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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h1> Chpater No 7: PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS<h1>"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15, Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "T=1.0*10**-6 #ms\n",
+ "A=10.0*10**-3\n",
+ "N=1*10**-11\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Eb=((A**2)*T)/2.0\n",
+ "Epb=math.sqrt(Eb/N)\n",
+ "Pb=(1.0/2)*math.erfc(Epb)*(1.0/4)\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Bit error probability = %.2f X 10^-4 \" %(Pb*(10**4)))\n",
+ "print('Approximation error')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Bit error probability = 1.96 X 10^-4 \n",
+ "Approximation error\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.16, Page No 420"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "Br=25*10**6 #bits/sec\n",
+ "N=2*10**-20 #Power spectral density of noise\n",
+ "A=1.0*10**-6\n",
+ "Ps=1*10**-12 # Normalized power\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Tb=1.0/Br\n",
+ "Ps=(A**2)/2.0\n",
+ "Pe=1.0/2*(math.erfc((0.6*Ps*Tb)/N))\n",
+ "#RESULTS\n",
+ "print(\"Average probability of bit error is Pe= %.2f X 10^-4 \" %(Pe*10))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average probability of bit error is Pe= 1.98 X 10^-4 \n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17, Page No 423"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Find probability of error\n",
+ "\n",
+ "#initialisation of variables\n",
+ "A=2.0\n",
+ "N0=2.0*10**-4 #power sepctral density\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Tmin=(6.76*N0)/4\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"The min time for which the signal should be extended is Tmin= %.3f X 10^-3 msec \" %(Tmin*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The min time for which the signal should be extended is Tmin= 0.338 X 10^-3 msec \n"
+ ]
+ }
+ ],
+ "prompt_number": 46
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 428"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#The average carrier\n",
+ "\n",
+ "#initialisation of variables\n",
+ "Pe=10**-4\n",
+ "N0=2*10**10\n",
+ "T=1.0/10**6\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "E=6.76*N0\n",
+ "P=E/T\n",
+ "Eb=8.5171*N0\n",
+ "P2=Eb/T\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"The average carrier = %.3f X 10^-3 mW \" %(P2/10**17))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The average carrier = 1.703 X 10^-3 mW \n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 430"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#The average carrier\n",
+ "\n",
+ "#initialisation of variables\n",
+ "A=0.2*10**-3 #V\n",
+ "T=2*10**-6\n",
+ "N0=2*10**-15\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Pe=(math.sqrt((A**2*T)/4*N0))\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"The average carrier = %.3f X 10^-4 mW \" %(Pe*10**15))\n",
+ "print(\"Approximation error\")"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The average carrier = 6.325 X 10^-4 mW \n",
+ "Approximation error\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 447"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "A=1.0\n",
+ "N0=2.0*10**-5 #power sepctral density\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "T=((3.71**2)*2*N0)/(A**2)\n",
+ "Br=1/T\n",
+ "#Results\n",
+ "print(\"Bit rate Br= %.2f k bits/sec\" %(Br/(10**3)))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Bit rate Br= 1.82 k bits/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 49
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.31, Page No 448"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "Pe=10.0**-4 #probability of error of PSK\n",
+ "N0=2.0*10**-10\n",
+ "Br=10**6 #Bit Rate\n",
+ "\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "T=1.0/Br\n",
+ "E=N0*6.76\n",
+ "P=E/T\n",
+ "Eb=8.5171*N0\n",
+ "Pb=Eb/T\n",
+ "#Results\n",
+ "print(\"i) PSK system The required carrier power = %.2f mW\" %(P*10**3))\n",
+ "print(\"ii) DPSK system The required carrier power = %.2f mW\" %(Pb*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "i) PSK system The required carrier power = 1.35 mW\n",
+ "ii) DPSK system The required carrier power = 1.70 mW\n"
+ ]
+ }
+ ],
+ "prompt_number": 50
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.32, Page No 450"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "A=0.2*10**-3 #V\n",
+ "T=2*10**-6 #Sec\n",
+ "N0=2*10**-15\n",
+ "\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "x=math.sqrt((A**2*T)/(4*N0))\n",
+ "Pe=(1.0/2)*math.erfc(x/math.sqrt(2.0))\n",
+ "\n",
+ "#Results\n",
+ "print(\"Probability of error = %.2f X 10^-4\" %(Pe*10**4))\n",
+ "#print(\"Channel Bandwidth = %.5f MHz\" %BW)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability of error = 7.83 X 10^-4\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.36, Page No 453"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "Ap=1 #mV\n",
+ "En=192.3 #mV\n",
+ "Arms=707 #mV\n",
+ "\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Z=Arms/En\n",
+ "Pe=1.0/2*(math.erfc(math.sqrt(2)*(Z/math.sqrt(2))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"Probability of error is %.7f \" %Pe)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability of error is 0.0000001 \n"
+ ]
+ }
+ ],
+ "prompt_number": 52
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.37, Page No 454"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "Br=2.08*10**-6 #Bit Rate\n",
+ "N0=2*10**-8\n",
+ "\n",
+ "#CALCULATIONS\n",
+ "Eb=(math.sqrt(3.3))/(5*10**7) #Eb=bit energy\n",
+ "Ps=Eb*Br\n",
+ "BW=2*Br #Bandwidth\n",
+ "Es=286.39*N0\n",
+ "Ps2=(Es*Br)/2\n",
+ "BW2=(2*Br)/4\n",
+ "\n",
+ "#Results\n",
+ "print(\"i) BPSK THe transmission bandwidth = %.2f MHz\" %(BW*10**6)) \n",
+ "print(\"ii) For 16 ary PSK THe transmission bandwidth = %.2f MHz\" %(BW2*10**6)) \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "i) BPSK THe transmission bandwidth = 4.16 MHz\n",
+ "ii) For 16 ary PSK THe transmission bandwidth = 1.04 MHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 53
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
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