{ "metadata": { "name": "", "signature": "sha256:c0c41dd0dd6cd4e5e80827588fac9665fffcc944b50f6542bc22a982c1d29798" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "CHAPTER 9 - A Basic Cellular System" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.2 - PG NO.315" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 315\n", "n1=17.#\n", "n2=16.#\n", "n3=14.#\n", "n4=12.#\n", "n5=11.#\n", "n6=10.#\n", "n7=7.#\n", "n8=5.#\n", "n9=3.#\n", "n10=2.\n", "t1=51.#\n", "t2=47.#\n", "t3=43.#\n", "t4=39.#\n", "t5=34.#\n", "t6=28.#\n", "t7=22.#\n", "t8=15.#\n", "t9=9.#\n", "t10=6.\n", "\n", "tncphr=n1+n2+n3+n4+n5+n6+n7+n8+n9+n10#no. of calls/hr.\n", "Y=tncphr/60.#rate of calls/min.\n", "toct=t1+t2+t3+t4+t5+t6+t7+t8+t9+t10#total system occupied time in min.\n", "H=toct/tncphr#avg. holding time/call in min\n", "Aav=Y*H\n", "print '%s %.1f %s' %('average traffic intensity Aav is =',Aav,'Erlangs')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "average traffic intensity Aav is = 4.9 Erlangs\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.3 - PG NO.316" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 316\n", "Y=2.#avg. no of calls/hr/user\n", "Hmin=3.\n", "H=Hmin/60.#avg. duration of a call\n", "Aav=Y*H#average traffic intensity\n", "print '%s %.1f %s' %('average traffic intensity per user Aav is =',Aav,' Erlangs')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "average traffic intensity per user Aav is = 0.1 Erlangs\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.4 - PG NO.316" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 316\n", "n1=2200.#\n", "n2=1900.#\n", "n3=4000.#\n", "n4=1100.#\n", "n5=1000.#\n", "n6=1200.#\n", "n7=1800.#\n", "n8=2100.#\n", "n9=2000.#\n", "n10=1580.#\n", "n11=1800.#\n", "n12=900.\n", "TBW=30.*10.**6.#total allocated bandwidth\n", "SBW=25000.#simplex channel bandwidth\n", "NS=TBW/SBW#no.of simplex channels\n", "DS=NS/2.#no.of duplex channels\n", "NCPC=10.\n", "NCPCL=12.\n", "TNCC=NCPC*NCPCL##no. of control channels\n", "TNTC=DS-TNCC#no. of traffic channels\n", "NTCPC=TNTC/NCPCL\n", "NUPC=8.\n", "NMCPC=8.\n", "TNCPC=NMCPC*NTCPC#total no. of calls/cell\n", "print '%s %d %s' %('total no. of calls/cell =',TNCPC,'calls/cell')\n", "H=5./100.*3600.\n", "Y=60./3600.\n", "Aav=H*Y#traffic intensity case(b)\n", "print '%s %d %s' %('average offered traffic load Aav for (case(b)) is =',Aav,'Erlangs')\n", "tc=n1+n2+n3+n4+n5+n6+n7+n8+n9+n10+n11+n12\n", "pbms=75./100.\n", "nbms=pbms*tc\n", "print '%s %.3f %s' %('number of mobile subscribers/cluster = ',nbms*10**(-3),'users')\n", "y=tc/NCPCL\n", "Y1=y/3600.\n", "H1=60.\n", "Aav1=Y1*H1#traffic intensity case(c)\n", "print '%s %d %s' %('average offered traffic load Aav for (case(c)) is =',round(Aav1),'Erlangs')\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total no. of calls/cell = 320 calls/cell\n", "average offered traffic load Aav for (case(b)) is = 3 Erlangs\n", "number of mobile subscribers/cluster = 16.185 users\n", "average offered traffic load Aav for (case(c)) is = 30 Erlangs\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.5 - PG NO.319" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 319\n", "Y=3000./3600.\n", "H=1.76*60.\n", "Aav=Y*H\n", "print '%s %.2f %s' %('offered traffic load Aav is =',Aav,'Erlangs')\n", "Pb=2./100.\n", "N=100.\n", "Y1=28000./3600.\n", "H1=105.6\n", "Aav1=Y1*H1\n", "N1=820.\n", "print '%s %d %s' %('max. no of channels/cell =',N,'channels/cell')\n", "print '%s %d %s' %('max. no of channels/cell wrt increased lambda =',N1,'channels/cell')\n", "#answer in the textbook is less accurate due to approximations. " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "offered traffic load Aav is = 88.00 Erlangs\n", "max. no of channels/cell = 100 channels/cell\n", "max. no of channels/cell wrt increased lambda = 820 channels/cell\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.6 - PG NO.320" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.320\n", "N=50.#no. of channels in cell\n", "Pb=0.02#blocking probability\n", "Aav=40.3#offered traffic load\n", "H=100./3600.#average call-holding time\n", "Y=Aav/H##no. of calls handled\n", "print'%s %d %s' %('no. of calls handled =',Y,'calls/hr')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "no. of calls handled = 1450 calls/hr\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.7 - PG NO.320" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 320\n", "At=0.1\n", "Pb=0.005\n", "N=10.\n", "Aav=3.96\n", "Nt=Aav/At\n", "N1=100.\n", "Aav1=80.9\n", "Nt1=Aav1/At\n", "print '%s %d %s' %('total no. of mobile users =',Nt,'users')\n", "print '%s %d %s' %('total no. of mobile users for increased N =',Nt1,'users')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total no. of mobile users = 39 users\n", "total no. of mobile users for increased N = 809 users\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.8 - PG NO.321" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.321\n", "N=40.#no. of channels in cell\n", "Pb=0.02#blocking probability\n", "Aav=31.#offered traffic load\n", "H=3./60.#holding time\n", "Z=Aav/(H*3.)#users per cell\n", "NC=20.#no. of cells in the system\n", "nms=NC*Z\n", "print'%s %d %s' %('number of mobile subscribers in the system =',nms,'users')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of mobile subscribers in the system = 4133 users\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.9 - PG NO.322" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.322\n", "N1=24.#no. of trunked channels\n", "N=10.#10 channels trunked together\n", "Pb=0.01#blocking probability\n", "Aav=4.46#offered traffic load\n", "N2=5.#2 groups of 5 trunked channels each\n", "Aav1=1.36\n", "Aav2=2.*Aav1\n", "Ex=Aav2/Aav#extent\n", "if Aav>Aav2:\n", " print('10 channels trunked together can support more traffic at a specific GOS(say 0.01) than two 5-channel trunk individually do')\n", "else:\n", " print('10 channels trunked together can support less traffic at a specific GOS(say 0.01) than two 5-channel trunk individually do')\n", "#end\n", "\n", "print'%s %d %s' %('\\nextent of more traffic supported by N=10 system as compared to two 5-channel trunked systems=',Ex*100,'%')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 channels trunked together can support more traffic at a specific GOS(say 0.01) than two 5-channel trunk individually do\n", "\n", "extent of more traffic supported by N=10 system as compared to two 5-channel trunked systems= 60 %\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.10 - PG NO.323" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 323\n", "Nch=395.\n", "ncpcl=7.\n", "Pb=.01\n", "N=Nch/ncpcl\n", "H=3./60.\n", "Aav=44.2\n", "Y=Aav/H\n", "print '%s %d %s' %('average number of calls/hr. i.e(omnidirectional case) Y is =',Y,'calls per hour')\n", "\n", "nspc=3.\n", "Nchps=N/nspc\n", "Aav1=11.2\n", "avnc=Aav1/H\n", "Y1=avnc*nspc\n", "print '%s %d %s' %('average number of calls/hr. ie.(3-sector case) Y is =',Y1+1,'calls per hour')\n", "DTRef=(Y-Y1)/Y\n", "print '%s %.2f %s %d %s' %('decrease in trunking efficiency =',DTRef,'or',(DTRef+0.01)*100,'%')\n", "\n", "nspc1=6.\n", "Nchps1=N/nspc1\n", "Aav2=4.1\n", "avnc1=Aav2/H\n", "Y2=avnc1*nspc1\n", "print '%s %d %s' %('average number of calls/hr. ie.(6-sector case) Y is =',Y2+1,'calls per hour')\n", "DTRef1=(Y-Y2)/Y\n", "print '%s %.2f %s %d %s' %('decrement in trunking efficiency =',DTRef1,'or',DTRef1*100,'%')\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "average number of calls/hr. i.e(omnidirectional case) Y is = 884 calls per hour\n", "average number of calls/hr. ie.(3-sector case) Y is = 672 calls per hour\n", "decrease in trunking efficiency = 0.24 or 24 %\n", "average number of calls/hr. ie.(6-sector case) Y is = 492 calls per hour\n", "decrement in trunking efficiency = 0.44 or 44 %\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.11 - PG NO.325" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 325\n", "Rkm=1.4#radius of the cell\n", "Acell=2.6*Rkm*Rkm#area (hexagonal cell)\n", "K=4.#no.of cells/cluster\n", "ntotal=60.\n", "ncell=ntotal/K\n", "avgtlpu=0.029\n", "Aav=9.\n", "Pb=0.05\n", "tnu=Aav/avgtlpu#total no. of users supported in a cell\n", "NupA=tnu/Acell\n", "print '%s %d %s' %('number of users per kmsqr area =',NupA,'users/(km^2) (approx.)')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of users per kmsqr area = 60 users/(km^2) (approx.)\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.12 - PG NO.327" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.327\n", "Bt=12.5*10.**6.\n", "BtMHz=12.5\n", "Bc=30.*10.**3.\n", "Bg=10.**3.\n", "Nt=(Bt-2*Bg)/Bc#total number of channels/cluster\n", "Nc=21.\n", "Nd=Nt-Nc#number of user data transmission/cluster\n", "K=7.#frequency reuse factor\n", "Ndpcell=Nd/K\n", "Acell=6\n", "n1=Ndpcell/(BtMHz*Acell)\n", "print '%s %d %s' %('total number of channels/cluster (Nt) =',Nt,'channels')\n", "print '%s %d %s' %('number of user data transmission/cluster (Nd) =',Nd,'data channels per cluster')\n", "print '%s %d %s' %('total number of transmission/cell (Nd/cell) if K= 7 is =',Ndpcell,'data channels per cell')\n", "print '%s %.3f %s' %('overall spectral efficiency n1 in channels/MHz/kmsqr for cell area 6kmsqr is =',n1,'channels/MHz/Km^2')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total number of channels/cluster (Nt) = 416 channels\n", "number of user data transmission/cluster (Nd) = 395 data channels per cluster\n", "total number of transmission/cell (Nd/cell) if K= 7 is = 56 data channels per cell\n", "overall spectral efficiency n1 in channels/MHz/kmsqr for cell area 6kmsqr is = 0.754 channels/MHz/Km^2\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.13 - PG NO.327" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.327\n", "Acell=6.\n", "Acellular=3024.\n", "Ncells=Acellular/Acell#number of cells in the system\n", "Bt=12.5*10.**6.\n", "BtMHz=12.5\n", "Bc=30.*10.**3.\n", "Bg=10.*10.**3.\n", "Nc=21.\n", "Nd=((Bt-2.*Bg)/Bc)-Nc#no. of data channels/cluster\n", "K=7.\n", "Ndpcell=Nd/K\n", "H=1./20\n", "ntr=0.95\n", "Ncallphr=1./H\n", "Ncallphrpcell=Ndpcell*ntr*Ncallphr#number of calls per hour per cell\n", "Ncallpuserphr=1.5\n", "Nusers=Ncallphrpcell/Ncallpuserphr\n", "n1=Ndpcell/(BtMHz*Acell)\n", "n=ntr*n1\n", "print '%s %d %s' %('number of cells in the system =',Ncells,'cells')\n", "print '%s %d %s' %('number of calls per hour per cell =',Ncallphrpcell,'calls/hour/cell')\n", "print '%s %d %s' %('average number of users per hour per cell =',Nusers,'users/hour/cell')\n", "print '%s %.3f %s' %('system spectral efficiency in the units of Erlangs/MHz/kmsqr =',n,'Erlangs/MHz/km^2')\n", "#answers in texbook are wrong due to approximations." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of cells in the system = 504 cells\n", "number of calls per hour per cell = 1072 calls/hour/cell\n", "average number of users per hour per cell = 714 users/hour/cell\n", "system spectral efficiency in the units of Erlangs/MHz/kmsqr = 0.715 Erlangs/MHz/km^2\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.14 - PG NO.330" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no.330\n", "Bt=25.*10.**6.#system bandwidth\n", "Bc=30.*10.**3.#channel bandwidth\n", "Bg=20.*10.**3.#guard spacing\n", "Nu=((Bt-2.*Bg)/Bc)\n", "Tf=40.*10.**-3.#frame time\n", "Tp=0.*10.**-3.#preamble time\n", "Tt=0.*10.**-3.#trailer time\n", "Ld=260.\n", "Ls=324.\n", "ntframe=((Tf-Tp-Tt)/Tf)*(Ld/Ls)\n", "ntsys=ntframe*(Nu*Bc*(1./Bt))\n", "Rs=7.95*10.**3.\n", "ntmod=Rs/Bc\n", "K=7.\n", "nt=ntsys*ntmod/K\n", "print '%s %d %s' %('number of simultaneous users that can be accomodated in each cell =',Nu,'users/cluster')\n", "print '%s %.1f' %('spectral efficiency per frame of a TDMA system =',ntframe)\n", "print '%s %.1f' %('spectral efficiency of the TDMA system =',ntsys)\n", "print '%s %.3f %s' %('overall spectral efficiency in bps/Hz/cell =',nt*10,'bps/Hz/cell')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of simultaneous users that can be accomodated in each cell = 832 users/cluster\n", "spectral efficiency per frame of a TDMA system = 0.8\n", "spectral efficiency of the TDMA system = 0.8\n", "overall spectral efficiency in bps/Hz/cell = 0.303 bps/Hz/cell\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "EXAMPLE 9.15 - PG NO.332" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#page no. 332\n", "import math\n", "Bc1=30.*10.**3.#\n", "cimin1=18.\n", "Bc2=25.*10.**3.#\n", "cimin2=14.\n", "Bc3=12.5*10.**3.#\n", "cimin3=12.\n", "Bc4=6.25*10.**3.#\n", "cimin4=9.\n", "Y=4.#path propogation constant\n", "BcI=6.25*10.**3.\n", "cieq1=cimin1+20.*math.log10(Bc1/BcI)\n", "cieq2=cimin2+20.*math.log10(Bc2/BcI)\n", "cieq3=cimin3+20.*math.log10(Bc3/BcI)\n", "cieq4=cimin4+20.*math.log10(Bc4/BcI)\n", "print'%s %.2f %s' %('(C/I)eq in dB for system I =',cieq1,'dB')\n", "print'%s %d %s' %('(C/I)eq in dB for system II =',cieq2,'dB')\n", "print'%s %d %s' %('(C/I)eq in dB for system III =',cieq3,'dB')\n", "print'%s %d %s' %('(C/I)eq in dB for system IV =',cieq4,'dB')\n", "\n", "\n", "if cieq1