HHQ+iBQM

6B;m`2 9XR b?Qrb i?2 72KiQ+2HH HBMF `2HB#BHBiv ;BMbi i?2 +?MM2Hb mb;2 `iBQ ρ 7Q` i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2b- r?2`2 dsf = 20 KX AM i?2 };m`2- i?2 72KiQ@iQ@72KiQ BMi2`72`2M+2 bB;MB}+MiHv z2+ib i?2 HBMF `2HB#BHBivX b i?2 +?MM2H mb;2 `iBQ ρ BM+`2b2b- i?2 HBMF `2HB#BHBiv T`Q##BHBiv /2+`2b2b /m2 iQ i?2 BM+`2bBM;

BMi2`72`2M+2 7`QK Qi?2` 72KiQ+2HHbX *QKT`2/ iQ i?2 `M/QK b2H2+iBQM b+?2K2- i?2 /2p2HQT2/ /Bbi`B#mi2/ +?MM2H b2H2+iBQM b+?2K2b ?b #2ii2` HBMF `2HB#BHBivX h?2`2@

7Q`2- ;Bp2M i?2 HBMF `2HB#BHBiv `2[mB`2K2Mi- i?2 /2p2HQT2/ +?MM2H b2H2+iBQM b+?2K2b +M mb2 KQ`2 bm#+?MM2HbX AM i?Bb 2tKTH2- mM/2` i?2 HBMF `2HB#BHBiv `2[mB`2K2Mi Prel ≥ 90W- i?2 KtBKmK HHQr#H2 +?MM2H mb;2 `iBQ Q7 i?2 `M/QK b2H2+iBQM b+?2K2 Bb yX3X h?2 KtBKmK HHQr#H2 +?MM2H mb;2 `iBQ Q7 i?2 /2p2HQT2/ +?MM2H b2H2+iBQM b+?2K2 +M BM+`2b2 iQ yXNX h?2 };m`2 HbQ b?Qrb i?i 7Q`  HQr2` ρ- i?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ b+?2K2 +M +?QQb2 i?2 bm#+?MM2Hb rBi? HQr2` BMi2`@

72`2M+2 iQ BKT`Qp2 i?2 HBMF `2HB#BHBivX >Qr2p2`- rBi?  ?B;?2` ρ- i?2 72KiQ+2HH rBHH mb2

HKQbi HH i?2 bm#+?MM2Hb- M/ i?2 BMi2`72`2M+2 7`QK M2B;?#Q`BM; +MMQi #2 pQB/2/X AM i?Bb bBimiBQM- i?2 ;BM@Q`B2Mi2/ b+?2K2 iQ b2H2+i i?2 bm#+?MM2H rBi? ?B;?2` ;BM +M +?B2p2 ?B;?2` HBMF `2HB#BHBivX

6B;m`2 9Xk b?Qrb i?2 72KiQ+2HH +T+Biv ;BMbi i?2 +?MM2H mb;2 `iBQ ρ BM i?2 2t+HmbBp2 bT2+i`mK b+?2K2- r?2`2 d^sf = 20 KX AM ;2M2`H- b i?2 72KiQ+2HH mb2b KQ`2 /i bm#+?MM2Hb rBi?  H`;2` ρ- i?2 72KiQ+2HH +M T`QpB/2 ?B;?2` +T+BivX LQi2rQ`i?BHv- i?2 +T+Biv 7Q` i?2 ;BM@Q`B2Mi2/ b+?2K2 Bb i?2 +QM+p2 7mM+iBQM Q7 ρX AM i?Bb 2tKTH2- i?2 QTiBKH 72KiQ+2HH +T+Biv Bb RyXd J#Tb i ρ = 0.8X h?Bb Bb #2+mb2 b ρ BM+`2b2b iQ  H`;2` pHm2- i?2 BM+`2bBM; 72KiQ@iQ@72KiQ BMi2`72`2M+2 /2;`/2b HBMF `2HB#BHBiv M/ i?2`2#v /BKBMBb?2b i?2 72KiQ+2HH +T+BivX AM i?Bb };m`2-i?2 T`QTQb2/ +?MM2H b2H2+iBQM b+?2K2b +M +?B2p2 ?B;?2` +T+Biv i?M };m`2-i?2 `M/QK

jj

b2H2+iBQM b+?2K2X 6Q` 2tKTH2- B7 i?2 HBMF `2HB#BHBiv `2[mB`2K2Mi P^rel≥ 90W Bb ;Bp2M-i?2 ;BM@Q`B2Mi2/ +?MM2H b2H2+iBQM b+?2K2 rBi? ρ = 0.8 +M +?B2p2 RdW ?B;?2`

72KiQ+2HH +T+Biv i?M i?2 `M/QK b2H2+iBQM b+?2K2 rBi? ρ = 0.8X h?Bb };m`2 HbQ b?Qrb i?i i?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ +?MM2H b2H2+iBQM b+?2K2 ?b ?B;?2`

72KiQ+2HH +T+Biv 7Q` i?2 +b2 rBi?  HQr2` ρX qBi?  HQr2` ρ- 2+? 72KiQ+2HH QMHv mb2b

 72r2` bm#+?MM2Hb h?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ +?MM2H b2H2+iBQM b+?2K2 +M +?QQb2 i?2 bm#+?MM2Hb rBi? HQr2` BMi2`72`2M+2X AM i?Bb +b2- i?2 HBMF `2HB#BHBiv M/

i?2M i?2 72KiQ+2HH +T+Biv +M #2 BKT`Qp2/X

AM 6B;bX 9XR M/ 9Xk- Bi Bb b?QrM i?i i?2 Jt@JBM M/ Jt@p; K2i?Q/b 7Q` ;BM@Q`B2Mi2/ b+?2K2 ?p2 +QKT`#H2 HBMF `2HB#BHBiv M/ 72KiQ+2HH +T+BivX AM i?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ b+?2K2- i?2 T2`7Q`KM+2 Q7 JBM@Jt K2i?Q/ M/

i?i Q7 JBM@p; K2i?Q/ `2 HKQbi i?2 bK2X

9XjXk GBMF _2HB#BHBiv M/ *T+Biv BM a?`2/ aT2+i`mK H@

HQ+iBQM

6B;m`2 9Xj BHHmbi`i2b i?2 BM/QQ` mb2`Ƕb `2HB#BHBiv T`Q##BHBiv 7Q` p`BQmb +?M@

M2H mb;2 `iBQ ρ- r?2`2 dsf = 20 KX q2 +QMbB/2` i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 M/ irQ@iB2` BMi2`72`2M+2X *QKT`2/ iQ 6B;X 9XR- i?Bb };m`2 b?Qrb i?i i?2 BMi2`72`2M+2 7`QK K+`Q+2HH `2K`F#Hv /2;`/2b i?2 HBMF `2HB#BHBiv Q7 BM/QQ` mb2`X 6Q` 2tKTH2- i?2 HBMF `2HB#BHBiv T`Q##BHBiv 7Q` i?2 `M/QK +?MM2H b2H2+iBQM b+?2K2

i ρ = 0.8 /2+`2b2b #v 3W b i?2 K+`Q+2HH M/ 72KiQ+2HHb b?`2 i?2 bK2 bT2+i`mKX Ai Bb b?QrM i?i i?2 T`QTQb2/ +?MM2H b2H2+iBQM b+?2K2b biBHH +M BKT`Qp2 i?2 HBMF `2@

HB#BHBivX h?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 ?b ?B;?2` HBMF `2HB#BHBivX AM i?2 b?`2/

bT2+i`mK b+?2K2- Bi +M #2 Q#b2`p2/ 7`QK i?2 bBKmHiBQM `2bmHib i?i i?2 K+`Q@iQ@

72KiQ BMi2`72`2M+2 /QKBMi2b i?2 irQ@iB2` BMi2`72`2M+2X aBM+2 i?2 K+`Q+2HH mb2b HH i?2 bm#+?MM2Hb iQ b2`p2 K+`Q+2HH mb2`b- i?2 BMi2`72`2M+2 7`QK K+`Q+2HH +MMQi #2

j9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.86

0.88 0.9 0.92 0.94 0.96 0.98 1

Channel Usage Ratio ρ

Femtocell Link Reliability

random selection scheme

channel gain oriented with MaxMin channel gain oriented with MaxAvg

interference avoidance oriented with MinMax interference avoidance oriented with MinAvg data6

6B;m`2 9XR, GBMF `2HB#BHBiv p2`bmb i?2 +?MM2H mb;2 `iBQ ρ rBi? i?2 2t+HmbBp2 bT2+@

i`mK b+?2K2X

j8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2

3 4 5 6 7 8 9 10 11

Channel Usage Ratio ρ

Femtocell Capacity (Mbps)

random selection scheme

channel gain oriented with MaxMin channel gain oriented with MaxAvg

interference avoidance oriented with minmax interference avoidance oriented with minavg

6B;m`2 9Xk, 62KiQ+2HH +T+Biv p2`bmb i?2 +?MM2H mb;2 `iBQ ρ rBi? i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2X

je

pQB/2/X AM i?Bb bBimiBQM- i?2 ;BM@Q`B2Mi b2H2+iBQM b+?2K2 iQ b2H2+i i?2 bm#+?MM2Hb rBi? ?B;?2` HBMF ;BM +M +?B2p2 #2ii2` HBMF `2HB#BHBivX h?2`27Q`2- mM/2`  HBMF `2@

HB#BHBiv `2[mB`2K2Mi- i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 +M mb2 KQ`2 bm#+?MM2Hb rBi? ?B;?2` 72KiQ+2HH +T+BivX 6Q` 2tKTH2- i?2 +?MM2H mb;2 `iBQ ρ 7Q` i?2 `M@

/QK b2H2+iBQM b+?2K2 b?QmH/ #2 H2bb i?M yXj iQ K22i i?2 HBMF `2HB#BHBiv `2[mB`2K2Mi Prel ≥ 90WX h?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 +M mb2 M2`Hv irB+2 bm#+?MM2Hb 7Q`

/i i`MbKBbbBQMX

6B;m`2 9X9 BHHmbi`i2b i?2 Qmi/QQ` mb2`Ƕb `2HB#BHBiv T`Q##BHBiv 7Q` i?2 p`BQmb MmK#2` Q7 /i bm#+?MM2Hb BM 72KiQ+2HHb- r?2`2 d^sf = 20 KX *QKT`2 iQ i?2 6B;

9Xj- i?Bb };m`2 b?Qrb i?i BMi2`72`2M+2 7`QK 72KiQ+2HHb `2K`F#Hv /2;`/2b i?2 Qmi@

/QQ` HBMF `2HB#BHBivX q?2M 72Ki+Q2HHb BM+`2b2 +?MM2H mb;2 `iBQ ρ- i?2 BMi2`72`2M+2 2z2+i QM i?2 Qmi/QQ` mb2`Ƕb HBMF `2HB#BHBiv bB;MB}+MiHvX h?2`27Q`2- 72KiQ+2HH ?p2 iQ /2+`2b2 i?2 i`MbKBii2/ bm#+?MM2Hb #v  HQr pHm2 7Q` 2Mbm`BM; i?2 K+`Q+2HH mb2`Ƕb HBMF `2HB#BHBiv `2[mB`2K2Mi P^rel ≥ 90WX AM i?Bb +b2- i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 M/ irQ@iB2` BMi2`72`2M+2 `2 +QMbB/2`2/X q2 +QKT`2 /Bz2`2Mi /Bbi`B#mi2/

+?MM2H b2H2+iBQM b+?2K2b M/ /Bz2`2Mi bm#b+`BTiBQM ivT2bX AM i?Bb };m`2- i?2 Pa:

72KiQ+2HH +M HHQr KQ`2 bm#+?MM2Hb 7Q` i`MbKBbbBQM i?M *a: 72KiQ+2HH mM/2` i?2 +QM/BiBQM Q7 i?2 K+`Q+2HH mb2`Ƕb HBMF `2HB#BHBiv `2[mB`2K2MiX q?2M i?2 Qmi/QQ` mb2`b 7+2 iQ i?2 irQ@iB2` BMi2`72`2M+2- i?2 Pa: 72KiQ+2HH +M T`QpB/2  QTTQ`imMBiv iQ +QMM2+i rBi? bi`QM;2` HBMF MQ Kii2` i?2 72KiQ+2HH Q` K+`Q+2HHX >Qr2p2`- B7 Qmi/QQ`

mb2` +?QQb2 i?2 72KiQ+2HH 7Q` +QKKmMB+iBQM- i?2 Qmi/QQ` mb2` ?p2 iQ 7+2 bi`QM;2`

irQ@iB2` BMi2`72`2M+2 i?M BM/QQ` mb2` rBi?Qmi i?2 T`Qi2+i #v i?2 rHHX h?2 *a: 72K@

iQ+2HH +M T`QpB/2 KQ`2 bm#+?MM2H 7Q` i`MbKBbbBQM #v ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2

#2+mb2 i?i +QmH/ KF2b i?2 K+`Q+2HH mb2` i`MbKBi #v /Bz2`2Mi bm#+?MM2H 7`QK Qi?2` 72KiQ+2HHbX JQ`2Qp2`- B7 r2 +QMbB/2` i?2 7+iQ` Q7 /Bbi`B#mi2/ +?MM2H b2H2+iBQM b+?2K2b- r2 +M }M/ Qmi i?2 +?MM2H ;BM M/ BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ b2H2+@

iBQM b+?2K2 T`QpB/2 /Bz2`2Mi T2`7Q`KM+2 iQ Pa: M/ *a: 72KiQ+2HHbX h?2 Pa:

jd

72KiQ+2HH +M T`QpB/2 KQ`2 bm#+?MM2H 7Q` i`MbKBbbBQM #v BMi2`72`2M+2@pQB/M+2@

Q`B2Mi2/ b2H2+iBQM b+?2K2X "2+mb2 i?2 72KiQ+2HHb rBHH +?QQb2 i?2 /Bz2`2Mi bm#+?M@

M2Hb 7`QK i?2 M2B;?#Q`BM; 72KiQ+2HH #v i?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ b2H2+iBQM b+?2K2- i?2 Qmi/QQ` mb2`b ?p2 H2bb BMi2`72`2M+2 r?2M Bi +QMM2+i iQ i?2 72KiQ+2HHX h?Bb };m`2 HbQ b?Qrb i?i i?2 T2`7Q`KM+2 Q7 `M/QK b2H2+iBQM b+?2K2 M/ ;BM@Q`B2Mi2/

b2H2+iBQM b+?2K2 `2 i?2 bK2X 6Q` i?2 Qmi/QQ` mb2`- 2+? BM/QQ` mb2` +?QQb2 i?2B`

?B;?2` HBMF ;BM Bb BM/2T2M/2Mi iQ 2+? Qi?2` M/ iQ i?2 Qmi/QQ` mb2`X h?2`27Q`2-r?2M i?2 BM/QQ` mb2` Bb b2`p2/ #v i?2 72KiQ+2HH rBi? ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2-Bi Bb HQQF HBF2 i?2 `M/QKHv b2H2+iBQM iQ i?2 Qmi/QQ` mb2`bX

6B;m`2 9X8 b?Qrb i?2 72KiQ+2HH +T+Biv 7Q` i?2 p`BQmb MmK#2` Q7 /i bm#@

+?MM2Hb BM i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2- r?2`2 d<sup>sf</sup> = 20 KX Ai Bb b?QrM i?i i?2 K+`Q+2HH@iQ@72KiQ+2HH BMi2`72`2M+2 /2;`/2b i?2 72KiQ+2HH +T+Biv `2K`F@

#HvX aBM+2 i?2 K+`Q+2HH BMi2`72`2b rBi? i?2 72KiQ+2HH- i?2 72KiQ+2HH ?p2 iQ mb2 72r2`

bm#+?MM2Hb iQ 2Mbm`2 HBMF `2HB#BHBivX AM i?Bb bBimiBQM- i?2 BMi2`72`2M+2@pQB/M+2@

Q`B2Mi2/ b+?2K2 Bb T`272``2/- #2+mb2 Bi +M 2z2+iBp2Hv /2+`2b2 BMi2`72`2M+2 M/ BK@

T`Qp2 +T+BivX AM i?Bb +b2- mM/2` i?2 HBMF `2HB#BHBiv `2[mB`2K2Mi P<sup>rel</sup> ≥ 90WX i?2 BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ b+?2K2 7Q` ρ = 0.5 +M +?B2p2 RyjW ?B;?2` +T+Biv i?M i?2 `M/QK b2H2+iBQM b+?2K2 7Q` ρ = 0.3X

9XjXj aT2+i`mK 1{+B2M+v AKT`Qp2K2Mi #v GQ+iBQM r`2@

M2bb

6B;m`2 9Xe b?Qrb i?2 p2`;2 2z2+iBp2 bT2+i`mK 2{+B2M+v ;BMbi i?2 2tBbiBM;

T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH pX 6`QK 6B;X 9X9- r2 FMQr i?i i?2 72KiQ+2HH ?b iQ TQb2 i?2B` +?MM2H mb;2 `iBQ ρ BM  p2`v HQr pHm2 7Q` 2Mbm`BM;

i?2 HBMF `2HB#BHBiv Q7 Qmi/QQ` mb2`b BM i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2X h?2`2@

7Q`2- 2z2+iBp2 bT2+i`mK 2{+B2M+v Q7 i?2 72KiQ+2HHb BM i?2 b?`2/ bT2+i`mK HHQ+iBQM

j3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8

0.82 0.84 0.86 0.88 0.9 0.92 0.94

Channel Usage Ratio ρ

Link Reliability of Indoor User

random selection scheme

channel gain oriented with MaxMin channel gain oriented with MaxAvg

interference avoidance oriented with MinMax interference avoidance oriented with MinAvg

6B;m`2 9Xj, GBMF `2HB#BHBiv Q7 BM/QQ` mb2` p2`bmb i?2 +?MM2H mb;2 `iBQ ρ rBi? i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2X

jN

0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Channel Usage Ratio

Link Reliability of Outdoor User

CSG, random

CSG, channel gain MaxMin CSG, channel gain MaxAvg CSG, interference avoidance MinMax CSG, interference avoidance MinAvg OSG, random

OSG, channel gain MaxMin OSG, channel gain MaxAvg OSG, interference avoidance MinMax OSG, interference avoidance MinAvg

6B;m`2 9X9, GBMF `2HB#BHBiv Q7 Qmi/QQ` mb2` p2`bmb i?2 +?MM2H mb;2 `iBQ ρ rBi? i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2X

9y

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1

2 3 4 5 6 7 8 9

Channel Usage Ratio ρ

Femtocell Capacity (Mbps)

random selection scheme

channel gain oriented with MaxMin channel gain oriented with MaxAvg

interference avoidance oriented with MinMax interference avoidance oriented with MinAvg

6B;m`2 9X8, 62KiQ+2HH +T+Biv p2`bmb i?2 +?MM2H mb;2 `iBQ ρ rBi? i?2 b?`2/

bT2+i`mK HHQ+iBQM b+?2K2X

9R

b+?2K2 `2 Km+? HQr2` i?M i?2 72KiQ+2HH BM i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2X

>Qr2p2`- B7 i?2 72KiQ+2HH ?b i?2 +T#BHBiv Q7 HQ+iBQM r`2M2bb- i?2M i?2 72KiQ+2HH +M `2/m+2 i?2 +?MM2H mb;2 `iBQ ρ QMHv r?2M i?2 72KiQ+2HH MQiB+2 i?2 Qmi/QQ` mb2`b Bb M2`#v i?Bb `2X h?2`27Q`2- i?2 72KiQ+2HH rBi? HQ+iBQM r`2M2bb +T#BHBiv +M KF2 i?2 2z2+iBp2 bT2+i`mK 2{+B2M+v Q7 i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 ?b T`Q##BHBiv ?B;?2` i?M i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2X AM i?Bb };m`2- B7 i?2 72KiQ+2HH ?b i?2 +T#BHBiv Q7 HQ+iBQM r`2M2bb- i?2 2z2+iBp2 bT2+i`mK 2{+B2M+v Q7 i?2 *a: M/ Pa: 72KiQ+2HHb /2+`2b2b b i?2 2tBbiBM; T`Q##BHBiv p BM+`2b2bX

"2bB/2b- i?2 2z2+iBp2 bT2+i`mK 2{+B2M+v Q7 i?2 2t+HmbBp2 bT2+i`mK b+?2K2 ?b i?2 +`Qbb TQBMi rBi? i?i Q7 i?2 b?`2/ bT2+i`mK b+?2K2X h?2 +`Qbb TQBMi +Q``2bTQM/b

M 2tBbiBM; T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` p<sup>∗</sup>X h?i K2Mb i?i i?2 b?`2/ bT2+i`mK b+?2K2 ?b #2ii2` 2z2+iBp2 bT2+i`mK 2{+B2M+v i?M i?2 2t+HmbBp2 bT2+i`mK b+?2K2

b p ≤ p^∗X JQ`2Qp2`- i?2 +`Qbb TQBMib BM 6B;X 9Xe +M #2 +H+mHi2/ b r2 bbmK2 i?2

p2`;2 2z2+iBp2 bT2+i`mK 2{+B2M+v Q7 i?2 b?`2/ bT2+i`mK b+?2K2 2[mHb i?i Q7 i?2 2t+HmbBp2 bT2+i`mK b+?2K2X

SELA = pCsh1+ (1 − p)Csh0

B = SEex = Cex

2B

p=p^∗

U9X3V h?2`27Q`2- i?2 +`Qbb TQBMi Bb +H+mHi2/ b

p^∗ = Csh0− ¹₂Cex

Csh0− Csh1 U9XNV

9XjX9 AKT+ib Q7 GQ+iBQM r`2M2bb QM aT2+i`mK 1{+B2M+v

6B;m`2 9Xd BHHmbi`i2b i?2 bT2+i`mK 2{+B2M+v p2`bmb i?2 72KiQ+2HH /2MbBiv BM /Bz2`2Mi bT2+i`mK HHQ+iBQM b+?2K2b M/ /Bz2`2Mi bm#b+`BTiBQM ivT2bX h?Bb };m`2 b?Qrb i?i r?2M i?2 /2Mb2` Q7 72KiQ+2HHb /2THQvK2Mi- i?2 bT2+i`mK 2{+B2M+v /2+`2b2 /m2 iQ i?2 ?2pB2` BMi2`72`2M+2 7`QK i?2 M2B;?#Q`BM; 72KiQ+2HHbX AM i?2 2t+HmbBp2 bT2+@

i`mK HHQ+iBQM b+?2K2- i?2 2tBbiBM; T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` /Q2b MQi 2z2+i

9k

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Probability of Outdoor User Nearby the Femtocell

Spectrum Efficiency

exclusive−spectrum

shared−spectrum with OSG scheme shared−spectrum with CSG scheme

shared−spectrum with OSG scheme (without location awareness) shared−spectrum with cSG scheme (without location awareness)

6B;m`2 9Xe, aT2+i`mK 2{+B2M+v p2`bmb i?2 72KiQ+2HH /2MbBiv 7Q` b?`2/ M/ 2t+HmbBp2

HHQ+iBQM b+?2K2bX

9j

QM i?2 72KiQ+2HH bT2+i`mK 2{+B2M+v #2+mb2 i?2 Qmi/QQ` mb2` M/ i?2 72KiQ+2HH mb2`

`2 mbBM; i?2 /Bz2`2Mi bT2+i`X q?2M r2 +QMbB/2` i?2 72KiQ+2HH rBi? i?2 +T#BHBiv Q7 HQ+iBQM r`2M2bb BM i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2- i?2 2tBbiBM; T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` 2z2+i QM i?2 72KiQ+2HH bT2+i`mK 2{+B2M+v bB;MB}+MiHvX q?2M r2 bbmK2 i?i i?2`2 `2 MQ Qmi/QQ` mb2`b `QmM/ i?2 72KiQ+2HH `2- i?i K2Mb i?2 72KiQ+2HH +M T`QpB/2 b ?B;?2` +T+Biv b TQbbB#H2 M/ /Q MQi +QMbB/2` i?2 HBMF

`2HB#BHBiv Q7 Qmi/QQ` mb2`X AM i?Bb +b2- i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 +M

+?B2p2 ?B;?2` bT2+i`mK 2{+B2M+v i?M 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2X >Qr@

2p2`- r?2M i?2 2tBbiBM; T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` Bb ?B;?2`- M/ 2Mbm`2 i?2 HBMF

`2HB#BHBiv Q7 Qmi/QQ` mb2`b- i?2 bT2+i`mK 2{+B2M+v BM i?2 b?`2/ bT2+i`mK HHQ+@

iBQM b+?2K2 Bb Km+? HQr2` i?M i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2 MQ Kii2`

i?2 72KiQ+2HH rBi? i?2 +HQb2/ bm#b+`B#2` ;`QmT Q` +HQb2/ bm#b+`B#2` ;`QmTX 6`QK i?2 6B;X 9X9- r2 FMQr i?i 72KiQ+2HHb ?p2 iQ TQb2 i?2 i`MbKBbbBQM bm#+?MM2Hb BM  p2`v HQr pHm2 7Q` 2Mbm`BM; i?2 Qmi/QQ` mb2`Ƕb HBMF [mHBivX h?2`27Q`2- h?2 2tBbiBM;

T`Q##BHBiv Q7 i?2 Qmi/QQ` mb2` Bb  BKTQ`iMi 7+iQ` B7 r2 +QMbB/2` i?2 K+`Q+2HH M/

72KiQ+2HH `2 HHQ+i2/ BM i?2 bK2 bT2+i`mKX

6B;m`2 9X3 BHHmbi`i2b i?2 T`Q##BHBiv Q7 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH p2`@

bmb i?2 72KiQ+2HH /2MbBiv BM /Bz2`2Mi 72KiQ+2HH bm#b+`BTiBQM ivT2bX q?2M i?2 72KiQ+2HH

?b i?2 +T#BHBiv Q7 HQ+iBQM r`2 7mM+iBQM- Bi K2Mb i?i i?2 72KiQ+2HH +M ;2i i?2 BM7Q`KiBQM i?i B7 i?2 Qmi/QQ` mb2`b `2 M2`#v i?2 72KiQ+2HHX h?2 72KiQ+2HH +M T`QpB/2 i?2 ?B;?2bi +T+Biv iQ i?2B` mb2`b B7 i?2`2 Bb MQ Qmi/QQ` mb2` M2`#v M/ `2@

/m+2 i?2 MmK#2` Q7 bm#+?MM2Hb 7Q` i`MbKBbbBQM r?2M i?2 Qmi/QQ` mb2` Bb M2`#v i?2 72KiQ+2HHX h?2b2 HBM2b BM i?2 6B;X 9X3 b?Qr i?i BM r?i T`Q##BHBiv Q7 Qmi/QQ` mb2`

M2`#v i?2 72KiQ+2HH- i?2 b?`2/ bT2+i`mK M/ 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2

?p2 i?2 bK2 bT2+i`mK 2{+B2M+v BM i?2 bK2 /2MbBiv Q7 72KiQ+2HH /2THQvK2MiX h?Bb HBM2b HbQ +mi mT i?2 };m`2 BM i?`22 T`ib M/ i?2b2 T`ib ?2HT mb iQ FMQr r?i Bb i?2 KQ`2 bmBi#H2 HHQ+iBQM b+?2K2 BM 2+? bBimiBQMbX 6Q` 2tKTH2- r?2M r2 FMQrb

99

i?i i?2 /2MbBiv Q7 72KiQ+2HH Bb R8yy 72KiQ+2HHb T2` 1km<sup>2</sup> M/ T`Q##BHBiv Q7 Qmi/QQ`

mb2` M2`#v i?2 72KiQ+2HH Bb eyW- M/ Bi HQ+i2/ BM i?2 mTT2` `2 Q7 i?Bb };m`2- i?2M r2 bm;;2bi i?i 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2 Bb bmBi#H2 #2+mb2 i?2 ?B;?2`

+T+Biv +M #2 +?B2p2 BM i?Bb HHQ+iBQM b+?2K2X JQ`2Qp2`- q?2M r2 FMQrb i?i i?2 72KiQ+2HH /2THQvK2Mi M/ T`Q##BHBiv Q7 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH Bb HQ+i2/

BM i?2 KB//H2 Q` HQr2` `2 Q7 i?Bb };m`2- i?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 +M KF2 Pa: 72KiQ+2HH rBi? #2ii2` bT2+i`mK 2{+B2M+vX >Qr2p2`- r?2M r2 ?p2 iQ mb2 i?2 *a: 72KiQ+2HH BM b?`2/ bT2+i`mK HHQ+iBQM b+?2K2- i?2 72KiQ+2HH /2THQvK2Mi

M/ T`Q##BHBiv Q7 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH Bb HQ+i2/ BM i?2 HQr2` `2 Q7 i?Bb };m`2 +M T`QpB/2 i?2 ?B;?2` +T+Biv i?M 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2X

9X9 *QM+HmbBQMb

AM i?Bb +?Ti2`- r2 /2p2HQT2/ i?2 /Bbi`B#mi2/ +?MM2H b2H2+iBQM T`BM+BTH2 iQ 2M@

bm`2 i?2 HBMF `2HB#BHBiv M/ BKT`Qp2 +T+Biv BM i?2 P6.J@#b2/ 72KiQ+2HH bvbi2KbX q2 +QMbB/2` i?2 BKT+i QM BM/QQ` mb2` M/ Qmi/QQ` mb2` rBi? /Bz2`2Mi bT2+i`mK HHQ@

+iBQMX 6Q` i?2 72KiQ+2HHb- i?2 72KiQ+2HH@iQ@72KiQ+2HH M/ i?2 K+`Q+2HH@iQ@72KiQ+2HH BMi2`72`2M+2 bB;MB}+MiHv /2;`/2 i?2 HBMF `2HB#BHBiv M/ +T+BivX q2 /2p2HQT ;BM@

Q`B2Mi2/ M/ BMi2`72`2M+2@pQB/M+2@Q`B2Mi2/ +?MM2H b2H2+iBQM T`BM+BTH2b iQ BKT`Qp2 +T+Biv M/ HBMF `2HB#BHBivX q?2M r2 `2[m2bi i?2 BM/QQ` mb2` mM/2` i?2 HBMF `2HB#BH@

Biv `2[mB`2K2Mi P^rel ≥ 90W- i?2 bBKmHiBQM `2bmHib b?Qr i?i i?2 /2p2HQT2/ +?MM2H b2H2+iBQM b+?2K2 +M +?B2p2 i KQbi RyjW ?B;?2` +T+Biv i?M i?2 `M/QK b2H2+iBQM b+?2K2X JQ`2Qp2`- 7Q` ;m`Mi22BM; i?2 HBMF [mHBiv Q7 K+`Q+2HH mb2`- 72KiQ+2HHb ?p2 iQ mb2 p2`v HQr `iBQ Q7 bm#+?MM2Hb 7Q` i`MbKBbbBQMX >Qr2p2`- HQ+iBQM r`2M2bb +M ?2HT 72KiQ+2HHb #2 r`2 Q7 i?2 HQ+iBQM Q7 Qmi/QQ` mb2`bX h?2M 72KiQ+2HHb +M

`2/m+2 i?2B` +?MM2H mb;2 `iBQ QMHv r?2M i?2 Qmi/QQ` mb2`b BM i?2 72KiQ+2HHbǶ +Qp@

2`;2X 62KiQ+2HHb +M b2`pB+2 i?2B` mb2` rBi? r?QH2 +T#BHBiv rBi?Qmi BMi2`72`BM; i?2

98

0 500 1000 1500 2000 2500 0.2

0.4 0.6 0.8 1 1.2 1.4 1.6

Number of Femtocell Per 1 km²

Spectrum Efficiency

exclusive−spectrum

OSG fBSs with outdoor user probability = 0 OSG fBSs with outdoor user probability = 1 OSG fBSs with outdoor user probability = 0.2 OSG fBSs with outdoor user probability = 0.5 OSG fBSs with outdoor user probability = 0.8

6B;m`2 9Xd, aT2+i`mK 2{+B2M+v p2`bmb i?2 T`Q##BHBiv Q7 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH BM /Bz2`2Mi HHQ+iBQM b+?2K2bX

9e

0 500 1000 1500 2000 2500 0.2

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Number of Femtocells Per 1 km²

existing probability of the outdoor user

CSG femtocell OSG femtocell

SE _ex =SE _sh

6B;m`2 9X3, S`Q##BHBiv Q7 Qmi/QQ` mb2` M2`#v i?2 72KiQ+2HH p2`bmb i?2 72KiQ+2HH /2MbBivX

9d

M2B;?#Qm` K+`Q+2HH mb2`bX 6m`i?2`KQ`2- 7`QK i?2 pB2rTQBMi Q7 bT2+i`mK 2{+B2M+v-i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM b+?2K2 Bb bmBi#H2 7Q` 2{+B2M+v-i?2 `2 ?pBM; Qmi/QQ` mb2`

rBi? ?B;? T`Q##BHBivX h?2 b?`2/ bT2+i`mK HHQ+iBQM b+?2K2 +M T`QpB/2 i?2 ?B;?2`

bT2+i`mK 2{+B2M+v r?2M i?2 T`Q##BHBiv Q7 b2`pBM; Qmi/QQ` mb2`b Bb HQrX

93

9N

*>Sh1_ 8

MHvbBb Q7 .Bbi`B#mi2/ *?MM2H a2H2+iBQM 7Q` 62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2,

aBM;H2 *``B2` *b2

AM i?Bb +?Ti2`- Qm` ;QH Bb iQ MHvx2 i?2 Qmi;2 Q7 72KiQ+2HH rBi? irQ@iB2`

BMi2`72`2M+2 BM i?2 bBM;H2 +``B2` +b2X "2bB/2b- r2 BMp2biB;i2 i?2 BKT+ib Q7 +?MM2H mb;2 `iBQ M/ i?2 K+`Q+2HH `/Bmb QM i?2 Qmi;2 T`Q##BHBiv Q7 72KiQ+2HH mb2`bX

8XR bbmKTiBQMb

8XRXR am#@+``B2` HHQ+iBQM

h?2`2 `2 irQ KBM +i2;Q`B2b Q7 bm#+?MM2H HHQ+iBQM b+?2K2 BM P6.J

bvbi2Kb, +QMiB;mQmb M/ `M/QKHv /Bbi`B#mi2/ bm#@+``B2` T2`KmiiBQM K2i?Q/X *QM@

iB;mQmb bm#@+``B2` T2`KmiiBQM HHQ+i2b +QMiB;mQmb bm#@+``B2`b BMiQ QM2 bm#+?MM2HX _M/QKHv /Bbi`B#mi2/ bm#@+``B2` T2`KmiiBQM HHQ+i2b MQM@+QMiB;mQmb bm#@+``B2`b /Bbi`B#mi2/ Qp2` i?2 2MiB`2 #M/rB/i? BMiQ bm#+?MM2HbX h?2 Q#D2+iBp2 Q7 `M/QKHv /Bbi`B#mi2/ T2`KmiiBQMb Bb iQ +?B2p2 i?2 BMi2`@+2HH BMi2`72`2M+2 p2`;BM; 7Q` i?2 KQpBM; mb2`bX h?2 +QMiB;mQmb bm#@+``B2` T2`KmiiBQM Bb KQ`2 bmBi#H2 7Q` i?2 }t2/

rB`2H2bb +QKKmMB+iBQMbX 62KiQ+2HH Bb mb2/ 7Q`  bKHH `2 M/ BM/QQ` 2MpB`QMK2Mi

HBF2 +KTmbf+QKKmMBiv 2MpB`QMK2MiX h?2`27Q`2- i?2 +QMiB;mQmb bm#@+``B2` T2`Km@

iiBQM Bb #2ii2` 7Q` i?2 72KiQ+2HH bvbi2Kb rBi? i?2 HQr KQ#BHBiv +QKKmMB+iBQM (k8)X

8XRXk _/BQ *?MM2H

Si? HQbb M/ S2M2i`iBQM GQbb

h?2 Ti? HQbb /2+vb rBi? i?2 T`QT;iBQM /BbiM+2 d #2ir22M i?2 i`MbKBii2`

M/ i?2 `2+2Bp2` (RN- ky)X h?i

Bb-Lpathloss(d) =

⎧⎨

⎩

LF S(d) = 20 HQ;₁₀(^4πd_λ ) , 7Q` d ≤ d<sup>BP</sup> LF S(dBP) + 35 HQ;<sub>10</sub>(<sub>dBP</sub><sup>d</sup> ) , 7Q` d > dBP

, U8XRV

r?2`2 λ Bb i?2 rp2H2M;i? Q7 QT2`iBM; 7`2[m2M+vX h?2 #`2F TQBMi /BbiM+2 Bb dBP = 8 K2i2`b 7Q` i?2 BM/QQ` HBMF M/ jy K2i2`b 7Q` i?2 Qmi/QQ`@iQ@BM/QQ` HBMFX LF S(d) Bb i?2 7`22 bT+2 Ti?HQbbX

h?2 T2M2i`iBQM HQbb Lpenetration Bb bbmK2/ iQ #2 8 /" T2` BMi2`MH rHH 7Q`

BM/QQ` HBMF- M/ Ry /" T2` 2ti2`MH rHH 7Q` Qmi/QQ`@iQ@BM/QQ` HBMFX h?i

Bb-Lpenetration = 5Win+ 10Wout, U8XkV

r?2`2 i?2 Win Bb i?2 MmK#2` Q7 i?2 +`Qbb2/ BMi2`MH rHH- M/ Wout Bb i?2 MmK#2` Q7 i?2 +`Qbb2/ 2ti2`MH rHHX

6`QK U8XRV M/ U8XkV- r2 +M FMQr i?2 Ti?HQbb M/ i?2 T2M2i`iBQM HQbbX h?2`27Q`2- i?2 iQiH HQbb #v i?2 i`MbKBbbBQM Ti? Bb /2}M2/ b

L(d) = Lpathloss(d) + Lpenetration. U8XjV

a?/QrBM;

a?/QrBM; Bb KQ/2H2/ #v  HQ;@MQ`KH `M/QK p`B#H2 10<sup>10ξ</sup> - r?2`2 ξ Bb  :mbbBM /Bbi`B#mi2/ `M/QK p`B#H2 rBi? x2`Q K2MX h?2 biM/`/ /2pBiBQM Bb 8

8y

/" 7Q` i?2 BM/QQ` HBMF #2ir22M i?2 72KiQ+2HH M/ i?2 BM/QQ` mb2`- M/ Ry /" 7Q` i?2 Qi?2` HBMFbX

JmHiBTi? 6/BM; QM am#+?MM2H

_vH2B;? 7/BM; Bb mb2/ BM i?2 Qmi;2 T`Q##BHBiv MHvbBb Q7 72KiQ+2HHb rBi? i?2 irQ@iB2` BMi2`72`2M+2X _vH2B;? 7/BM; +?`+i2`Bx2b i?2 BKT+i Q7 KmHiBTi? T`QT;@

iBQM /Bbi`B#miBQMX h?2 T`Q##BHBiv Q7 /2MbBiv 7mM+iBQM 7Q` _vH2B;? /Bbi`B#mi2/ `M/QK p`B#H2 h b

fh(h) = 2he^−h2. U8X9V

G2i Y = h²X h?2M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Y +M #2 r`Bii2M b

FY(y) = 1 − e^−y. U8X8V

8XRXj aB;MH iQ AMi2`72`2M+2 M/ LQBb2 _iBQ

q2 +QMbB/2` i?2 irQ@iB2` BMi2`72`2M+2 BM+Hm/BM; i?2 72KiQ@iQ@72KiQ- K+`Q@iQ@

72KiQ- 72KiQ@iQ@K+`Q BMi2`72`2M+2X G2i P<sup>k,j</sup> #2 i?2 i`MbKBbbBQM TQr2` Q7 i?2 k@i?

#b2 biiBQM i i?2 j@i? bm#+?MM2H- `2bT2+iBp2HvX a?/QrBM; +M #2 +?`+i2`Bx2/ #v

 HQ;@MQ`KH `M/QK p`B#H210<sup>ξk,j10</sup> - r?2`2 ξ^k,j Bb  :mbbBM `M/QK p`B#H2 QM i?2 j@i? bm#+?MM2H Q7 i?2 k@i? 72KiQ+2HHX h?2 bm#+?MM2H ;BM #2ir22M i?2 k@i? #b2 biiBQM M/ i?2 +QMbB/2`2/ mb2` Bb yk,jX h?2`27Q`2- i?2 `2+2Bp2/ bB;MH TQr2` i i?2 72KiQ+2HH KQ#BH2 i2`KBMH +M #2 r`Bii2M b (Rk- ke- kd)

Pi,j = Pk,j10^ξk,j10 yk,j/L(rk). U8XeV

bbmK2 i?i i?2`2 `2 K #b2 biiBQMb i?i BM+Hm/2 i?2 (K − 1) 72KiQ+2HHb M/

 K+`Q+2HH BM i?2 bvbi2K- H#2H2/ 7`QK k iQ KX G2i i?2 /2bB`2/ mb2` #2 BM/2t2/ rBi?

8R

RX h?2M i?2 iQiH BMi2`72`2M+2 P^Ij `2+2Bp2/ 7`QK i?2 Qi?2` (K − 1) #b2 biiBQMb Q7 bm#+?MM2H j +M #2 2tT`2bb2/ b

PI_j =

K k=2

εk,jPk,j10^ξ/10yk,j/L(rk), U8XdV

r?2`2 ε<sup>j</sup> Bb i?2 miBHBiv 7mM+iBQMX A7 i?2 bm#+?MM2H j Bb b2H2+i2/ iQ i`MbKBi /i-εj = 1c Qi?2`rBb2- εj = 0X

h?2M- i?2 bB;MH@iQ@BMi2`72`2M+2 MQBb2 `iBQ UaAL_V QM i?2 j@i? bm#+?MM2H Q7 i?2 }`bi 72KiQ+2HH +M #2 2tT`2bb b

SINR = P1,j

PI_j + N0, U8X3V

r?2`2 N0 Bb i?2 MQBb2 TQr2`X

8Xk Pmi;2 S`Q##BHBiv Q7 aBM;H2 62KiQ+2HH

q2 +QMbB/2`  b+2M`BQ i?i QMHv  72KiQ+2HH BM i?Bb `2- MQM2 Qi?2` K+`Q+2HH Q` 72KiQ+2HHbX "v b2iiBM; i?2 `2[mB`2/ `2+2Bp2/ i?`2b?QH/ γ^th- i?2 Qmi;2 T`Q##BHBiv +M #2 2tT`2bb2/ b

Poutage

= S`[SNR < γth]

= S`[Pi,j10^ξi,j10 yi,j/L(ri)

N0 < γth]

= S`[yi,j < γthN₀ Pi,j

10^−ξi,j10 L(ri)]

= ∞

−∞

R

0

FY[γthN0

Pi,j10^−ξi,j10 L(ri)]fr_i(ri)fξ(ξ)dridξ

8k

=

8Xj Pmi;2 S`Q##BHBiv Q7 _M/QK *?MM2H a2H2+@

iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2` AM@

i2`72`2M+2

AM i?Bb +b2- r2 +QMbB/2` i?2 irQ@iB2` BMi2`72`2M+2 BM+Hm/BM; i?2 72KiQ@iQ@72KiQ-K+`Q@iQ@72KiQ- 72KiQ@iQ@K+`Q BMi2`72`2M+2X h?2 2z2+i Q7 MQBb2 Kv #2 M2;H2+i2/

UBX2X N0 = 0V BM i?2 BMi2`72`2M+2 HBKBi2/ bvbi2KX h?mb- i?2 Qmi;2 T`Q##BHBiv Q7

`M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b Poutage,random

G2i r = (r2, r₃, ..., rK) M/ ξ = (ξ₂, ξ₃, ..., ξK)X h?2M i?2 Qmi;2 T`Q##BHBiv Q7 `M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b

Poutage,random(r1, ξ1|r, ξ)

8X9 Pmi;2 S`Q##BHBiv Q7 :BM@P`B2Mi2/ *?MM2H a2H2+iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2`

AMi2`72`2M+2

AM a2+iBQMX 9Xk- r2 /2p2HQT i?2 ;BM@Q`B2Mi2/ +?MM2H b2H2+iBQM T`BM+BTH2 7Q`

72KiQ+2HH bvbi2KbX h?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 BKb iQ i`MbKBi /i BM i?2 bm#+?MM2H rBi? ?B;?2` HBMF ;BMX h?Bb b2H2+iBQM b+?2K2 QT2`i2 BM  /Bbi`B#mi2/

KMM2`X 1+? 72KiQ+2HH +M b2H2+i i?2 bm#+?MM2Hb 7Q` i`MbKBbbBQM #v Bib2H7X q2 /2iBH i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2b BM a2+iBQMbX 9XkXR M/ 9XkXkX

89

8X9XR Pmi;2 S`Q##BHBiv Q7 JtBKH GBMF :BM *?MM2H 7Q`

62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2

q2 bbmK2 i?i i?2 ;BM pHm2 Q7 2+? bm#+?MM2H Bb _vH2B;? /Bbi`B#miBQMX _2+HH 1[miBQMb 8X9 M/ 8X8 BM a2+iBQM 8XRXk- r2 +M ?p2 i?2 /Bbi`B#miBQM Q7 `2+2Bp2/

TQr2` Z b i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Z +M #2 r`Bii2M b

fZ(z) = e^−z U8XRkV

FZ(z) = 1 − e^−z. U8XRjV

*QMbB/2` i?i i?2`2 `2 iQiH N bm#+?MM2HbX A7 r2 mb2 QMHv QM2 b2#+?MM2H 7Q` i`MbKBbbBQM- r2 rBHH +?QQb2 i?2 ?B;?2bi HBMF ;BM +?MM2H #v i?2 ;BM@Q`B2Mi2/

b2H2+iBQM b+?2K2X AM i?Bb +b2- H2i Y = max(z1, z2, ..., zN) M/ z1, z2, ..., zN `2 BM/2@

T2M/2Mi M/ B/2MiB+HHv /Bbi`B#mi2/ UBXBX/XV- i?2M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Y +M #2 r`Bii2M b

FY(y) = P {z1 ≤ y, z2 ≤ y, ..., zN ≤ y}

= Fx₁,z₂,...,z_N(y, y, ..., y)

= N i=1

Fz_i(y)

= (1 − e^−y)^N, U8XR9V

M/ i?2 T`Q##BHBiv /2MbBiv 7mM+iBQM Bb 2tT`2bb2/ b fY(y) = d

dyFY(y)

= d

dy(1 − e^−y)^N

= Ne^−y(1 − e^−y)^N−1. U8XR8V

88

6B;m`2 8XR, S`Q##BHBiv /2MbBiv 7mM+iBQM 7Q` i?2 Kt +?MM2H ;BM b2H2+iBQMX

6B;m`2 8X9XR b?Qrb i?i i?2 T`Q##BHBiv /2MbBiv 7mM+iBQM Q7 i?2 KtBKH bm#@

+?MM2H HBMF ;BM b2H2+iBQM 7`QK R bm#+?MM2H- k bm#+?MM2Hb- M/ 9y bm#+?MM2HbX Ai

HbQ BHHmbi`i2b i?i B7 r2 +M +?QQb2 i?2 KtBKH bm#+?MM2H HBMF ;BM 7`QK KQ`2 bm#+?MM2Hb- i?2M i?2 ?B;?2` T`Q##BHBiv r2 +M +?QQb2 i?2 bm#+?MM2H rBi? ?B;?2`

HBMFX

q?2M r2 bbmK2 HH i?2 72KiQ+2HHb rBi? i?2 +T#BHBiv Q7 +?MM2H ;BM b2H2+iBQM 7mM+iBQMX h?2 BMi2`72`2M+2 7`QK K+`Q+2HH M/ 72KiQ+2HHb b?QmH/ #2 +QMbB/2`2/X AM i?Bb BMi2`72`2M+2 HBKBi2/ bvbi2K- i?2 2z2+ib Q7 MQBb2 Kv #2 M2;H2+i2/X h?mb- i?2 Qmi;2 T`Q##BHBiv Q7 KtBKH HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2`

8e

BMi2`72`2M+2 +M #2 r`Bii2M b HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b

Poutage,(1−st)(r1, ξ1|r, ξ)

=

8X9Xk Pmi;2 S`Q##BHBiv Q7 n@i? >B;?2bi GBMF :BM *?MM2H 7Q` 62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2

6Q` i?2 #b2 biiBQM HBF2 72KiQ+2HH- KmHiBTH2 bm#+?MM2Hb `2 mb2/ BM i?2 bK2 iBK2X ++Q`/BM; iQ i?2 ;BM@Q`B2Mi2/ T`BM+BTH2- 72KiQ+2HH mb2b i?2 iQT ?B;?2` bm#@

+?MM2H 7Q` b2M/BM; BM7Q`KiBQMX AM //BiBQM- i?2 iQiH N bm#+?MM2Hb `2 +QMbB/2`2/

BM i?2 72KiQ+2HH bvbi2KX A7 r2 mb2 n bm#+?MM2Hb 7Q` i`MbKBbbBQM- r2 +?QQb2 i?2 R@bi iQ n@i? ?B;?2bi HBMF ;BM +?MM2H #v i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2X AM i?Bb +b2- H2i Y = {y1, y2, ..., yN} #2 i?2 Q`/2` biiBbiB+b Q7 BM/2T2M/2Mi M/ B/2MiB+HHv /Bbi`B#mi2/ UBXBX/XV `M/QK p`B#H2 7`QK (z1, z2, ..., zN) r?2`2 y1 ≤ y2 ≤ ... ≤ yN -i?2M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Yn +M #2 r`Bii2M b

FY_n(y) =

M/ i?2 T`Q##BHBiv /2MbBiv 7mM+iBQM Bb 2tT`2bb2/ b fY_n(y) = N!

(N − n)!(n − 1)!fZ(y)[FZ(y)]^N−n[1 − FZ(y)]ⁿ⁻¹. U8XRNV AM i?Bb +b2- i?2 Qmi;2 T`Q##BHBiv Q7 n@i? ?B;?2bi HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b

Poutage,(n−th)

= S`[P1,j10^ξi,j/10yi,j

?B;?2bi HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b Poutage,(n−th)(r1, ξ1|r, ξ)

=

q2 BMp2biB;i2 i?2 /QrMHBMF Qmi;2 Q7 i?2 P6.J 72KiQ+2HHb #v MHvbBb BM a2+iBQMb 8Xj M/ 8X9X q2 +QMbB/2` i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM M/ i?2 b?`2/

bT2+i`mK HHQ+iBQM b+?2K2b 7Q` i?2 72KiQ+2HHb M/ K+`Q+2HHX h?2 ;BM@Q`B2Mi2/

/Bbi`B#mi2/ +?MM2H b2H2+iBQM b+?2K2 M/ `M/QK b2H2+iBQM b+?2K2 `2 +QMbB/2`2/X q2 bbmK2 i?2 72KiQ+2HH HvQmi b b?QrM BM 6B;X jXRX h?2`2 `2 k9 72KiQ+2HHb `QmM/

i?2 +QMbB/2`2/ 72KiQ+2HH- M/ i?2 ;`QmT Q7 k8 72KiQ+2HHb Bb mMB7Q`KHv /Bbi`B#mi2/

BM  K+`Q+2HH rBi? i?2 +Qp2`;2 Q7 8yy K2i2`bX h?2 b2T`iBQM /BbiM+2b #2ir22M 72KiQ+2HHb `2 d<sup>sf</sup> = 20 K2i2`bX h?2 HBMF `2HB#BHBiv `2[mB`2K2Mi Bb H`;2` i?M NyWX h?2 MQKBMH bvbi2K T`K2i2`b `2 HBbi2/ BM h#H2 9XRX

8X8XR Pmi;2 S`Q##BHBiv BM 1t+HmbBp2 aT2+i`mK HHQ+iBQM

6m;m`2 8Xk b?Qrb i?2 Qmi;2 T`Q##BHBiv Q7 /Bz2`2Mi +?MM2Hb rBi? /Bz2`2Mi

?B;?2bi HBMF ;BM ;BMbi i?2 72KiQ+2HH bm#@+?MM2H mb;2 `iBQ ρ rBi? i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM- r?2`2 dsf = 20 K2i2`bX h?Bb };m`2 b?Qrb i?2 72KiQ+2HH@iQ@

72KiQ+2HH BMi2`72`2M+2 BM i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM bB;MB}+MiHv BKT+ib QM i?2 Qmi;2 T`Q##BHBivX b i?2 bm#+?MM2H mb;2 `iBQ BM+`2b2b- i?2 Qmi;2 T`Q#@

ey

在文檔中 正交分頻多工毫微微細胞系統子載波分配與功率控制之研究 (頁 50-77)