Jkkncet-digital Communication Laboratory-matlab Programs 4j1g4p

JKKNCET/Digital Communication laboratory-MATLAB Programs

Experiment No.1 PHASE SHIFT KEYING (PSK/BPSK) Aim: To generate and demodulate phase shift keyed (PSK) signal using MATLAB

Generation of PSK signal PSK is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). PSK uses a finite number of phases, each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. In a coherent binary PSK system, the pair of signal S1(t) and S2 (t) used to represent binary symbols 1 & 0 are defined by S1 (t) = √2Eb/ Tb Cos 2πfct S2 (t) =√2Eb/Tb (2πfct+π) = - √ 2Eb/Tb Cos 2πfct where 0 ≤ t< Tb and Eb = Transmitted signed energy for bit The carrier frequency fc =n/Tb for some fixed integer n. Antipodal Signal: The pair of sinusoidal waves that differ only in a relative phase shift of 180° are called antipodal signals. BPSK Transmitter

Binary Wave (Polar form)

Product Modulator

BPSK signal

c1 (t) = √2/Tb cos 2πfct

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The input binary symbols are represented in polar form with symbols 1 & 0 represented by constant amplitude levels √Eb & -√Eb. This binary wave is multiplied by a sinusoidal carrier in a product modulator. The result in a BSPK signal. BSPK Receiver: PSK signal X

∫ dt

x

Decision device

Choose ‘1’ if x > 0 Choose ‘0’ if x < 0

c1 (t).

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The received BPSK signal is applied to a correlator which is also supplied with a locally generated reference signal c1 (t). The correlated o/p is compared with a threshold of zero volts. If x> 0, the receiver decides in favour of symbol 1. If x< 0, it decides in favour of symbol 0.

Algorithm Initialization commands PSK modulation 1. 2. 3. 4. 5. 6. 7.

Generate carrier signal. Start FOR loop Generate binary data, message signal in polar form Generate PSK modulated signal. Plot message signal and PSK modulated signal. End FOR loop. Plot the binary data and carrier.

PSK demodulation 1. Start FOR loop Perform correlation of PSK signal with carrier to get decision variable 2. Make decision to get demodulated binary data. If x>0, choose ‘1’ else choose ‘0’ 3. Plot the demodulated binary data.

Program

%

PSK modulation

clc; clear all; close all; %GENERATE CARRIER SIGNAL Tb=1; t=0:Tb/100:Tb; fc=2; c=sqrt(2/Tb)*sin(2*pi*fc*t); %generate message signal N=8; m=rand(1,N); t1=0;t2=Tb for i=1:N t=[t1:.01:t2] if m(i)>0.5 m(i)=1; m_s=ones(1,length(t)); 3


else m(i)=0; m_s=-1*ones(1,length(t)); end message(i,:)=m_s; %product of carrier and message signal bpsk_sig(i,:)=c.*m_s; %Plot the message and BPSK modulated signal subplot(5,1,2);axis([0 N -2 2]);plot(t,message(i,:),'r'); title('message signal(POLAR form)');xlabel('t--->');ylabel('m(t)'); grid on; hold on; subplot(5,1,4);plot(t,bpsk_sig(i,:)); title('BPSK signal');xlabel('t--->');ylabel('s(t)'); grid on; hold on; t1=t1+1.01; t2=t2+1.01; end hold off %plot the input binary data and carrier signal subplot(5,1,1);stem(m); title('binary data bits');xlabel('n--->');ylabel('b(n)'); grid on; subplot(5,1,3);plot(t,c); title('carrier signal');xlabel('t--->');ylabel('c(t)'); grid on;

% PSK Demodulation

t1=0;t2=Tb for i=1:N t=[t1:.01:t2] %correlator x=sum(c.*bpsk_sig(i,:)); %decision device if x>0 demod(i)=1; else demod(i)=0; end t1=t1+1.01; t2=t2+1.01; end %plot the demodulated data bits subplot(5,1,5);stem(demod); title('demodulated data');xlabel('n--->');ylabel('b(n)'); grid on

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Modal Graphs

Result The program for PSK modulation and demodulation has been simulated in MATLAB and necessary graphs are plotted.

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Experiment No.2 FREQUENCY SHIFT KEYING (FSK/BFSK) Aim: To generate and demodulate frequency shift keyed (FSK) signal using MATLAB

Theory Generation of FSK Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the "1" is called the mark frequency and the "0" is called the space frequency. In binary FSK system, symbol 1 & 0 are distinguished from each other by transmitting one of the two sinusoidal waves that differ in frequency by a fixed amount. Si (t) = √2E/Tb cos 2πf1t

0≤ t ≤Tb

0 elsewhere Where i=1, 2 & Eb=Transmitted energy/bit Transmitted freq= ƒi = (nc+i)/Tb, and n = constant (integer), Tb = bit interval Symbol 1 is represented by S1 (t) Symbol 0 is represented by S0 (t)

BFSK Transmitter X

Binary wave (On-Off signaling Form)

c1 (t) = √2/Tb cos 2πƒ1t

+ Σ

Inverter

X

+

FSK signal

c2 (t) = √2/Tb cos 2πƒ2t The input binary sequence is represented in its ON-OFF form, with symbol 1 represented by constant amplitude of √Eb with & symbol 0 represented by zero volts. By using inverter in the lower channel, we in effect make sure that when symbol 1is at the input, The two frequency f1& f2 are chosen to be equal integer multiples of the bit rate 1/Tb.By summing the upper & lower channel outputs, we get BFSK signal. 6


10

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BFSK Receiver

x1 X

Tbƒdt 0

+ x = x1-x2 L Decision E Device choose ‘1’ if x >0

c1 (t) FSK signal T ƒdt X

c2 (t)

x2

choose ‘0’ if x < 0

The receiver consists of two correlates with common inputs which are supplied with locally generated coherent reference signals c1(t) and c2 (t). The correlator outputs are then subtracted one from the other, and the resulting difference x is compared with a threshold of zero volts. If x >0, the receiver decides in favour of symbol 1 and if x <0, the receiver decides in favour of symbol 0. Algorithm Initialization commands FSK modulation 1. 2. 3. 4. 5. 6. 7. 8.

Generate two carriers signal. Start FOR loop Generate binary data, message signal and inverted message signal Multiply carrier 1 with message signal and carrier 2 with inverted message signal Perform addition to get the FSK modulated signal Plot message signal and FSK modulated signal. End FOR loop. Plot the binary data and carriers.

FSK demodulation 1. Start FOR loop 2. Perform correlation of FSK modulated signal with carrier 1 and carrier 2 to get two decision variables x1 and x2. 3. Make decisionon x = x1-x2 to get demodulated binary data. If x>0, choose ‘1’ else choose ‘0’. 4. Plot the demodulated binary data.

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Program % FSK Modulation clc; clear all; close all; %GENERATE CARRIER SIGNAL Tb=1; fc1=2;fc2=5; t=0:(Tb/100):Tb; c1=sqrt(2/Tb)*sin(2*pi*fc1*t); c2=sqrt(2/Tb)*sin(2*pi*fc2*t); %generate message signal N=8; m=rand(1,N); t1=0;t2=Tb for i=1:N t=[t1:(Tb/100):t2] if m(i)>0.5 m(i)=1; m_s=ones(1,length(t)); invm_s=zeros(1,length(t)); else m(i)=0; m_s=zeros(1,length(t)); invm_s=ones(1,length(t)); end message(i,:)=m_s; %Multiplier fsk_sig1(i,:)=c1.*m_s; fsk_sig2(i,:)=c2.*invm_s; fsk=fsk_sig1+fsk_sig2; %plotting the message signal and the modulated signal subplot(3,2,2);axis([0 N -2 2]);plot(t,message(i,:),'r'); title('message signal');xlabel('t---->');ylabel('m(t)');grid on;hold on; subplot(3,2,5);plot(t,fsk(i,:)); title('FSK signal');xlabel('t---->');ylabel('s(t)');grid on;hold on; t1=t1+(Tb+.01); t2=t2+(Tb+.01); end hold off %Plotting binary data bits and carrier signal subplot(3,2,1);stem(m); title('binary data');xlabel('n---->'); ylabel('b(n)');grid on; subplot(3,2,3);plot(t,c1); title('carrier signal-1');xlabel('t---->');ylabel('c1(t)');grid on; subplot(3,2,4);plot(t,c2); title('carrier signal-2');xlabel('t---->');ylabel('c2(t)');grid on; 10


%

FSK Demodulation

t1=0;t2=Tb for i=1:N t=[t1:(Tb/100):t2] %correlator x1=sum(c1.*fsk_sig1(i,:)); x2=sum(c2.*fsk_sig2(i,:)); x=x1-x2; %decision device if x>0 demod(i)=1; else demod(i)=0; end t1=t1+(Tb+.01); t2=t2+(Tb+.01); end %Plotting the demodulated data bits subplot(3,2,6);stem(demod); title(' demodulated data');xlabel('n---->');ylabel('b(n)'); grid on;

11


Modal Graphs

Result The program for FSK modulation and demodulation has been simulated in MATLAB and necessary graphs are plotted.

12


Experiment No.3 SPREAD SPECTRUM COMMUNICATION Aim: To study the spread spectrum communication using MATLAB Theory: Spread spectrum is a digital modulation technology and a technique based on principals of spreading a signal among many frequencies to prevent interference and signal detection. It is a technique to spread the transmitted spectrum over a wide range of frequencies. Direct sequence spread spectrum (DSSS): In Direct sequence spread spectrum (DSSS) each bit in the original signal is represented by multiple bits after signal is transmitted into channel. In this technique when the signal is transmitted spreading code spreads the signal in wider frequency band. When PN bits are generated the number of bits used to represent each original is directly proportional to Number of PN sequence generated and used. In the next section you will see how this process works.

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DSSS Transmitter Example:  Data Input A shown the input original message which is ready to encode or spread by using a PN sequence as illustrated in the above section.  2nd diagram shows the locally generated PN sequence. In this diagram each bit of original message is represented by 4-bits of PN sequence.  Now by Exclusive-Or first and 2nd diagram 3rd signal is obtained simply by Xor between 1 bit of original data with 4 bits of PN sequence.

DSSS Receiver Example:   

On receiver side we received signal which was transmitted from transmitter side. Assume that there is no error or no bit corrupted in the received signals. When signal is received same PN sequence is generated on receiver side, the signal which was generated on transmitted side. Received signal and PN sequence is Xor. By this original Signal is received.

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Frequency Hopping spread spectrum: Frequency hopping spread spectrum is a transmission technology used in wireless networks and a technique to generate spread spectrum by hopping the carrier frequency. FHSS uses narrow band signal which is less than 1 MHz, In this method data signal is modulated with a narrowband carrier signal that "hops" in random and hopping happens in pseudo-random "predictable" sequence in a regular time from frequency to frequency which is synchronized at both ends. Using FHSS technology improves privacy, it is a powerful solution to avoid interference and multi path fading (distortion), it decreases narrowband interference, increases signal capacity, improve the signal to noise ratio, efficiency of bandwidth is high and difficult to intercept also this transmission can share a frequency band with many types of conventional transmissions with minimal interference. For frequency hopping a mechanism must be defined to transmit data in a clear channel and to avoid the congested channels. Frequency hopping is the periodic change of transmission frequency and hopping happens over a frequency bandwidth which consists of numbers of channels. Channel which is used as a hopped channel is instantaneous bandwidth while the hopping spectrum is called total hopping bandwidth. Frequency hopping categorized into slow hopping and fast hopping which by slow hopping more than one data symbol is transmitted in same channel and by fast hopping frequency changes several times during one symbol. Hopping sequence means which next channel to hop; there are two types of hopping sequence: random hopping sequence and deterministic hopping sequence. The focus of this work is on slow and deterministic frequency hopping sequence. In a frequency hopping network, there can be different number of receivers which one sender is designed as Base that is responsible to transmit the synchronization data to the receivers. PROGRAMS: %PN sequence generation %Maximum-length sequence generator %Program to generate Maximum Length Pseudo Noise Sequence clc; %Assign Initial value for PN generator x0= 1; x1= 0; x2 =0; x3 =0; N = input('Enter the period of the signal') for i =1:N x3 =x2; x2 =x1; x1 = x0; x0 =xor(x1,x3); disp(i,'The PN sequence at step') x = [x1 x2 x3]; 15


disp(x,'x=') end m = [7,8,9,10,11,12,13,17,19]; N = 2^m-1; disp('Table Range of PN Sequence lengths') disp('_________________________________________________________') disp('Length of shift (m)') disp(m) disp('PN sequence Length (N)') disp(N) disp('_________________________________________________________') Alternate Method: GENERATION OF PN-SEQUENCE: clear clc G=63; % Code length %Generation of first m-sequence using generator polynomial [45] sd1 =[0 0 0 0 1]; % Initial state of Shift PN1=[]; % First m-sequence for j=1:G PN1=[PN1 sd1(5)]; if sd1(1)==sd1(4) temp1=0; else temp1=1; end sd1(1)=sd1(2); sd1(2)=sd1(3); sd1(3)=sd1(4); sd1(4)=sd1(5); sd1(5)=temp1; end subplot(3,1,1) stem(PN1) title('M-sequence generated by generator polynomial [45]')

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Direct Sequence Spread Spectrum: function DSSS clc PNbit_stream = round(rand(1,32)); input_signal=[0 1 0 0 1 0 1 1]; PNbit_stream for i=1:1:8 for j=1:4:32 for k=1:1:4 a(j)=xor(PNbit_stream(k+j-1),input_signal(i)); a(j); end end end figure(1) stem(PNbit_stream) title('PNbit_stream'); figure(2) stem(input_signal) title('input_signal'); figure(3) stem(a) title('DSSS');

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Model graph:

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Result,

The program for spread spectrum communication has been simulated in MATLAB and necessary graphs are plotted.

19


Experiment No.3 ERROR CONTROL CODING USNG MATLAB

AIM To write a mat lab program for the simulation of error detection implementation of linear block code. APPARATUS REQUIRED MATLAB 7.0.1 Software PROCEDURE 1. Select MATLAB 7.0.1 from Programs menu. 2. Select File-New-M File. 3. Type the program in the new file. 4. Save the file using .m extension. 5. Select debug-run. 6. Any errors if present can be viewed by selecting windows-0 command window. 7. If no error, the signal appears in the screen. 8. The output signal thus viewed. THEORY ERROR DETECTION IMPLEMENTATION OF LINEAR BLOCK CODE INFORMATION ON CYCLIC CODE Cyclic codes are an important sub-class of linear block codes for error detection, where a new codeword in the code can be formed by shifting the elements along one place and taking one off the end and putting it on to the beginning. Instead of being generated by a matrix, a cyclic code is generated by a polynomial so that the codes are sometimes called polynomial codes. Importantly, cyclic codes have a structure that makes it possible for the encoding and decoding to be performed by simple circuitry. Satellite communications systems commonly use cyclic codes. INFORMATION ON CONVOLUTIONAL CODE A convolutional code extends the concept of a block code to allow memory from block to block. Each encoded symbol is therefore a linear combination of information symbols in the current block and a selected number of preceding blocks. Therefore, for example, if the final output is a ‘1’ followed by a ‘0’, then these two digits could only have been arrived at by via a certain sequence of 0s and 1s preceding them. The longer the sequence, the easier it becomes for the receiver to detect where the received sequence deviates from a possible sequence and so correct one or more errors. Decoding of convolutional codes is based on the principle of the Viterbi decoding algorithm or sequential decoding. Satellite communications systems commonly use a convolutional code to protect all data carried on the link. 20


PROGRAM clf; clc; clear all; close all; % Input Generator Matrix g=input('Enter The Generator Matrix: ') disp ('G = ') disp ('The Order of Linear block Code for given Generator Matrix is:') [n,k] = size(transpose(g)) for i = 1:2^k for j = k:-1:1 if rem(i-1,2^(-j+k+1))>=2^(-j+k) u(i,j)=1; else u(i,j)=0; end end end u; disp('The Possible Codewords are :') c = rem(u*g,2) disp('The Minimum Hamming Distance dmin for given Block Code is= ') d_min = min(sum((c(2:2^k,:))')) % Code Word r = input('Enter the Received Code Word:') p = [g(:,n-k+2:n)]; h = [transpose(p),eye(n-k)]; disp('Hammimg Code') ht = transpose(h) disp('Syndrome of a Given Codeword is :') 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:') i disp('The Corrected Codeword is :') r

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OUTPUT Enter The Generator Matrix: [1 0 0 0 1 0 1;0 1 0 0 1 1 1;0 0 1 0 1 1 0;0 0 0 1 0 1 1] g= 1000101 0100111 0010110 0001011 G= The Order of Linear block Code for given Generator Matrix is: n= 7 k= 4 The Possible Codewords are : c= 0000000 0001011 0010110 0011101 0100111 0101100 0110001 0111010 1000101 1001110 1010011 1011000 1100010 1101001 1110100 1111111 The Minimum Hamming Distance dmin for given Block Code is= d_min = 3 Enter the Received Code Word:[1 0 0 0 1 0 0] r= 1000100 22


Hammimg Code ht = 101 111 110 011 100 010 001 Syndrome of a Given Codeword is : s= 001 The Error is in bit: i= 7 The Corrected Codeword is : r= 1000101

RESULT Thus the simulation of MATLAB program for error detection implementation of linear block code was done and verified.

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