WORKSHOP ON ADVANCED WIRELESS COMMUNICATION SYSTEM.pptx

WORKSHOP ON ADVANCED WIRELESS
COMMUNICATION SYSTEM
Name: L. Venkateshprasad
SECTION:EM014
Reg no:11603474
Submitted to Dr. Shakti raj Chopra

PROJECT-1
Performance and comparison analysis of
time division multiple access(TDMA) and
frequency division multiple access(FDMA)

TDMA(Time division multiple access)
 Time-division multiplexing (TDM) is a method of transmitting and receiving
independent signals over a common signal path by means of synchronized
switches at each end of the transmission line so that each signal appears on the
line only a fraction of time in an alternating pattern.
 Each frame consists of a set of time slots
 Usually used with digital signal or analog signal carrying digital data
 Each source is assigned one or more time slots per frame

ADVANTAGES of TDMA
 In addition to increasing the efficiency of transmission, TDMA offers a number of other
advantages over standard cellular technologies. First and foremost, it can be easily adapted
to the transmission of data as well as voice communication. TDMA offers the ability to
carry data rates of 64 kbps to 120 Mbps (expandable in multiples of 64 kbps).
 It is the most cost effective technology for upgrading analog to digital.
 It provides the user with extended battery life and talk time.
 It is the only technology that offers an efficient utilization of hierarchal cell structures like
Pico, micro and macro cells.
 Dual band 800/1900 MHz

The Disadvantages of TDMA
 One of the disadvantages of TDMA is that each user has a predefined time slot. However,
users roaming from one cell to another are not allotted a time slot.
 Another problem with TDMA is that it is subjected to multipath distortion. A signal coming
from a tower to a handset might come from any one of several directions. It might have
bounced off several different buildings before arriving

FDMA(Frequency division multiple access)
 Number of signals are carried simultaneously on the same medium
 Each signal is modulated to a different carrier frequency
 Useful bandwidth of medium should exceed required bandwidth of channels
 Carrier frequency separated so signal do not overlap
 Eg: FM radio, CATV

ADVANTAGES Of FDMA
 It does not need synchronization between its transmitter and receiver.
 Frequency division multiplexing (FDM) is simpler and easy demodulation.
 Due to slow narrow band fading only one channel gets affected.
 It is used for analog signals.
 A large number of signals (channels) can be transmitted simultaneously.

Disadvantages of FDMA
• It does not differ significantly from analog systems; improving the capacity
depends on the signal-to-interference reduction, or a signal-to-noise ratio (SNR).
• The maximum flow rate per channel is fixed and small.
• Guard bands lead to a waste of capacity.
• Hardware implies narrowband filters, which cannot be realized in VLSI and
therefore increases the cost.

CODE
clc
clear all
close all
x=0:.5:4*pi;
sig1=8*sin(x);
l=length(sig1);
sig2=8*triang(l);
sig3=8*sawtooth(x);
figure('Name','Transmit Signal"TDMA"','NumberTitle','Off');
subplot(3,2,1);
plot(sig1);
grid on
title('Sinusoidal Signal');
xlabel('Time--->');
ylabel('Amplitude--->');
subplot(3,2,3);
plot(sig2);
grid on
title('Triangular Signal');
xlabel('Time--->');

subplot(3,2,5);
plot(sig3);
grid on;
title('Sawtooth Signal');
xlabel('Time--->');
subplot(3,2,2);
stem(sig1);
grid on
title('Sampled Sinusoidal Signal');
xlabel('Time--->');
subplot(3,2,4);
h=stem(sig2);
grid on
%set(h(1),'MarkerFaceColor','red')
title('Sampled Triangular Signal');
xlabel('Time--->');
subplot(3,2,6);
stem(sig3);

grid on
title('Sampled Sawtooth Signal');
xlabel('Time--->');
l1=length(sig1);
l2=length(sig2);
l3=length(sig3);
for i=1:l1
sig(1,i)=sig1(i);
sig(2,i)=sig2(i);
sig(3,i)=sig3(i);
end
tdmsig=reshape(sig,1,[]);
figure('Name','TDMA-Modulated-Signal','NumberTitle','Off');
stem(tdmsig);
grid on
title('TDM Signal');
xlabel('Time--->');
demux=reshape(tdmsig,3,l1);
for i=1:l1

sig4(i)=demux(1,i);
sig5(i)=demux(2,i);
sig6(i)=demux(3,i);
end
figure('Name','Recieved signal"TDMA"','NumberTitle','Off');
subplot(3,1,1)
plot(sig4);
grid on
title('Recovered Sinusoidal Signal');
xlabel('Time--->');
subplot(3,1,2)
plot(sig5);
grid on
title('Recovered Triangular Signal');
xlabel('Time--->');
subplot(3,1,3)
plot(sig6);
grid on
title('Recovered Sawtooth Signal');

xlabel('Time--->');
samples=1000;
%number of users
nos=3;
%modulating signal freq
mfreq=[60 80 100];
%carrier freq
cfreq=[1200 1800 2400];
%freq deviation
freqdev=10;
%generate modulating signal
t=linspace(0,1000,samples);
parfor i=1:nos
m(i,:)=sin(2*pi*mfreq(1,i)*t)+2*sin(pi*8*t);
end
%generate modulated signal
parfor i=1:nos
y(i,:)=fmmod(m(i,:),cfreq(1,i),10*cfreq(1,i),freqdev);
end

ch_op=awgn(sum(y),0,'measured’);
for i=1:nos
z(i,:)=fmdemod(y(i,:),cfreq(1,i),10*cfreq(1,i),freqdev);
end
C={'k','b','r'}; %cell array of colors
for i=1:nos
figure
hold on
plot(y(i,:),'color',C{i});
xlabel('time index');
ylabel('amplitude');
title('Signal from diff users combined in the channel');
figure
subplot(3,1,1)
plot(m(i,:))
title('Modulating signal from user');
subplot(3,1,2)
plot(y(i,:),'color',C{i});
xlabel('time index')

title('modulated Signal from user');
subplot(3,1,3)
plot(z(i,:),'color',C{i}); % demodulated signal
title('demodulated Signal from
user at the base station');
end
figure
plot(ch_op) %
xlabel('time index’);
title('Signal after passing
through the channel')

PROJECT-2
Performance analysis of orthogonal
space time block codes (OSTBC)

OSTBC(orthogonal space time block code)
 The OSTBC Encoder block encodes an input symbol sequence using orthogonal
space-time block code (OSTBC). The block maps the input symbols block-wise
and concatenates the output codeword matrices in the time domain.

SNR
 The SNR is a ratio of the signal power to the total noise power. To get total noise
power, we assume that the shot noise is approximately Gaussian with of course
mean equal to the average photo-current. Then since shot and thermal
processes are independent Gaussian random processes, the variance of the
total noise is equal to the sum of the variances of the two noises.
 SNR is the difference between the . Also, in terms of definition, the noise floor is
the specious background transmissions that are produced by other devices or by
devices that are unintentionally generating interference on a similar frequency.
Therefore, to ascertain the signal to noise ratio, one must find the quantifiable
difference between the desired signal strength and the unwanted noise by
subtracting the noise value from the signal strength value

BER
 In digital transmission, the number of bit errors is the number of received bits of a
data stream over a communication channel that have been altered due to noise,
interference, distortion or bit synchronization errors. The bit error rate (BER) is
the number of bit errors per unit time.
 BER=Errors / Total Number of Bits
 The main reasons for the degradation of a data channel and the corresponding
bit error rate, BER is noise and changes to the propagation path

CODE
clc;
snr=6;
soglia=20;
S_ML=zeros(1,4);
X_dec=zeros(1,2);
Nt=2;
Nr=2;
dec=zeros(1,2);
no_bit_sym=1;
no_it_x_SNR=10000;
iter=0;
err = 0;
tot_err_h = 0;
tot_err_ml = 0;
while tot_err_ml<soglia
iter=iter+1;
for i=1:no_it_x_SNR
Data=(2*round(rand(Nt,1))-1)/(sqrt(Nt));
H=ones(2,2);
sig = sqrt(0.5./(10.^(snr./10)));
n = sig * (randn(Nr,Nt) + j*randn(Nr,Nt));
X=[Data(1) -conj(Data(2)); Data(2) conj(Data(1))];

R=H*X + n ;
s0=conj(H(1,1))*R(1,1)+H(1,2)*conj(R(1,2))+conj(H(2,1))*R(2,1)+H(2,2)*conj(R(2,2));
s1=conj(H(1,2))*R(1,1)-H(1,1)*conj(R(1,2))+conj(H(2,2))*R(2,1)-H(2,1)*conj(R(2,2));
S=[s0 s1];
dh = sqrt(2)*[1 -1]/2;
d11=((dh(1)-real(S(1)))^2+(imag(S(1)))^2);
d12=((dh(2)-real(S(1)))^2+(imag(S(1)))^2);
D1=[d11 d12];
for k=1:2
X1_dec(k)=((abs(dh(k)))^2)*sum(sum((abs(H)).^2)-1)+D1(k);
end
d21=((dh(1)-real(S(2)))^2+(imag(S(2)))^2);
d22=((dh(2)-real(S(2)))^2+(imag(S(2)))^2);
D2=[d21 d22];
for x=1:2
X2_dec(x)=((abs(dh(k)))^2)*sum(sum((abs(H)).^2)-1)+D2(x);
end
[scelta1, posizione1]=min(X1_dec);
[scelta2, posizione2]=min(X2_dec);
decoded=[dh(posizione1) dh(posizione2)];
err_ml = sum(round(Data')~=round(decoded));
tot_err_ml = err_ml + tot_err_ml;

end
end
ber_ml=tot_err_ml/(no_it_x_SNR*iter*2)
PLOT
SNR = [1 2 3 4 5 6];
BER = [0.0123 0.0053 0.0025 8.5000e-04 2.0000e-04 3.4483e-05 ]
figure
plot(SNR,BER)

PROJECT-3
PERFORMANCE AND
COMPARSION ANALYSIS OF
OFDM AND MIMO

ABOUT THE PROJECT
 It is based on the performance and comparsion analysis of the orthogonal
frequency division multiplexing(OFDM) and multiple input and multiple
output(MIMO)
 By using BPSK modulation at the transmitting end via multiple Txs we get a
medium propagation signal in many-many layout
 It improve the reliability of the network with multi-path potential.

MIMO
 MIMO systems use a combination of multiple antennas and multiple signal paths
to gain knowledge of the communications channel. By using the spatial dimension
of a communications links.
 Increased data rates
 Multiplexing increases capacity and spectral efficiency with no additional power or
bandwidth expenditure

OFDM
 Stands for orthogonal Frequency division multiplexing
 It has improved the quality of long-distance communication by eliminating Inter
Symbol Interference (ISI) and improving Signal-to-Noise ratio (SNR).
 It reduce multi-path fading
 It ability for high –data rate transmission over multipath fading channel
 High spectral efficiency , low receiver complexity

BEAMFORMING
 Beamforming is a technique that focuses a wireless signal towards a specific
receiving device, rather than having the signal spread in all directions from a
broadcast antenna.
 improves the spectral efficiency by providing a better signal-to-noise ratio (SNR).
 Spatial randomness of the signal is optimized

code
 clc;
 clear all;
 close all;
 N=10^6;
 a=randi([0,1],1,N);
 b=2*a-1;
 ntx=2;
 snr=0:1:30;
 for i=1:length(snr)
 n=1/sqrt(2)*(randn(1,N)+j*randn(1,N));
 h=1/sqrt(2)*(randn(ntx,N)+j*randn(ntx,N));

code
 x=[b;b];
 h_tx=h.*exp(-j*angle(h));
 y1=sum(h.*x,1)+(10^(-snr(i)/20)*n);
 y2=sum(h_tx.*x,1)+(10^(-snr(i)/20)*n);
 y_e=y1./sum(h,1);
 y_b=y2./sum(h_tx,1);
 d_1=real(y_e)>0;
 d_2=real(y_b)>0;
 err_1(i)=length(find([a-d_1]));
 end
 n1tx=3;
 n3=1/sqrt(2)*(randn(1,N)+j*randn(1,N));
 h3=1/sqrt(2)*(randn(n1tx,N)+j*randn(n1tx,N));

CODE
 x=[b;b];
 y1=sum(h.*x,1)+(10^(-snr(i)/20)*n);
 y2=sum(h_tx.*x,1)+(10^(-snr(i)/20)*n);
 y_e=y1./sum(h,1);
 d_1=real(y_e)>0;
 d_2=real(y_b)>0;
 end

CODE
 n1tx=3;
 x=[b;b;b];
 h3_tx=h3.*exp(-j*angle(h3));
 y3=sum(h3_tx.*x,1)+(10^(-snr(i)/20)*n3);
 y3_b=y3./sum(h3_tx,1);
 d_3=real(y3_b)>0;
 End

CODE
 ber=err_1/N;
 ber_b=err_2/N;
 ber_b3=err_3/N;
 figure
 semilogy(snr,ber,'-',snr,ber_b,'*',snr,ber_b3,'+');
 xlabel('SNR');
 ylabel('BER');
 title('Beamforming In MIMO System');
 legend('General MIMO','MIMO with 2 Beamforming','MIMO with 3
Beamforming');
 hold on;
 N=10^4;
 a=randi([0,1],1,N);
 b=(2*a-1);

CODE
 c=ifft(b);
 SNR=0:3:50;
 for i=1:length(SNR)
 n=(1/sqrt(2))*[rand(1,N)+j*rand(1,N)];
 h=(1/sqrt(2))*[rand(1,N)+j*rand(1,N)];
 y=sum(c.*h,1)+10^(-(SNR(i))/20)*n;
 ye=y./sum(h,1);
 s=fft(ye);
 r=real(s)>0;
 e(i)=size(find(r-a),2);
 end
 d=pskmod(a,4);
 f=ifft(d);
 SNR=0:3:50;

Code
 for i=1:length(SNR)
 n=(1/sqrt(2))*[rand(1,N)+j*rand(1,N)];
 h=(1/sqrt(2))*[rand(1,N)+j*rand(1,N)];
 y=sum(f.*h,1)+10^(-(SNR(i))/20)*n;
 ye=y./sum(h,1);
 s=fft(ye);
 r=pskdemod(s,4);
 e1(i)=size(find(r-a),2);
 end
 BER=e/N;
 BER1=e1/N;
 figure(1)
 semilogy(SNR,BER,'r');
 xlabel('b')
 ylabel(‘BER’)

CODE
 hold on
 semilogy(SNR,BER1,'g');
 xlabel('d')
 ylabel('BER')
 title('snr vs ber')

PROJECT-4
Implementation of linear block
coding

Introduction
The purpose of error control coding is to enable the
receiver to detect or even correct the errors by
introducing some redundancies in to the data to be
transmitted. There are basically two mechanisms for
adding redundancy:
 1. Block coding
2. Convolutional coding

Linear Block Codes
 The encoder generates a block of n coded bits from k
information bits and we call this as (n, k) block codes. The
coded bits are also called as code word symbols.
 Why linear??? A code is linear if the modulo-2 sum of two
code words is also a code word.
 n code word symbols can take 2^𝑛 possible values. From that
we select 2^𝑘 code words to form the code. A block code is
said to be useful when there is one to one mapping between
message m and its code word c

Generation Matrix
 All code words can be obtained as linear combination of basis vectors.
• The basis vectors can be designated as {𝑔1, 𝑔2, 𝑔3,….., 𝑔𝑘}
• For a linear code, there exists a k by n generator matrix such that 𝑐1∗𝑛 = 𝑚1∗𝑘 . 𝐺𝑘
∗𝑛 where c={𝑐1, 𝑐2, ….., 𝑐𝑛} and m={𝑚1, 𝑚2, ……., 𝑚𝑘}
• In this form, the code word consists of (n-k) parity check bits followed by k bits of
the message.
• The rate or efficiency for this code R= k/n
• G = [ 𝐼𝑘 P] , C = m.G = [m mP] Message part Parity part

PARITY CHECK MATRIX (H)
 When G is systematic, it is easy to determine the parity check
matrix H as: H = [𝐼𝑛−𝑘 𝑃 𝑇 ]
 The parity check matrix H of a generator matrix is an (n-k)-by-
n matrix satisfying: 𝐻(𝑛−𝑘)∗𝑛𝐺𝑛∗𝑘 = 0
 Then the code words should satisfy (n-k) parity check
equations 𝑐1∗𝑛𝐻𝑛∗(𝑛−𝑘) = 𝑚1∗𝑘𝐺𝑘∗𝑛𝐻𝑛∗(𝑛−𝑘) = 0

SYNDROME AND ERROR DETECTION
 For a code word c, transmitted over a noisy channel, let r be the received vector at the output
of the channel with error
 Syndrome of received vector r is given by: s = r.H =(𝑠1, 𝑠2, 𝑠3, … … . . , 𝑠𝑛−𝑘)
 Properties of syndrome:
 The syndrome depends only on the error pattern and not on the transmitted word. s = (c+e).H
= c.H + e.H = e.H
 All the error pattern differ by atleast a code word have the same syndrome s.

MINIMUM DISTANCE OF A BLOCK CODE
 Hamming weight w(c ) : It is defined as the number of non-zero components of c. For
ex: The hamming weight of c=(11000110) is 4
 Hamming distance d( c, x): It is defined as the number of places where they differ . The
hamming distance between c=(11000110) and x=(00100100) is 4
 The hamming distance satisfies the triangle inequality d(c, x)+d(x, y) ≥ d(c, y)
 The hamming distance between two n-tuple c and x is equal to the hamming weight of
the sum of c and x d(c, x) = w( c+ x) For ex: The hamming distance between
c=(11000110) and is 4 and the weight of c + x = (11100010) is 4. x=(00100100)
 The Hamming distance between two code vectors in C is equal to the Hamming weight
of a third code vector in C. d = min{w( c+x):c, x €C, c≠x} = min{w(y):y €C, y≠ 0} = w min
≠

 Minimum min hamming distance d : It is defined as the smallest distance between
any pair of code vectors in the code.
 For a given block code C, d min is defined as: d min =min{ d(c, x): c, min x€C, c x}
 The Hamming distance between two code vectors in C is equal to the Hamming
weight of a third code vector in C.
 d min= min{w( c+x):c, x €C, c≠x}
 = min{w(y): y €C, y≠ 0}
 = w min

Applications
 Communications:
 Satellite and deep space communications.
 Digital audio and video transmissions.
 Storage:
 Computer memory (RAM).
 Single error correcting and double error detecting code.

 ADVANTAGES
 It is the easiest and simplest
technique to detect and correct
errors.
 Error probability is reduced.
 DISADVANTAGES
 Transmission bandwidth
requirement is more.
 Extra bits reduces bit rate of
transmitter and also reduces its
power

Code:
 %Given H Matrix
 H = [1 0 1 1 1 0 0;
 1 1 0 1 0 1 0;
 0 1 1 1 0 0 1]
 k = 4;
 n = 7;
 % Generating G Matrix
 % Taking the H Matrix Transpose
 P = H';
 % Making a copy of H Transpose Matrix
 L = P;
 % Taking the last 4 rows of L and storing

 L((5:7), : ) = [];
 % Creating a Identity matrix of size K x K
 I = eye(k);
 % Making a 4 x 7 Matrix
 G = [I L]
 % Generate U data vector, denoting all information sequences
 no = 2 ^ k
 % Iterate through an Unit-Spaced Vector
 for i = 1 : 2^k

 if rem(i - 1, 2 ^ (-j + k + 1)) >= 2 ^ (-j + k)
 u(i, j) = 1;
 else
 u(i, j) = 0;
 end

 % To avoid displaying each iteration/loop value
 echo off;
 end
 end

 echo on;
 u
 % Generate CodeWords
 c = rem(u * G, 2)
 % Find the min distance
 w_min = min(sum((c(2 : 2^k, :))'))
 % Given Received codeword
 r = [0 0 0 1 0 0 0];
 r

 %Find Syndrome
 ht = transpose(H)
 s = rem(r * ht, 2)

 for i = 1 : 1 : size(ht)
 if(ht(i,1:3)==s)
 r(i) = 1-r(i);
 break;
 end
 end

 disp('The Error is in bit:')
 disp(i)
 disp('The Corrected Codeword is :')
 disp(r)

PROJECT-5
PERFORMANCE ANALYSIS OF
DIFFERENT DIVERSITY COMBAINING
TECHNIQUE

TABLE OF CONTENT
 Introduction to the phenomena of diversity
 Classification of diversity
 Types of diversity on the basis of resource
 Diversity techniques
 Maximal ratio technique
 Equal gain technique
 Matlab code
 Output

INTRODUCTION TO THE PHENOMENA OF
DIVERSITY
 Used for wireless communication systems
 Applied to improve the performance over a Fading radio channel
 Rx.is catered with multiple intel signal transmitted over multiple channels
 It is based on the fact that individual channels experience different levels of fading
and interference

Types of diversity on the basis of resource
 Time diversity: Multiple versions of the same signal are transmitted at different time
instants.
 Frequency diversity : The signal is transmitted using several frequency channels or
spread over a wide spectrum that is affected by frequency-selective fading
 Space diversity : The signal is transmitted over several different propagation paths.
In the case of wired transmission, this can be achieved by transmitting via multiple
wires. In the case of wireless transmission, it can be achieved by using multiple
transmitter antennas and multiple receiving antennas.
 Multiuser diversity : it is a diversity technique using user scheduling
in multiuser wireless channels where user scheduling allows the base station to
select high quality channel users so as to transmit information through a relatively
high quality channel in time, frequency and space domains based on the channel
quality

CLASSIFICATION OF DIVERSITY
 Macro diversity: It is a form of antenna combining, and requires an infrastructure
that mediates the signals from the local antennas or receivers to a central receiver
or decoder. Transmitter may be a form of simulcasting, where the same signal is
sent from several nodes.
 Micro diversity: Provides a method to mitigate the effects of multipath fading as in
case of small scale fading

DIVERSITY TECHNIQUE
• Time diversity:
Transmission in which signals representing the same information are sent over the
same channel at different times. The delay between replicas > coherence time
uncorrelated channels
 Space diversity: Two antennas separated by several wavelengths will not generally
experience fades at the same time
Space Diversity can be obtained by using two receiving antennas and switching instant-
by- instant to whichever is best
 Frequency diversity: Using frequency channel separated in frequency more than the
channel coherence bandwidth
 Polarization diversity: using antenna with different polarizations

Maximal Ratio Technique
 In maximal-ratio combining, the signals from all of the M branches are weighted
according to their individual SNRs and then summed. The individual signals must
be cophased before being summed.
 the signals from each channel are added together
 The Gain of each channel is made Proportional to the rms signal level and
inversely proportional to the mean square noise level in that channel.

Equal gain technique
 It combining is similar to maximal-ratio combining except that the weights are all
set to unity. The possibility of achieving an acceptable output SNR from a number
of unacceptable inputs is still retained. The performance is marginally inferior to
maximal ratio combining.

CODE
 clc;
 clear all;
 close all;
 N=10^6; %Length of Sequence
 a=randi([0,1],1,N); %random Signal
 b=2*a-1; %BPSK Modulation
 ntx=2;
 snr=0:1:30;
 n=1/sqrt(2)*(randn(1,N)+j*randn(1,N));
 h=1/sqrt(2)*(randn(ntx,N)+j*randn(ntx,N));
 x=[b;b];
 y1=sum(h.*x,1)+(10^(-snr(i)/20)*n);
 y2=sum(h_tx.*x,1)+(10^(-snr(i)/20)*n);
 y_e=y1./sum(h,1);

 d_2=real(y_b)>0;
 end
 n1tx=3;
 x=[b;b;b];
 h3_tx=h3.*exp(-j*angle(h3));
 y3=sum(h3_tx.*x,1)+(10^(-snr(i)/20)*n3);
 y3_b=y3./sum(h3_tx,1);
 d_3=real(y3_b)>0;
 end

 ber=err_1/N;
 ber_b=err_2/N;
 ber_b3=err_3/N;
 figure
 semilogy(snr,ber,'-',snr,ber_b,'*',snr,ber_b3,'+');
 xlabel('SNR');
 ylabel('BER');
 title('diversity of antenna')
 legend('1 antenna',' 2 antenna','3 antenna');
 x = 1; % signal to transmit Eb = 1
 TRIAL = 10000; %number of simulation runs per EbN0 %50000
 for EbN0 = 0:1:20 %dB
 linear_EbN0 = 10^(EbN0/10); nvar = 1/(linear_EbN0); %calculation of N0, remember Eb = 1
 error1 = 0; %set error counter to 0
 for trial = 1:TRIAL % monte carlo trials.. count the errors
 n1 = sqrt(nvar/2)*randn; %noise for the first
 n2 = sqrt(nvar/2)*randn; %noise for the first
 h1 = sqrt(0.5)*abs(randn + j*randn); %rayleigh amplitude 1
 h2 = sqrt(0.5)*abs(randn + j*randn); %rayleigh amplitude 1

 y1 = x*h1+n1; % Signal 1
 y2 = x*h2+n2; % Signal 2
 y_equal = 0.5*(y1+y2);
 %Maximal Ratio combining
 a1 = (abs(h1))^2;
 a2 = (abs(h2))^2;
 y_maximal = x*(a1*h1+a2*h2)+a1*n1+a2*n2;
 %Selection combining
 P1 = chi2rnd(4);
 P2 = chi2rnd(4);
 as1 = P1*(abs(h1))^2;
 as2 = P2*(abs(h2))^2;
 if as1 >= as2
 y_selection = x*(as1*h1)+as1*n1;
 end
 if as1 < as2
 y_selection = x*(as2*h2)+as2*n2;
 end
 if y_equal < 0 %define decision region as 0
 error1 = error1 + 1;
 end
 if y_maximal < 0
 end


 end
 if y_selection < 0
 end
 end
 BER1(EbN0+1) = error1/(TRIAL);
 end
 % plot simulations
 figure
 EbNo=0:1:20; %changed from 10
 mu = 10.^(EbNo./10);
 ber_theory = (1/2)*(1 - sqrt(mu ./ (mu + 1)));
 semilogy(EbNo,BER1,'r*-',EbNo,BER2,'b--o',EbNo,BER3,'c-
o',EbNo,ber_theory,'b'); % plot EG BER vs EbNo
 legend('EG','MR','SC','theory');
 xlabel('EbNo(dB)') %Label for x-axis
 ylabel('Bit error rate') %Label for y-axis

WORKSHOP ON ADVANCED WIRELESS COMMUNICATION SYSTEM.pptx

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