TRANSMITER --------------------------------------
%%------------------------------------------------------------------------
%% Generate Data to be modulated on the subcarriers
Data = randi([0,M-1], Subcarriers, numOfSym);
TxData = Data;
%% Implement QAM modulation
TxData_Modulated = qammod(TxData',M);
%% Perform IFFT
TxData_IFFT = ifft(TxData_Modulated);
TxData_IFFT = TxData_IFFT';
%% Adding cyclic Prefix
TxData_GI = [TxData_IFFT((1-GI)*...
Subcarriers+1:end,:);TxData_IFFT];
%% Plotting OFDM signal in time domain
[row , col] = size(TxData_GI);
len = row*col;
ofdm_signal = reshape(TxData_GI, 1, len);
figure(1);
plot(real(ofdm_signal));
xlabel('Time');
ylabel('Amplitude');
title('OFDM Signal');
grid on;
[y,f] = periodogram(ofdm_signal(1,:), [], [], Fs, 'centered');
figure;
plot(f, 10*log10(y)); grid on

8. Lab10 OFDM 8
%% Channel
Recieve_Channel = awgn(TxData_GI ,snr,'measured');
%% --------------------- RECEIVER
%% CP removal
Recieve_GIremoved = Recieve_Channel(GI*Subcarriers+1 :
Subcarriers+GI*Subcarriers, :);
%% FFT operation
% % RecieveData_FFT_transpose = fft(Recieve_GIremoved');
% % RecieveData_FFT = RecieveData_FFT_transpose';
RecieveData_FFT = fft(Recieve_GIremoved');
RecieveData_FFT = RecieveData_FFT';
Signal_Magnitude = real(RecieveData_FFT);
Signal_Phase = imag(RecieveData_FFT);
%% plot the received constellations
scatterplot(RecieveData_FFT(1,:));
title('FFT Output 4-QAM');
%% Demodulation
RecieveData = qamdemod(RecieveData_FFT',M);
%% Mean Error Rate computation and % Bit Error Rate computation
[num , BER] = symerr(RecieveData,TxData');

9. Lab10 OFDM 9
C ) Simulation of OFDM System (IEEE 802.11) under AWGN channel
%% --------Simulation parameters----------------
nSym=10^4; %Number of OFDM Symbols to transmit
EbN0dB = -20:2:8; % bit to noise ratio
%---------------------------------------------
%% --------OFDM Parameters - Given in IEEE Spec--
N=64; %FFT size or total number of subcarriers (used + unused) 64
Nsd = 48; %Number of data subcarriers 48
Nsp = 4 ; %Number of pilot subcarriers 4
ofdmBW = 20 * 10^6 ; % OFDM bandwidth
%----------------------------------------------
%% --------Derived Parameters--------------------
deltaF = ofdmBW/N;
%=20 MHz/64 = 0.3125 MHz
Tfft = 1/deltaF;
% IFFT/FFT period = 3.2us
Tgi = Tfft/4;
%Guard interval duration - duration of cyclic prefix
Tsignal = Tgi+Tfft;
%duration of BPSK-OFDM symbol
Ncp = N*Tgi/Tfft;
%Number of symbols allocated to cyclic prefix
Nst = Nsd + Nsp;
%Number of total used subcarriers
nBitsPerSym=Nst;
%For BPSK the number of Bits per Symbol is same as num of
subcarriers

10. Lab10 OFDM 10
EsN0dB = EbN0dB + 10*log10(Nst/N) + 10*log10(N/(Ncp+N)); %
converting to symbol to noise ratio
errors= zeros(1,length(EsN0dB));
theoreticalBER = zeros(1,length(EsN0dB));
%Monte Carlo Simulation
for i=1:length(EsN0dB)
for j=1:nSym
%-----------------Transmitter--------------------
s=2*round(rand(1,Nst))-1; %Generating Random Data with BPSK modulation
%IFFT block
%Assigning subcarriers from 1 to 26 (mapped to 1-26 of IFFT input)
%and -26 to -1 (mapped to 38 to 63 of IFFT input); Nulls from 27 to 37
%and at 0 position
X_Freq=[zeros(1,1) s(1:Nst/2) zeros(1,11) s(Nst/2+1:end)];
% Pretending the data to be in frequency domain and converting to time
domain
x_Time=N/sqrt(Nst)*ifft(X_Freq);
%Adding Cyclic Prefix
ofdm_signal=[x_Time(N-Ncp+1:N) x_Time];
%--------------Channel Modeling ----------------
noise=1/sqrt(2)*(randn(1,length(ofdm_signal))+1i*randn(1,length(ofdm_signal)));
r= sqrt((N+Ncp)/N)*ofdm_signal + 10^(-EsN0dB(i)/20)*noise;
%-----------------Receiver----------------------
%Removing cyclic prefix
r_Parallel=r(Ncp+1:(N+Ncp));
%FFT Block
r_Time=sqrt(Nst)/N*(fft(r_Parallel));
%Extracting the data carriers from the FFT output
R_Freq=r_Time([(2:Nst/2+1) (Nst/2+13:Nst+12)]);
%BPSK demodulation / Constellation Demapper.Force +ve value --> 1, -ve
value --> -1
R_Freq(R_Freq>0) = +1;
R_Freq(R_Freq<0) = -1;
s_cap=R_Freq;
numErrors = sum(abs(s_cap-s)/2); %Count number of errors
%Accumulate bit errors for all symbols transmitted
errors(i)=errors(i)+numErrors;
end
theoreticalBER(i)=(1/2)*erfc(sqrt(10.^(EbN0dB(i)/10))); %Same as BER for BPSK
over AWGN
end
simulatedBER = errors/(nSym*Nst);
plot(EbN0dB,log10(simulatedBER),'r-o');
hold on;
plot(EbN0dB,log10(theoreticalBER),'k*');
grid on;
title('BER Vs EbNodB for OFDM with BPSK modulation over AWGN');
xlabel('Eb/N0 (dB)');ylabel('BER');legend('simulated','theoretical');

11. Lab10 OFDM 11

12. Lab10 OFDM 12
Exercise B
1) Change the modulation order (M = 8, 16 and 32) realize the output