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Assignment 2.Sol (2)

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  THE UNIVERSITY OF WESTERN ONTARIOFACULTY OF ENGINEERINGDEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING SE 410a – WIRELESS LANs AND WANsAssignment # 2 (Solutions)[Rl!s D!t No#$%& ' **+, Su%$ission D!t No#$%& * **+- ./I0 ! 1&o#i2& 3!s * 4lls to 4o#& t3 53ol s&#i4 !&! 5it3 !43 4ll 3!#in6 7*43!nnls 3o5 $!n8 us&s 4!n t3 1&o#i2& su11o&t i0 ! %lo49in6 1&o%!%ilit8 o0 : is &;ui&2< Assu$ t3!t !43 us& $!9s !n !#&!6 o0 t3& 4!lls 1& 3ou& !n2 !43 4!ll 2u&!tion is !n !#&!6 o0 t3& $inuts/ Number of channes!ce 40ffere$ traffic at %S of 2& '0())* Erangs!ce+arrie$ traffic 0(), - '0())* '0('** Erangs!ce.ota traffic carrie$ '0('** - 20 /0*(4 Erangs.raffic Intensit er user '- 3'!/0 0(1 Erang.ota Number of users that can be suorte$ is /0*(4!(1 400 /T5o s&#i4 1&o#i2&s I !n2 II !& 1l!nnin6 to 1&o#i2 4llul!& s&#i4 to !nu&%!n !&!/ P&o#i2& I 3!s * 4lls to 4o#& t3 53ol !&! 5it3 !43 4ll 3!#in67* 43!nnls !n2 1&o#i2& II 3!s '* 4lls !43 5it3 '* 43!nnls/ Ho5 $!n8 us&s4!n % su11o&t2 %8 t3 t5o 1&o#i2&s i0 ! GOS o0 : is &;ui&2< Assu$ t3!t!43 us& $!9s !n !#&!6 o0 t3& 4!lls 1& 3ou& !n2 !43 4!ll l!stin6 !n!#&!6 o0 ' $inuts/ 5R6IDER INumber of channes!ce 40ffere$ traffic at %S of 2& '0())* Erangs!ce+arrie$ traffic 0(), - '0())* '0('** Erangs!ce.ota traffic carrie$ '0('** - 20 /0*(4 Erangs.raffic Intensit er user '- 3'!/0 0(1 Erang.ota Number of users that can be suorte$ is /0*(4!(1 4005R6IDER IINumber of channes!ce '0ffere$ traffic at %S of 2& 21()'2 Erangs!ce+arrie$ traffic 0(), -21()'2 21(4)' Erangs!ce.ota traffic carrie$ 21(4)' - '0 /44(,0 Erangs.raffic Intensit er user '- 3'!/0 0(1 Erang.ota Number of users that can be suorte$ is /44(,0!(1 42),.ota ,7'4, users can be accommo$ate$  '/In ! 4llul!& s8st$ t3 &4i#2 1o5& !t t3 $o%il unit is =>? 2@$/ T3 4llst&u4tu& is ! s#n=4ll &us 1!tt&n/ I0 t3 t3&$!l nois 1o5& is =.* 2@$ !n2Co=C3!nnl Int&0&n4 (CCI) 0&o$ !43 int&0&in6 st!tion is =.. 2@$4!l4ul!t t3 Si6n!l=to=CCI R!tio !n2 t3 o#&!ll Si6n!l=to=Nois R!tio (R!tio o0 &4i#2 si6n!l 1o5& 2i#i22 %8 su$ o0 t3&$!l nois !n2 CCI)/ +on8erting $9m to mW7 :e obtain signa o:er =  s  P   ?/> .* − mW( .hetherma noise o:er thermal   P    .) .* − mW7 ++I 5o:er is CCI   P   ./.) .* − mW3a8era Signa;to;Noise Ratio wer TotalCCIPothermal  Power   signal  Power  + )()( ./.. ?/> .*+.*.* −− ×+= 2*(4, 14(')$93b Signa;to;++I Ratio ./.?/> .*+.* −− ×=   ''(24 1(22 $9 7/An !n!lo6 4llul!& s8st$ 3!s ! tot!l o0 '' MH o0 %!n25i2t3 !n2 uss t5o B9H si$1l 43!nnls to 1&o#i2 0ull 2u1l #oi4 !n2 4ont&ol 43!nnls/ (!) W3!tis t3 nu$%& o0 43!nnls !#!il!%l 1& 4ll 0o& ! 0&;un48 &us 0!4to& o0 (i) 74lls, (ii)  4lls, !n2 (iii) . 4lls< (%) Assu$ t3!t . MH is 22i4!t2 to 4ont&ol43!nnls %ut t3!t onl8 on 4ont&ol 43!nnl is n22 1& 4ll/ Dt&$in !&!son!%l 2ist&i%ution o0 4ont&ol 43!nnls !n2 #oi4 43!nnls in !43 4ll 0o& t3t3& 0&;un48 &us 0!4to&s o0 1!&t (!)/ a( T3 tot!l nu$%& o0 !#!il!%l 43!nnls is  ''***B*  ++*/ Fo& ! 0&;un48 &us 0!4to&  N   !43 4ll 4!n us  K    N   43!nnls/Fo&  N    7  K/N    .+B 43!nnlsFo&  N      K/N  >7 43!nnlsFo&  N    .  K/N  BB 43!nnls b( ' MH is !#!il!%l 0o& #oi4 43!nnls 0o& ! tot!l o0 +7* 43!nnls/Fo&  N    7 5 4!n 3!# .+* #oi4 43!nnls !n2 on 4ont&ol 43!nnl 1& 4llFo&  N     5 4!n 3!# 7 4lls 5it3 >. #oi4 43!nnls !n2 ' 4lls 5it3 > #oi4 43!nnls !n2 on 4ont&ol 43!nnl 1& 4ll/Fo&  N    . 5 4!n 3!# ? 4lls 5it3 B' #oi4 43!nnls !n2 7 4lls 5it3 B7 #oi443!nnls !n2 on 4ont&ol 43!nnl 1& 4ll/B/A tl13on8 4onn4tion 3!s 2u&!tion o0 ' $inuts/ T3is is t3 onl8 4onn4tion$!2 %8 t3is 4!ll& 2u&in6 t3 4ou&s o0 !n 3ou&/ Ho5 $u43 is t3 !$ount o0 t&!00i4 in E&l!n6s o0 t3is 4onn4tion<   32'!/0 0(',' Erangs  +/A 4llul!& s8st$ uss FDMA 5it3 ! s14t&u$ !llo4!tion o0 ./B MH in !432i&4tion ! 6u!&2 %!n2 !t t3 26 o0 t3 !llo4!t2 s14t&u$ o0 .* 9H !n2 !43!nnl %!n25i2t3 o0 '* 9H/ W3!t is t3 nu$%& o0 !#!il!%l 43!nnls< .ota ban$:i$th 12( - 2 < =>%uar$ ban$ 10 - 2 ? =>.herefore7 Number of Due- +hannes 312(-2 < =>;10-2 ?=>!/0 ?=> 20,r7 41/ sime- channes /Consi2& ! =4ll s8st$ 4o#&in6 !n !&! o0 '.** 9$  ) / T3 t&!00i4 in t3 s#n4lls is !s 0ollo5s Cllnu$%& .'7B+T&!00i4(E&l!n6s)'*/?++/7?/+''/'?/'/?'/+E!43 us& 6n&!ts !n !#&!6 o0 */*' E&l!n6s o0 t&!00i4 1& 3ou& 5it3 ! $!n 3ol2in6 ti$ o0 .*s/ T3 s8st$ 4onsists o0 ! tot!l o0 '>B 43!nnls !n2 is 2si6n!t2 0o& ! GOS o0 */*/(i)Dt&$in t3 nu$%& o0 su%s4&i%&s in !43 4ll(ii)Dt&$in t3 nu$%& o0 4!lls 1& 3ou& 1& su%s4&i%& (iii) Dt&$in t3 nu$%& o0 4!lls 1& 3ou& in !43 4ll(i#)Dt&$in t3 nu$%& o0 43!nnls &;ui&2 in !43 4ll(#)Dt&$in t3 tot!l nu$%& o0 su%s4&i%&s(#i)Dt&$in t3 !#&!6 nu$%& o0 su%s4&i%&s 1& 43!nnl(#ii)Dt&$in t3 su%s4&i%& 2nsit8 in 1& 9$  ) (#iii)W3!t is t3 &!2ius o0 !43 4ll<(i) Nu$%& o0 su%s4&i%&s  T&!00i4*/*' Cell number 1 2 3 4 5 6 7Subscribers 1026.7 2223.3 1620.0 1106.7 1273.3 1260.0 1086.7 3ii  Nu$%& o0 4!lls 1& 3ou& 1& su%s4&i%&  */*'(.*'+**)  */> 3iii Multi1l8 &sults o0 1!&t (i) %8 */> Cell number 1 2 3 4 5 6 7Calls per hour 924 2001 1458 996 1146 1134 978 3i8 T3 t!%l in t3 1&o%l$ st!t$nt 6i#s t3 #!lu o0  A / Us  P    */*/ Fin2  N  / Cell number 1 2 3 4 5 6 7Channels 40 78 59 43 48 48 42  38 Tot!l nu$%& o0 su%s4&i%&s  t3 su$ o0 t3 #!lus 0&o$ 1!&t (!)  >B> 38i F&o$ (2) t3 tot!l nu$%& o0 43!nnls &;ui&2  'B?A#&!6 nu$%& o0 su%s4&i%&s 1& 43!nnl  >B>'B?  +/? 38ii Su%s4&i%& 2nsit8  >B>'.**  '/. su%s4&i%&s 1& 9$  38iii Tot!l t&!00i4  t3 su$ o0 t3 #!lus 0&o$ t!%l in t3 1&o%l$ st!t$nt  ?/> 3i- E&l!n6s 1& 9$    ?/>'.**  */*> 3- T3 !&! o0 ! 3!6on o0 &!2ius  R  is  A   1.5  R 2 3 / Fo& A  '.**  77/?+9$  5 3!# R  .' 9$?/A 4llul!& s8st$ 5it3 =4ll 4lust&s 3!s t3 0ollo5in6 !#&!6 nu$%& o0 4!lls !t! 6i#n ti$ Cll nu$%& i A#&!6 nu$%& o0 4!lls 1& unit ti$ (  ) i λ  .>*****'B**7..**B.**+.?**.***I0 t3 s8st$ is !ssi6n2 7> t&!00i4 43!nnls 3o5 5oul2 8ou 2ist&i%ut t3 43!nnl i0 (!)St!ti4 !llo4!tion is us2(%)A si$1l %o&&o5in6 s43$ is us2(4)A 28n!$i4 43!nnl !llo4!tion s43$ is us2 3aDistribute the channes accor$ing to the traffic oa$ of each ceLet ∑ = = D. ii λ λ  ( .hen7 the number of channes aocate$ to ce i  is e@ua to 7> ×= λ λ  ii C  ( .he channe aocation is sho:n beo: Cllnu$%& i A#&!6 nu$%& o0 4!lls 1& unitti$ (  ) i λ   Nu$%& o0 C3!nnls i C  .>**7***>'B**.7..**BB.**+
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