Three transmitters use direct sequence spread spectrum for multiple access to a

Question

Three transmitters use direct sequence spread spectrum for multiple access to a channel. Their transmitted baseband signals consist of five pulses with amplitudes

X1: -1, 1, 1, -1, -1

X2: -1,-1, 1, -1, -1

X3: -1, 1,-1, -1, 1

The transmitters spread their baseband pulses at a chip rate of 6/1 according to the following spreading sequences

C1: -1, -1, -1, -1, 1, 1

C2: 1, 1, -1, 1, 1, -1

C3: -1, -1, 1, -1, 1, -1

The sum of the spread signals is then transmitted over the channel.

a)Show the composite signal transmitted over the channel.

The receiver attempts to reconstruct the original signal xi by multiplying the received composite signal over each pulse period with the corresponding chipping sequence of xi, summing the result over the pulse period and comparing the sum to a zero threshold value. If the sum is positive the receiver decides that the original pulse value was 1. Otherwise, it decides that the pulse value was -1.

b)Determine the decoded sequence of pulses for each of the three transmitted signals and determine the number of errors in each of them.

Explanation / Answer

composite signal transmitted over the channel.

composite signal is obtained as

y=(X1*C1)+(X2*C2)+(X3*C3).

I obtain below through matlab code of spreading message signal(X1,X2,X3) using given spread sequences(C1,C2,C3).

for convenient have given the matlab code also.

MATLAB CODE

clc;
close all;
clear all;
x1=[-1 1 1 -1 -1 ];
x2=[-1 -1 1 -1 -1];
x3=[-1 1 -1 -1 1];
c1=[-1 -1 -1 -1 1 1];
c2=[1 1 -1 1 1 -1];
c3=[-1 -1 1 -1 1 -1];

yy1=[];
for i1=1:5
y1=x1(i1)*c1;
yy1=[yy1 y1];
end
disp(yy1);

yy2=[];
for i2=1:5
y2=x2(i2)*c2;
yy2=[yy2 y2];
end
disp(yy2);

yy3=[];
for i3=1:5
y3=x3(i3)*c3;
yy3=[yy3 y3];
end
disp(yy3);

%copmposite signal
y=yy1+yy2+yy3;

disp(y);

disp(y)
Columns 1 through 11

1 1 1 1 -3 1 -3 -3 1 -3 1

Columns 12 through 22

1 1 1 -3 1 1 1 1 1 1 1

Columns 23 through 30

-3 1 -1 -1 3 -1 -1 -1

At Reciever we get the signal without noise according to given problem.

Hence the recieved signal obtained from given formula

x1=y*C1

x2=y*C2

x3+y*C3

For this case ,as there is no adding of noise in the channel

x1=X1

x2+X2

x3=X3

i.e

Recived message signals

x1: -1, 1, 1, -1, -1

x2: -1,-1, 1, -1, -1

x3: -1, 1,-1, -1, 1

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