Terlampir
% A simple code to illustrate the operation of an OFDM transmitter and Receiver including
% RF upconversion and down-conversion ;
% References: IEEE802.11 standards, Simulation of Digital communication
% systems with MATLAB by Mathuranathan Viswanathan
clc;
%---------------------------------------------
%--------OFDM Parameters, an example of MCS0 of WLAN standard for a 20MHz wide channel ---
%Modulation scheme used is BPSK
N = 64; %FFT size or total number of subcarriers (used + unused) 64
N_s_data = 48; %Number of data subcarriers
N_s_pilots = 4 ; %Number of pilot subcarriers
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 and also the duration of cyclic prefix
Tsignal = Tgi + Tfft; %duration of BPSK-OFDM symbol
Ncp = N* Tgi/ Tfft; %Number of symbols allocated to cyclic prefix
Nst = N_s_data + N_s_pilots; %Number of total used subcarriers
nBitsPerSym = Nst; %For BPSK the number of Bits per Symbol is same as num of subcarriers
%-----------------Transmitter--------------------
s = 2*randi([0 1], 1, Nst)-1; %Generating Random Data with BPSK modulation
% The number of bits being generated is limited to the total number of
% used sub-carriers. There could be more number of bits generated and the
% bits be re-arranged in a number of rows and columns equal to 'Nst' as
% in the commented code below
%data=randi([0 1], numbits, 1); % Generate vector of of length 'numbits'
% s= [];
%for 0=0:Nst:numbits
%s1 = [data(i+1:(i+(Nst))]
% s = [ s; s1]
%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)];
% Assuming that the data is in frequency domain and converting to time domain
% and scaling the amplitude appropriately
x_Time = N/ sqrt( Nst)* ifft( X_Freq);
%Adding Cyclic Prefix
ofdm_signal =[ x_Time( N-Ncp + 1: N) x_Time]; %Generation of the OFDM baseband signal complete
%%----------------------Up-conversion to RF----------------------------
Tsym = Tsignal/(N+Ncp); % duration of each symbol on the OFDM signal
t=Tsym/50:Tsym/50:Tsym; % define a time vector
%fc = 10*ofdmBW; % set the carrier frequency at 10 times the bandwidth of the OFDM channel
fc = 2.412 * 10 ^ 9; % set the carrier frequency at a WLAN cchannel's centre frequency
Carr_real=[];
Carr_imag=[];
Carr = [];
for n=1:length(ofdm_signal)
Carr_real = real(ofdm_signal(n))*cos(2*pi*fc*t); %modulate the real part on a cosine carrier
Carr_imag = imag(ofdm_signal(n))*sin(2*pi*fc*t); %modulate the imaginary part on a sine carrier
% Carr_real=[Carr_real Carr_real];
% Carr_imag=[Carr_imag Carr_imag];
Carr = [Carr Carr_real+Carr_imag];
end
%% Addition of quantization noise.
%The OFDM modulation operation is done in a Digital Signal processor in
%most cases whose digital output needs to be converted to analogue domain
%using a digital to analogue converter (DAC). The output of a DAC is
%quantized to discrete levels depending on the reference voltage and bit
%resolution of the DAC. This is generally done before up conversion and
%with individual DACs for the real and imaginary parts of the baseband
%signal. The quantization has been added after up-conversion in this code
%to avoid complexity of having two individual quantization codes for the
%real and imaginary parts of the base band. In either case, the output of
%the up-converter will have amplitudes at discrete staps depending on the
%quantization levels.
n1 = 10; % Number of bits of the ADC/DAC
max1= (2^n1)-1; %maximum n1 bit value
m=length(Carr);
Ac = max(abs(Carr));%Carrier amplitude of 1V
%conversion of the signal ybb to n1 bits digital values quantized to the
%nearest integer value
Vref = Ac*2; % Reference voltage of the converter
conv_fact1 = max1/Vref; %conversion scale for the analogue samples to convert to 16 bits
resolution = Vref/max1;
z1 = [];
for q=1:1:m
z1(q)=(Carr(q)+Ac)*conv_fact1; %generating 'n1' bit digital representation
%of each sample of the carrier
end
x1 = nearest(z1); % Each value is quantized to its nearest n1 bit number
y_tx = [];
for q=1:1:m
y_tx(q) = ((x1(q)*Vref/max1)-Ac); %generating the analogue equivalent voltage of
%each 'n1' bit sample
qerr1(q) = Carr(q)-y_tx(q);
end
%--------------Channel Modeling ----------------
% AWGN and other channel impairments could be added here. AWGN is added for
% inllustrative purpose. Further impairments such as doppler effect,
% Rayleigh fading may be added.
snr = 1;
rx_carr = awgn(y_tx,snr, 'measured');
%%-----------------Receiver----------------------
%I-Q or vector down-conversion to recover the OFDM baseband signal from the
%modulated RF carrier
r = [];
r_real= [];
r_imag = [];
for n=1:1:length(ofdm_signal)
%%XXXXXX inphase coherent dector XXXXXXX
Z_in=rx_carr((n-1)*length(t)+1:n*length(t)).*cos(2*pi*fc*t); %extract a period of the
%signal received and multiply the received signal with the cosine component of the carrier signal
Z_in_intg=(trapz(t,Z_in))*(2/Tsym);% integration using Trapizodial rule
%over a period of half bit duration
r_real=Z_in_intg;
%%XXXXXX Quadrature coherent dector XXXXXX
Z_qd=rx_carr((n-1)*length(t)+1:n*length(t)).*sin(2*pi*fc*t);
%above line indicat multiplication ofreceived & Quadphase carred signal
Z_qd_intg=(trapz(t,Z_qd))*(2/Tsym);%integration using trapizodial rull
r_imag = Z_qd_intg;
r=[r r_real+1i*(r_imag)]; % Received Data vector
end
%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
R_Freq( R_Freq < 0) = 0
s(s < 0) = 0;
[numErrors, ber] = biterr(s, R_Freq);
fprintf('\nThe bit error rate = %5.2e, based on %d errors\n', ...
ber, numErrors)
