DSSS is a wireless analog encoding scheme based on a technique spread spectrum.
It represents each data bit by multiple bits in the transmitted signal using a chip code/spreading code. The spreading code spreads the signal across a wider frequency band in direct proportion to the length of the chip code.
Task 1: Study and implement the matlab functions and show the output:
Hadamard:
This MATLAB function returns the Hadamard matrix of order n.
Syntax:
Hadamard(n) % n n must be an integer and n, n/12 or n/20 must be a power of 2.
Command: Hadamard(4);
Output:
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
randperm
It stands for random permutation
Syntax:
P = randperm(n); % returns a row vector containing a random permutation of the integer from 1 to n inclusive.
P= randperm(n,k) % return a row vector containing k unique integers selected randomly from 1 to n inclusive.
Command:
randperm(7);
output: 6 3 7 5 1 2 4
Command:
Randperm(7,3);
Output:
6 2 7
randint
It generates a matrix of uniformly distributed random integers.
Syntax:
Out= randint % generate either 0 or 1
Out = randint(n) % generate a matrix of order nxn containing randomly 0’s and 1’s.
Out = randint(n,m,range)% generates a matrix of order nxm, if rg is 0 it will generate matrix containing all zeros, otherwise it will have integer containing in the specified range.
Command: randint(2,2,9)
Output:8 4
4 2
biterr
It computes the number of bit errors and bit error rate(BER).
Syntax:
[number, ratio]= biterr(x,y) % compare the unsigned binary representation of each element of x matrix with that of y matrix.
[number, ratio]= biterr(x,y,k) % it considers that elements of x and y have k bits.
[number, ratio]= biterr(x,y,k,flg) % flg can be ‘overall’ (element by element comparison), ‘rsow_wise’ (compare nth row of x with nth row of y) and ‘column_wise’.
[number,ratio, individual]= biterr(….) % individual have dimension greater then that of x and y matrix. Each element of individual represent the difference of bits between the corresponding elements of x and y matrix and number of comparisons.
Command:
[number,ratio,individual] = biterr([0;0;0],randi([0 1],3,5));
Output:
number = 2 1 2 1 1
ratio = 2/3 1/3 2/3 1/3 1/3
individual =0 0 0 1 0
1 0 1 0 1
1 1 1 0 0
bi2de
convert binary vector to decimal equivalent number.
Syntax:
Bin2de(v)
Command: v=[1 0 1 0 1]
bi2de(v);
Output= 21
bin2gray
Converts binary integer to corresponding Gray-encoded integer.
Syntax:
Y= bin2gray(x,modulation,M)
or
[y,map]= bin2gray(x,modulation,M)
Code:
% To Gray encode a vector x with a 16-QAM Gray encoded
% constellation and return its map, use:
x=randi([0 5],1,100);
[y,map] = bin2gray(x,'qam',16);
% Obtain the symbols for 16-QAM
hMod = modem.qammod('M', 16);
symbols = hMod.Constellation;
% Plot the constellation
scatterplot(symbols);
set(get(gca,'Children'),'Marker','d','MarkerFaceColor',...
'auto'); hold on;
% Label the constellation points according
% to the Gray mapping
for jj=1:16
text(real(symbols(jj))-0.15,imag(symbols(jj))+0.15,...
dec2base(map(jj),2,4));
end
set(gca,'yTick',(-4:2:4),'xTick',(-4:2:4),...
'XLim',[-4 4],'YLim',...
[-4 4],'Box','on','YGrid','on', 'XGrid','on');
Output:
de2bi
It converts decimal number to equivalent binary vector.
Command: de2bi(3)
Output: 1 0 1
gray2bin
Convert Gray-encoded positive integers to corresponding Gray-decoded integers.
Syntax:
Y= gray2bin(x,Modulation, M);
or
[Y,map]= gray2bin(x,Modulation,M);
Code:
% To Gray decode a vector x with a 16-QAM Gray encoded
% constellation and return its map, use:
x=randi([0 15],1,100);
[y,map] = gray2bin(x,'qam',16);
% Obtain the symbols for 16-QAM
hMod = modem.qammod('M', 16);
symbols = hMod.Constellation;
% Plot the constellation
scatterplot(symbols);
set(get(gca,'Children'),'Marker','d','MarkerFaceColor','auto');
hold on;
% Label the constellation points according
% to the Gray mapping
for jj=1:16
text(real(symbols(jj))-0.15,imag(symbols(jj))+0.15,...
dec2base(map(jj),2,4));
end
set(gca,'yTick',(-4:2:4),'xTick',(-4:2:4),...
'XLim',[-4 4],'YLim',...
[-4 4],'Box','on','YGrid','on', 'XGrid','on');
Output:
vec2mat
It converts a vector into matrix.
Command: v=[1 2 3 4 5];
vec2mat(v);
Output: 1 2 3
4 5 0
Task 2: Implement DSSS receiver in Matlab and show the complete results:
Matlab code:
At transmitter side the data=[1 0 1 1 1 1] was encoded as coded=[1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1]; by spread spectrum technique.
Matlab function for receiver side.
coded=[1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1];
ct=hadamard(8);
p=8;
code=ct(p,1:end)';
data=[];
l=length(coded);
for i=1:8:l
matrix=coded(1,i:i+7);
original=(matrix*code)/length(code);
if(original ==-1)
original=0;
else
original=1;
end
data=[data original];
end
Data: 1 0 1 1 1 1
Coded data received from transmitter: 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1
Decoded data at Receiver: 1 0 1 1 1 1
Task 3: Implement Frequency Hopping Spread Spectrum (FHSS) Transmitter in Matlab and show the complete results.
Frequency-hopping spread spectrum (FHSS) is a method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using a pseudorandom sequence known to both transmitter and receiver. It is used as a multiple access methodin the frequency-hopping code division multiple access (FH-CDMA) scheme
Matlab code for transmitter:
clc
clear all
close all
data=[1 0 1 1 1 1];
size=length(data);
M=2;
NRZ_signal=[]; %unipolar NRZ signal
k=[];
for (t=1:size)
if (data(t)==0)
NRZ_signal(t)=-1;
else
NRZ_signal(t)=1;
end
k=[k NRZ_signal(t)];
end
rand_freq=[2 3 4 5 6 7 8 9];
chip=8;
r=randperm(chip);
t=[];
bpsk_datasig=[];
for b=1:length(k)
f=rand_freq(r(b));
fs=50;
t1=b-1:1/fs:b;
t2=0:1/fs:1;
x=cos(2*pi*f*t2);
y=sin(2*pi*f*t2);
t=[t t1];
if (k(b)==1)
a=x;
else
a=y;
end
bpsk_datasig=[bpsk_datasig a];
end
plot([1:length(bpsk_datasig)], abs(fft(bpsk_datasig)));
