path: root/Wireless_Communications_and_Networking_by_V._Garg/ch6.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6: Multiple Access Techniques"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.1, Page 158"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "Area=8;  #in km^2\n",
      "Cover=4000.;# in km^2\n",
      "CallBH=1.2;  #Avg calls during BH\n",
      "HT=100; # Avg holding time in sec\n",
      "Block=0.02; #Blocking=2%\n",
      "N=4.;#Frequency reuse factor\n",
      "Spectrum=12.5;# in MHz\n",
      "CHBW=200;# in kHz\n",
      "User_CH=8;#No of  users per RF channel\n",
      "\n",
      "#Calculations&Results\n",
      "RFCH=Spectrum*1000/CHBW;\n",
      "TCH=int(RFCH)*User_CH;\n",
      "SigCH=3;#No of signalling channels per cell\n",
      "TCH_cell=TCH/N-SigCH;\n",
      "Cells=Cover/Area;\n",
      "OffLoad=108.4;  # in Erlangs\n",
      "print 'Using Erlang-B Tables, Total traffic offered by %d channels at 0.02 blocking = %.1f Erlangs/cell'%(TCH_cell,OffLoad*(1-Block));\n",
      "CarLoad=OffLoad*(1-Block);\n",
      "Calls_hr_cell=CarLoad*3600/HT;\n",
      "MaxUser_hr_cell=Calls_hr_cell/CallBH;\n",
      "Seff=CarLoad*Cells/(Spectrum*Cover);\n",
      "print 'Spectral Efficiency is %.2f Erlangs/MHz/km^2'%Seff;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using Erlang-B Tables, Total traffic offered by 121 channels at 0.02 blocking = 106.2 Erlangs/cell\n",
        "Spectral Efficiency is 1.06 Erlangs/MHz/km^2\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.2, Page 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "TCH=395;  # Traffic Channels\n",
      "SysBW=12.5;  #in MHz\n",
      "CHspace=30.;  # in kHz\n",
      "\n",
      "#Calculations\n",
      "Eff=TCH*CHspace/(SysBW*1000);\n",
      "\n",
      "#Result\n",
      "print 'Multiple access spectral efficiency of FDMA System is %.3f'%Eff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Multiple access spectral efficiency of FDMA System is 0.948\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.3, Page 160"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "Tf=40;  #Frame duration in msec\n",
      "Mt=6;   # Frames per slot\n",
      "Bu=30; #bandwidth(KHz) of an individual user during his or her time slot\n",
      "Nu=395.;#  number of users sharing the same time slot in the system, but having access to different frequency sub-bands\n",
      "Bw=12.5; # in MHz\n",
      "DR=16.2;#Data rate in kbps\n",
      "FDur=40.; # Frame duration in msec\n",
      "slots=6; #No of slots per time frame\n",
      "IndiRate=16.2; #Individual data rate in kbps\n",
      "Srate=13.;  #Speech rate in kbps\n",
      "\n",
      "#Calculations\n",
      "TimeSlot=(Srate/IndiRate)*(FDur/slots);\n",
      "Seff=TimeSlot*slots*Bu*Nu/(FDur*Bw*1000);\n",
      "\n",
      "#Results\n",
      "print 'Multiple access spectral efficiency of TDMA is %.2f'%Seff;\n",
      "print 'The overhead portion of the frame is %d percent'%((1-Seff)*100);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Multiple access spectral efficiency of TDMA is 0.76\n",
        "The overhead portion of the frame is 23 percent\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.4, Page 161"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "nb=0.9; #BW efficiency factor\n",
      "u=2;  # Bit Efficiency with QPSK\n",
      "Vf=1;  # Voice activity factor\n",
      "BW=12.5; #in MHz\n",
      "IR=16.2; # in kbps\n",
      "N=19; #frequency reuse factor\n",
      "\n",
      "#Calculations\n",
      "Nu=nb*u*BW*1000/(Vf*IR*N);# number of channels (mobile users) per cell\n",
      "Seff=int(Nu)*IR/(BW*1000);\n",
      "\n",
      "#Results\n",
      "print 'Capacity of system is %d mobile users per cell'%Nu;\n",
      "print 'Spectral efficiency of TDMA system is %.3f bit/sec/Hz'%Seff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Capacity of system is 73 mobile users per cell\n",
        "Spectral efficiency of TDMA system is 0.095 bit/sec/Hz\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.5, Page 163"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "Nr=2.;# number of reference bursts per frame\n",
      "Nt=24;  # number of traf\ufb01c bursts (slots) per frame(120msec)\n",
      "FL=120;  #Frame length in msec\n",
      "Br=148;  # number of overhead bits per reference burst\n",
      "Bp=34; # number of overhead bits per preamble per slot \n",
      "Bg=8.25;#number of equivalent bits in each guard time interval \n",
      "Tf=120; # frame duration in msec\n",
      "Rrf=270.83333333;  # bit rate of the RF channel in kbps\n",
      "R=22.8;  #bit rate of each channel in kbps\n",
      "\n",
      "#Calculations\n",
      "B0=Nr*(8*Br)+Nt*(8*Bp)+(Nt+Nr)*(8*Bg);#The number of overhead bits per frame\n",
      "Bt=FL*10**-3*Rrf*10**3;#The total number of bits per frame \n",
      "Eff=(1-B0/Bt)*100;\n",
      "CH_Frame=(Eff/100)*Rrf/R;#No of channels/frame\n",
      "\n",
      "#Results\n",
      "print 'The frame efficiency is %.2f percent'%Eff;\n",
      "print 'Number of channels/frame are %d'%(CH_Frame)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The frame efficiency is 67.35 percent\n",
        "Number of channels/frame are 7\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.6, Page 170"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "nb=0.9;#bandwidth ef\ufb01ciency\n",
      "nf=0.45;#frequency reuse ef\ufb01ciency \n",
      "Cd=0.8; #capacity degradation factor \n",
      "Vf=0.4;#voice activity factor \n",
      "Eb_I0=7; # desired energy-to-interference ratio in dB\n",
      "L=1;#  ef\ufb01ciency of sector-antenna in cell \n",
      "BW=12.5;#One way system BW in MHz\n",
      "R=16.2;#Information rate in kbps\n",
      "\n",
      "#Calculations\n",
      "Eb_I=10**(Eb_I0*0.1);#To convert from dB to a normal value\n",
      "Nu=(nf*nb*Cd*L/Vf)*(BW*1000/(Eb_I*R));#Capacity of system\n",
      "Seff=round(Nu)*R/(12.5*10**3);\n",
      "\n",
      "#Results\n",
      "print 'Capacity of system is %d mobile users per cell'%round(Nu);\n",
      "print 'Spectral efficiency of TDMA system is %.3f bits/sec/Hz'%Seff;\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Capacity of system is 125 mobile users per cell\n",
        "Spectral efficiency of TDMA system is 0.162 bits/sec/Hz\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.7, Page 171"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "#Given Data from Exa 6.4 and Exa 6.6\n",
      "Cd=0.8; #capacity degradation factor\n",
      "R=16.2;#Data rate in kbps\n",
      "Eb_I0=7; #in dB\n",
      "Eb_I=10**(Eb_I0*0.1);#To convert from dB to a normal value\n",
      "Vf=0.4;#voice activity factor \n",
      "u=2;  # Bit Efficiency\n",
      "IR=16.2; # in kbps\n",
      "N=19; #frequency reuse factor\n",
      "nf=0.45;#frequency reuse ef\ufb01ciency \n",
      "\n",
      "#Calculations\n",
      "Ncdma_by_Ntdma=Cd*N*nf*IR/(Eb_I*Vf*u*R);\n",
      "\n",
      "#Result\n",
      "print 'The ratio of capacity of DS-CDMA to TDMA is %.3f'%Ncdma_by_Ntdma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The ratio of capacity of DS-CDMA to TDMA is 1.706\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.8, Page 172"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Bss=600;  #Hopping bandwidth in MHz\n",
      "stepsize=400; # in Hz\n",
      "\n",
      "#Calculations\n",
      "No_of_Tones=Bss*10**6/stepsize;\n",
      "Min_chips_required=math.log(No_of_Tones,2);\n",
      "\n",
      "#Result\n",
      "print 'Minimum number of chips required are %d chips'%Min_chips_required"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Minimum number of chips required are 20 chips\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.9, Page 179"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "e=2.71828; #Euler's number\n",
      "Tprop=0.4; #Max propogation delay in sec\n",
      "R=10; #data rate in Mbps\n",
      "PackLen=400; #packet length in bits\n",
      "\n",
      "#Calculations\n",
      "Tp=PackLen/R; #packet transmission time in microsec\n",
      "a=Tprop/Tp;\n",
      "G=Tp*10**-6*R*10**6/PackLen;#normalized offered traf\ufb01c load \n",
      "#Slotted nonpersistent\n",
      "S0=a*G*e**(-a*G)/(1-e**(-a*G)+a);#normalized throughput \n",
      "#Unslotted nonpersistent\n",
      "S1=G*e**(-a*G)/(1+(2*a)+e**(-a*G));#normalized throughput \n",
      "#Slotted 1-persistent\n",
      "S2=G*e**(-G*(1+a))*(1+a-e**(-a*G))/((1+a)*(1-e**(-a*G))+a*e**(-G*(1+a)));#normalized throughput \n",
      "\n",
      "#Results\n",
      "print 'The Normalized throughput with an unslotted non persistent,a slotted persistent and a slotted 1-persistent CSMA protocol are \\n %.3f,%.3f and %.3f respectively'%(S0,S1,S2);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Normalized throughput with an unslotted non persistent,a slotted persistent and a slotted 1-persistent CSMA protocol are \n",
        " 0.496,0.493 and 0.531 respectively\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.10, Page 188"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "Tprop=4;  #maximum propogation delay in sec\n",
      "R=10; # data rate in Mbps\n",
      "PackLen=400.; #data packet length in bits\n",
      "ACK=20;  #length of ACK packet in bits\n",
      "Tproc=1; #processing time(sec)\n",
      "p=0.01;#probability that a data packet or its ACK can be corrupted during transmission\n",
      "\n",
      "#Calculations\n",
      "Tp=PackLen/R; #packet transmission time in microsec\n",
      "Ta=ACK/R; # transmission time for an ACK in microsec\n",
      "T=Tp+2*Tprop+2*Tproc+Ta;# total time for transmission time \n",
      "# Stop and wait ARQ\n",
      "Eff0=(1-p)*Tp/((1-p)*T+p*Tp);\n",
      "#SRP with window size W=8\n",
      "W=8;\n",
      "Eff1=(2+p*(W-1))/(2+p*(3*W-1));\n",
      "#Go-Back-N protocol with window size W=8\n",
      "Eff2=1./(1+W*(p/(1-p)));\n",
      "\n",
      "#Results\n",
      "print 'The data link protocol efficiency with Stop and Wait protocol, SRP and GBN are \\n %.3f, %.3f abd %.3f respectively'%(Eff0,Eff1,Eff2);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The data link protocol efficiency with Stop and Wait protocol, SRP and GBN are \n",
        " 0.763, 0.928 abd 0.925 respectively\n"
       ]
      }
     ],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}