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The main aim of this tutorial is introduce a MATRIX LABROTARY (MATLAB) software, pure mathematics calculations, elements and practicalities of computer programming through the MATLAB, to find out the simulation environment and analyse the results to design a simple telecommunication system with the help of MATLAB script by using binary phase shift- keying modulation (BPSK) technique with additive white Gaussian noise(AWGN)channel and also to plot the characteristics .
2.1 INTRODUCTION TO MATLAB:
MATLAB (Matrix Laboratory) is interactive system software. Specially designed for mathematics system computations like we can solving the systems of vectors, linear equations, numerical functions, and Eigen values, matrix operations, scalar functions, Array operations and extra other system problems can be solved the using MATLAB and many other languages compared like system language c, c++, java, Linux and Unix ,java It was developed by Cleve Moller in the late 1970's when he was doing his research in the laboratory. (www.mathworks.co.uk). MATLAB is most commonly used scientific and engineering numerical software. There are number of built in functions that are useful for obtaining different types of operations. Some of the important built in functions which we regularly use are clc, clear, xlabel, ylabel, plot,subplot, legend, rand(), randn(), randint(), grid,sqrt,help, xor(), zeroes, ones.
Clc and Clear both are same function but by using clc function, it will clear the screen but not the data which we have already been given and used for some variables, whereas clear function will clear the hole data from that. X-label and Y-label are used to represent the data on X-axis and Y-axis, plot function is used to plot the graph. Similarly, by using zeroes and ones functions we can get only zeroes or only ones. rand() is used to represent the rows and columns of a matrix, randn( ) generates with negative numbers. Planer Plot is to create x-axis, y-axis for plots plot is nothing but a we can create a graph, subplot is multi full graphical window.
2.2 GENERAL TELECOMMUNICATION SYSTEMS:
The general telecommunication system is to communicate different networks like digital technology, voice and radio frequencies and radar signals. To broadcasting the signals like telephone The prototype of telephone, which is the most typical communication device, is constructed by A.G.Bell in the year 1876, which used a cable based device. Later it was adopted as wireless technology.
2.2(a) BLOCK DIAGRAM OF GENERAL TELECOMMUNICATION SYSTEMS:
DETECTOR Y_det Y=x_mod
NOISE SOURCE n0n0
Where X= Variable signal
X_mod= Modulated signal
n0= Added noise
Y= Demodulated Input and
In the general Telecommunication system, when the random signal passed through the source function it is called has transducer, and now we can get an electrical signal it is passed in to the modulator, it should be under modulation process. A random variable signal 'X' is passed in to the modulator. The output modulator contains 'X_mod' is all passed through the input channel and noise signal all so added to the channel and then output get disturbed. The signal comes in to the -1 and +1 it is called has signal to noise ratio, and the output indicates by 'Y' it is called has demodulator to the original signal comes through demodulated. The demodulator is Y_det is passed through the receiver it should be get an original signal
3.1.1 PSK(PHASE SHIFT KEYING):
Phase shift keying is a digital signal modulation system it is change the data signals, psk is used to the number of phases, it is called to binary digits, it is use to the high noise phase signals, each phase encodes an equal number bits .
3.1.2 BPSK (BINARY PHASE SHIFT KEYING):
Bpsk is all so called Phase Reversal Keying, it is simple to psk, it is used to two phases it separated by 180degrees, psk is use to the high level noise.
3.1.3 QPSK( QUADRATURE PHASE SHIFT KEYING):
The mathematical analysis Qpsk can be used double data rate while compared to the bpsk system while maintain the same bandwidth of the signal, there are phase ambiguity problems at the receiving end.
But here when we assume the general telecommunication system, the most useful method is binary phase shift keying using the concept of phase shift keying.
3.2 BPSK(BINARY PHASE SHIFT KEYING) :
BPSK(Binary Phase Shift Keying),it is used general telecommunication system. Signals are default has been difficult. The digital signal waveform has been changed to the PSK modulating system, when the BPSK signal is transmitting is signal is sinusoid, it is a fixed amplitude To the carry the data signals levels 0(zero)degree or 180degree phase shift keying .When compared with all the other PSK'S,BPSK is the most robust as it has the highest level of noise to show the incorrect values.
3.2(a)BLOCK DIAGRAM OF BPSK:
ADDITIVE WHITE GAUSSIAN NOISE
In this above method, Information source is passed through towards BPSK modulator. The modulator signal modulate in to different voltage levels i.e. level +1 and level -1, generally represented by logic 0 and logic 1respectively.And if these bits passed at the receiver, it gets mixed with noise present in that channel. So, due to this extra additive nature, it is called as Additive White Gaussian Noise. For example The transmission of data from the GMS weather satellite is a BPSK signal, at a carrier frequency of 1.6871 GHz with a 660 kbit/sec data rate. Because of the >200 dB free space loss of the transmitted signal, the received CNR is only a few dB above the minimum value required to demodulate the data with acceptable error rates. To receive these signals, a low cost BPSK demodulator is required, which can accurately demodulate BPSK signals at these low carriers to noise ratios. http://www.jcu.edu.au
4. SOFTWARE SIMULATION:
In the process of simulation first open the Matlab software and go to the work space page in which we type the program .The graphical picture of the work space window is shown below. After typing the program to get the results we use the script window and the required results are obtained.
H:\work space window.png
4.1 FIGURE (a)
3. After typing the program, the result is displayed in the script window which is shown below:
4.1 FIGURE (b)
After substitution of all the values of SNR from SNR=0 to SNR=10, BER values noted down and table is drawn for signal to noise ratio and bit error rate .Using the table, characteristics of the basic telecommunication system is plotted and shown.
5.1 (a) TABULAR COLUMN:
SIGNAL TO NOISE RATIO
BIT ERROR RATE
From the above tabular column drawn between SNR and BER, by varying the values of SNR from SNR=0 to SNR=10, values of BER is decreasing gradually from top to bottom. Now, when we plot a graph between SNR and BER we observe that the curve gradually decreases from top to bottom.
The basic communication system using the BPSK system is designed and simulated using the MATLAB software and the result is obtained for the different values and the graph is plotted the obtained values.
Snr = 0 %signal to noise ratio
x = randiant(1,10000);
x_mod = (x*2)-1;
sig = 10^(-snr/10);
n = randn(1,10000)*sqrt(sig/2);
y = x_mod+n;
y_det = sign(y);
x_est = (y_edt+1)/2;
error = sum(xor(x,x_est));
error = sum(error);
ber = error/10000
snr = [0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5,10,10.5,11]