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W K H S U R S R V H G H Q F R G LQ J D Q G G H F R G LQ J V F K H P H V D Q G ZH H [D P LQ H W K H LU S H U IR U P D Q F H LQ ' 6 &' 0$
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ZLU H OH V V F K D Q Q H O P R G H O W K D W ZH X V H LQ
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3 K\VLFDO ( QYLU RQPHQW DQG &KDQQHO 3 DU DPHWHU V
7K H R S H U D W LQ J H Q YLU R Q P H Q W D Q G W K H F K D Q Q H O F R Q G LW LR Q V R I % :
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s 7 HU U DLQ 3 U RpOH 2E V W D F OH V V X F K D V P R X Q W D LQ V K LOOV E X LOG LQ J V ZD OOV D Q G YH K LF OH V OR F D W H G LQ W K H YLF LQ LW \ R I W K H W U D Q V P LW W H U V D Q G W K H U H F H LYH U V D U H U H V S R Q V LE OH IR U W K H U H q H F W LR Q V F D W W H U LQ J D Q G
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R I U D G LR V LJ Q D OV 7K H U H F H LYH G
V LJ Q D OV D U H
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OH YH O ' H S H Q G LQ J R Q W K H G H Q V LW \ R I
W K H X V H U V W K H U D G LX V R I H D F K F H OO F D Q E H OH V V W K D Q P S LF R F H OOV E H W ZH H Q P D Q G NP P LF U R F H OOV D Q G P R U H W K D Q NP P D F U R F H OOV 7\S LF D OO\ LQ F U H D V H G F H OO U D G LX V F R U U H V S R Q G V W R S D W K D U U LYD OV ZLW K OR Q J H U G H OD \V D Q G G H F U H D V LQ J S R ZH U V s )U HTXHQF\ DQG % DQGZLGWK 7K H F D U U LH U IU H TX H Q F \ V LJ Q Lp F D Q W O\ D oH F W V W K H F K D Q Q H O F K D U D F W H U LV W LF V E H F D X V H LW G H W H U P LQ H V W K H S U R S D J D W LR Q U D Q J H W K H ID G LQ J U D W H R I W K H V LJ Q D OV D Q G W K H D E LOLW \ R I U D G LR V LJ Q D OV W R S U R S D J D W H ZLW K R X W / LQ H R I 6 LJ K W / 26 7K H V \V W H P
E D Q G ZLG W K G H W H U P LQ H V W K H U H V R OX W LR Q OH YH O R I W K H P X OW LS D W K F R P S R Q H Q W V
s 8VHU 9HORFLW\ 7K H YH OR F LW \ R I W K H X V H U V W R J H W K H U ZLW K W K H F D U U LH U IU H TX H Q F \ G H W H U P LQ H W K H ID G LQ J U D W H R I W K H V \V W H P + LJ K H U W U D Q V P LW W H U D Q G U H F H LYH U YH OR F LW \ F R U U H V S R Q G V W R ID V W H U ID G LQ J + R ZH YH U D F K D Q Q H O F D Q YD U \ U D S LG O\ H YH Q LQ p [H G V \V W H P V E H F D X V H R I W K H P R YH P H Q W R I R W K H U U H q H F W LQ J R U V F D W W H U LQ J R E MH F W V s $QWHQQDV 7K H D Q W H Q Q D S U R p OH V R I W K H W U D Q V P LW W H U V D Q G U H F H LYH U V D oH F W W K H F K D Q Q H O F K D U D F W H U LV W LF V V LJ Q Lp F D Q W O\ ,Q J H Q H U D O Q D U U R Z D Q W H Q Q D E H D P V U H G X F H W K H Q X P E H U
D Q G W K H G H OD \ R I V LJ Q D O D U U LYD OV % H F D X V H R I W K H F R P S OH [LW \ D Q G W K H OD U J H Q X P E H U R I ID F W R U V D oH F W LQ J U D G LR S U R S D J D W LR Q D G H W H U P LQ LV W LF D S S U R D F K LQ P R G H OLQ J W K H ZLU H OH V V F K D Q Q H O LV Q R W S R V V LE OH ,Q V W H D G V W D W LV W LF D O P R G H OLQ J LV X V H G W R G H V F U LE H W K H P D LQ F K D U D F W H U LV W LF V R I W K H ZLU H OH V V F K D Q Q H OV 7ZR W \S H V R I P R G H OV D U H X V H G W R F D S W X U H W K H ORQJWHU P D Q G W K H VKRU WWHU P W H P S R U D O V S D F LD O YD U LD W LR Q V U H V S H F W LYH O\ / R Q J W H U P
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D Q H W ZR U N OH YH O W R P R G H O W K H D YH U D J H D W W H Q X D W LR Q D Q G W K H U H IR U H U H F H LYH G V LJ Q D O S R ZH U 7K H D YH U D J H S R ZH U D W W H Q X D W LR Q $ G R I W K H V LJ Q D OV LV G X H W R S U R S D J D W LR Q SDWKORVV D Q G VKDGRZLQJ D Q G F D Q E H P R G H OH G D V $ G
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S H U IH F W S R ZH U F R Q W U R O D Q G ZH LJ Q R U H W K H H oH F W R I D W W H Q X D W LR Q E \ V H W W LQ J $ G 6 K R U W W H U P
W H P S R U D O V S D W LD O YD U LD W LR Q V D U H G X H W R W K H V X S H U S R V LW LR Q R I D OD U J H Q X P E H U
R I ZD YH V ZLW K U D S LG O\ F K D Q J LQ J S K D V H V D Q G W R D OH V V H [W H Q W D P S OLW X G H V ZK LF K F R U U H V S R Q G W R H D F K U H V R OYH G S D W K D U U LYD O 7K H S K D V H R I H D F K ZD YH F D Q E H YH U \ G LoH U H Q W H YH Q IR U U D Q G R P P R YH P H Q W V R I W K H R U G H U R I D ZD YH OH Q J W K 7K LV LP S OLH V W K D W H D F K U H V R OYH G S D W K D U U LYD O ZK LF K U H V X OW V IU R P
W K H LU V X S H U S R V LW LR Q F D Q E H P R G H OH G D V D U D Q G R P
W K H OD U J H Q X P E H U R I ZD YH V W K H F H Q W U D O OLP LW W K H R U H P UD Q G R P
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K H Q W K H U H LV D G H W H U P LQ LV W LF F R P S R Q H Q W D V LV W \S LF D O LQ W K H S U H V H Q F H
R I / 26 W K H P H D Q V R I W K H *D X V V LD Q S U R F H V V H V D U H G LoH U H Q W W K D Q ] H U R D Q G W K H LU P D J Q LW X G H LV 5 LF H G LV W U LE X W H G 7K H V H F K D Q Q H OV D U H F K D U D F W H U L] H G D V 5 LFHDQ IDGLQJ $ Q R W K H U G LV W U LE X W LR Q K D YLQ J 5 D \OH LJ K D Q G 5 LF H D V V S H F LD O F D V H V LV W K H 1 D ND J D P LP
G LV W U LE X W LR Q D Q G LW F D Q E H
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V \V W H P V R S H U D W LQ J LQ W K H P P ZD YH E D Q G
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U H p Q H W K H U H V X OW V ZK H Q D S S OLH G W R V S H F Lp F % :
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W K H G H OD \ YD U LD E OH V H W W LQ J W K H W LP H YD U LD E OH W R D F R Q V W D Q W LV H V V H Q W LD OO\
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70
80
90
100
0 −1
−2 0
10
20
30
40 50 60 Number of symbol
70
80
90
100
−2 0
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b
ID V W ID G LQ J
7K H H V W LP D W LR Q H U U R U YD U LD Q F H LV F D OF X OD W H G LQ D Q LW H U D W LYH ZD \ (O Q
)
(O Q b K AG Q b (O Q b O
)LJ X U H J LYH V D Q H [D P S OH R I D U H D OL] D W LR Q R I W K H F K D Q Q H O X V LQ J W K H P R G H O R I D Q G R I W K H F K D Q Q H O H V W LP D W LR Q S U R F H V V X V LQ J W K H . D OP D Q H V W LP D W R U /0
6 ( VWLPDWRU 7K H / 06 H V W LP D W R U F D OF X OD W H V W K H H V W LP D W H V R I W K H F K D Q Q H O E \
P LQ LP L] LQ J W K H 06 (
A O Q GA O Q M J 7K H Q H Z F K D Q Q H O H V W LP D W H D W W LP H (IMUO Q b K
Q X V LQ J LQ IR U P D W LR Q D YD LOD E OH X S W R W LP H Q LV A O Q K ZK H U H O
A O Q z A O Q GA O Q @GA e Q K a >UO Q b K O
1V D Q G z a ! LV W K H V W H S V L] H R I W K H / 06 D OJ R U LW K P
5/6 ( VWLPDWRU 7K H 5 / 6 H V W LP D W R U F D OF X OD W H V W K H H V W LP D W H V R I W K H F K D Q Q H O E \ P LQ LP L] LQ J W K H F R V W IX Q F W LR Q
3Q
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A O Q >UO Q b K A O Q GA O Q @. e Q K O
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Estimation Error Variance vs SNR (Nu=64,Ns=64) Estimation Error Variance vs Fading Rate (Nu=64,Ns=64)
0.4
0.25
0.35 SNR=17 dB SNR=15 dB SNR=13 dB simulation (SNR=15 dB)
0.2
Estimation Error Variance
Estimation Error Variance
0.3
0.25 ωdT=10−4
0.2
−3
ωdT=10
ωdT=10−2 −1
ωdT=10
0.15
simulation
0.15
0.1
0.1 0.05
0.05
0 4
6
8
10 12 SNR (dB)
14
16
18
0 −4 10
−3
10
−2
Fading Rate ωdT
10
−1
10
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A O Q LV D OV R ] H U R P H D Q *D X V V LD Q D Q G LW V YD U LD Q F H (O Q F D Q KO Q b K
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ZK H U H LW F D Q E H V H H Q W K D W W K H H U U R U YD U LD Q F H
G H S H Q G V R Q W K H G D W D YH F W R U E Q b W K U R X J K W K H W H U P W K LV G H S H Q G H Q F \ D Q G W R R E W D LQ D TX D V LV W H D G \ IR U P WH UP
GO Q b ,Q R U G H U W R H OLP LQ D W H
R I H TX D W LR Q ZH D S S U R [LP D W H W K H
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b
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G H W H F W R U V $ F F R U G LQ J
W R W K H p U V W IR U P W K H F K D Q Q H O F R H r F LH Q W V KO Q D U H H [S OLF LW O\ H V W LP D W H G X V LQ J R Q H R I W K H P H W K R G V G H V F U LE H G LQ 6 H F W LR Q D Q G W K H Q W K H P D W U L[ : Q LV F D OF X OD W H G E \ X V LQ J A O Q LQ V W H D G R I KO Q LQ D Q G $ F F R U G LQ J W R W K H V H F W K H F K D Q Q H O H V W LP D W H V K R Q G IR U P D Q G D U H V R OYH G LQ D Q D G D S W LYH P D Q Q H U X V LQ J W K H / 06 D Q G 5 / 6 D OJ R U LW K P V ,Q W K LV F D V H W K H D G D S W LYH 006 ( S H U 8 V H U D OJ R U LW K P /0
6 $OJRU LWKP 7K H / 06 D OJ R U LW K P
W D NH V W K H IR OOR ZLQ J IR U P
H V W LP D W H V W K H V R OX W LR Q ZK LF K P LQ LP L] H V W K H
06 ( (IN E Q b : Q U Q N J 7K H Q H Z H V W LP D W H D W W LP H Q X V LQ J LQ IR U P D W LR Q D YD LOD E OH X S W R W LP H Q LV : Q
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3Q
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D W W LP H Q X V LQ J LQ IR U P D W LR Q D YD LOD E OH X S W R W LP H Q LV : Q
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+
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K D V E H H Q V X J J H V W H G LQ > @ D Q G
> @ D OW K R X J K Q R S H U IR U P D Q F H U H V X OW V ZH U H J LYH Q ,Q W K H U H V W R I W K LV F K D S W H U ZH ZLOO IR F X V R Q W K H S H U IR U P D Q F H R I W K H 006 ( S H U &D U U LH U G H W H F W R U ZLW K H [S OLF LW D G D S W LYH F K D Q Q H O H V W LP D W LR Q D Q G R Q W K H D G D S W LYH 006 (
S H U 8 VH U
G H W H F W R U G H V F U LE H G LQ D Q G 7K H U H D V R Q LV W K D W W K H D G D S W LYH 006 ( S H U 8 V H U
LV W R R F R P S OH [ W R E H LP S OH P H Q W H G
X V LQ J H [S OLF LW F K D Q Q H O H V W LP D W LR Q V LQ F H LW LQ YR OYH V
D Q 1V [1V P D W U L[ LQ YH U V LR Q D Q G P X OW LS OLF D W LR Q LQ H D F K V \P E R O S H U LR G 7K H U H IR U H LW LV Q H F H V V D U \ W R F D OF X OD W H W K H 1X [1V P D W U L[ : Q X V LQ J W K H / 06 R U 5 / 6 D OJ R U LW K P 2Q W K H R W K H U K D Q G W K H 006 ( S H U F D U U LH U G H W H F W R U F D Q E H H D V LO\ LP S OH P H Q W H G D G D S W LYH O\ E \ X V LQ J H [S OLF LW F K D Q Q H O H V W LP D W H V LQ
W K H H [D F W H [S U H V V LR Q
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LQ YR OYH V R Q O\ LQ YH U V LR Q D Q G P X OW LS OLF D W LR Q R I 1V V F D OD U V
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,Q W K LV V H F W LR Q ZH J LYH V H YH U D O Q X P H U LF D O D Q G V LP X OD W LR Q U H V X OW V W K D W LOOX V W U D W H W K H S H U IR U P D Q F H R I W K H S U R S R V H G D G D S W LYH 0&&' 0$ G H W H F W R U V : H H [D P LQ H W K H S H U IR U P D Q F H R I W K H 725 & G H W H F W R U E \ H YD OX D W LQ J H [S U H V V LR Q IR U W K H S U R E D E LOLW \ R I H U U R U D Q G E \ S U H V H Q W LQ J V LP X OD W LR Q U H V X OW V ZK LF K G H P R Q V W U D W H F OR V H D J U H H P H Q W ZLW K W K H W K H R U H W LF D OO\ S U H G LF W H G S H U IR U P D Q F H : H S U H V H Q W S H U IR U P D Q F H U H V X OW V R I W K H G LoH U H Q W D G D S W LYH 006 (
G H W H F W R U V P D NH F R P S D U LV R Q V ZLW K W K H 725 & G H W H F W R U D Q G H [D P LQ H W K H S H U IR U
P D Q F H V H Q V LW LYLW \ W R W K H F K R LF H R I D G D S W D W LR Q S D U D P H W H U V )LQ D OO\ ZH S U H V H Q W D G LV F X V V LR Q ZK LF K F R P S D U H V W K H G H F LV LR Q G LU H F W H G D Q G S LOR W D LG H G D S S U R D F K H V D Q G H [S OR U H V W K H W U D G H R oV E H W ZH H Q F K D Q Q H O H V W LP D W LR Q R YH U K H D G D Q G S H U IR U P D Q F H ,Q D OO F D V H V ZH Q R U P D OL] H W K H F K D Q Q H O F R H r F LH Q W V V R W K D W (IMKO Q M J
( [F H S W ZK H U H W K H -D NH V P R G H O LV V S H F Lp H G W K H F K D Q Q H O P R G H O G H V F U LE H G X V H G LQ W K H V LP X OD W LR Q V D Q G W K H Q E H F R P H V K b )
LQ
LV
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U H IH U V W R
W K H G H p Q LW LR Q LQ ,W LV R E YLR X V W K D W LQ R U G H U W R NH H S D F R Q V W D Q W U H IH U H Q F H LQ W K H G H p Q LW LR Q R I 6 1 5 W K H YD U LD Q F H K V K R X OG E H YD U LH G D F F R U G LQ J O\ D V )
HbG 7 F K D Q J H V IR U
G LoH U H Q W ID G LQ J U D W H V G 7 ,Q R U G H U W R G H P R Q V W U D W H W K H YD OLG LW \ R I R X U E D V LF D V V X P S W LR Q V ZH S U H V H Q W D V \V W H P G H V LJ Q H [D P S OH ZLW K R X W K R ZH YH U U H V W U LF W LQ J W K H V F R S H R I R X U U H V X OW V W R W K H V S H F Lp F G H V LJ Q
BER vs SNR (Nu=64, Ns=64, Threshold 0.09)
0
10
−1
10
−2
BER
10
−3
10
theoretical known channel Kalman (ωdT=10−3 ) Kalman (ω T=10−2 ) d Kalman (ωdT=10−1 )
−4
10
6
8
10
12
14
16
SNR
)LJ X U H 3 H U IR U P D Q F H R I 725 & G H W H F W R U ZLW K . D OP D Q H V W LP D W LR Q D V D IX Q F W LR Q R I 6 1 5 $ V V X P H W K D W D Q 0&&' 0$ V \V W H P IU H TX H Q F \ I& 1
G H V LJ Q X V H V W K H IR OOR ZLQ J TX D Q W LW LH V F H Q W U D O F D U U LH U
*+ ] W R W D O E D Q G ZLG W K %:
0+ ] W R W D O Q X P E H U R I V X E F K D Q Q H OV
D Q G W K H Q X P E H U R I V LP X OW D Q H R X V X V H U V \P E R OV z y ZK LF K D OOR ZV IR U 1V x
,Q S U D F W LF H z ZR X OG E H V OLJ K W O\ V P D OOH U W R D OOR Z IR U R U X Q P R G X OD W H G F D U U LH U V W R E H X V H G D J D LQ V W IU H TX H Q F \ D OLD V LQ J D W W K H U H F H LYH U 7K H V X E F K D Q Q H O V S D F LQ J LV W K H Q c I
. + ] D Q G W K H V \P E R O G X U D W LR Q 7E
zV H F F R K H U H Q F H E D Q G ZLG W K c I
zV H F : H D OV R D V V X P H W K H G H OD \ V S U H D G LV 7P F
. + ] D Q G X VH U VS H H G V D UH X S WR Y
NP K
: H Q R W LF H W K D W W K LV G H V LJ Q D OOR ZV IR U W K H IU H TX H Q F \ LQ W H U OH D YH G F K LS V F R U U H V S R Q G LQ J W R H D F K
X V H U V \P E R O W R E H W U D Q V P LW W H G
WK UR X J K
D S S U R [LP D W H O\ LQ G H S H Q G H Q W O\ ID G H G
F K D Q Q H OV z 7E ! 7P D Q G IR U D U H D V R Q D E OH J X D U G LQ W H U YD O R YH U K H D G R I zV H F 7K H ' R S S OH U V K LIW R I W K H O
1 V X E F D U U LH U R I W K H V \V W H P
7
VX E
LV J LYH Q E \ I'O
I& O b 1 c I Y F 6 LQ F H W K H G LoH U H Q F H LQ W K H ID G LQ J U D W H H [S H U LH Q F H G E \ D Q \ W ZR V X E F K D Q Q H OV LV D W P R V W
1 bI I' ' I'
} LW LV U H D V R Q D E OH W R D V V X P H W K D W D OO
BER vs Threshold (Nu=64, Ns=64, SNR=15 dB)
0
10
−1
10
−2
BER
10
−3
10
theoretical known channel Kalman (ω T=10−3 ) d Kalman (ωdT=10−2 ) Kalman (ωdT=10−1 )
−4
10
0
0.05
0.1
0.15
0.2 Threshold
0.25
0.3
0.35
0.4
)LJ X U H 725 & G H W H F W R U S H U IR U P D Q F H ZLW K . D OP D Q H V W LP D W LR Q D V D IX Q F W LR Q R I K7 +5 V X E F K D Q Q H OV H [S H U LH Q F H D S S U R [LP D W H O\ W K H V D P H ID G LQ J U D W H )R U Y x NP K K D YH c W
F
ZH
7 y D Q G W K H U H IR U H LW LV U H D V R Q D E OH W R D V V X P H W K D W W K H F K D Q Q H O U H P D LQ V
D S S U R [LP D W H O\ F R Q V W D Q W G X U LQ J R Q H 0& V \P E R O S H U LR G 7K H S H U IR U P D Q F H D Q D O\V LV R I W K H 725 & G H W H F W R U LQ 6 H F W LR Q S U R YLG H V LQ V LJ K W LQ W R W K H P H F K D Q LV P
D oH F W LQ J W K H S H U IR U P D Q F H R I 0&&' 0$ G H W H F W R U V LQ ID V W ID G LQ J F K D Q Q H OV $ V
W K H F K D Q Q H O ID G LQ J E H F R P H V ID V W H U G 7 LQ F U H D V H V W K H H V W LP D W LR Q H U U R U D Q G LW V YD U LD Q F H (a O LQ
J U R Z OD U J H U W K X V LQ F U H D V LQ J W K H YD U LD Q F H R I W K H W H U P
c
L
Q D V V K R ZQ
LQ
7K LV LQ W X U Q G H J U D G H V W K H S H U IR U P D Q F H R I W K H 725 & G H W H F W R U D V G H S LF W H G LQ )LJ X U H : H V H H W K D W IR U D S U R E D E LOLW \ R I H U U R U E \ G %
IR U D ID G LQ J U D W H R I G 7
ZK LOH IR U YH U \ ID V W ID G LQ J G 7
b
b
E \ G %
b
W K H S H U IR U P D Q F H G H W H U LR U D W H V
IR U D ID G LQ J U D W H R I G 7
b
W K H G H W H F W R U S H U IR U P D Q F H LV X Q D F F H S W D E OH 6 LP LOD U
S H U IR U P D Q F H G H J U D G D W LR Q LV R E V H U YH G LQ )LJ X U H ZK LF K G H S LF W V W K H G H S H Q G H Q F H R I W K H S U R E D E LOLW \ R I H U U R U R Q W K H W K U H V K R OG K7 +5 7K H U H LV D Q R S W LP D O V H OH F W LR Q R I W K H W K U H V K R OG
BER vs SNR (Threshold 0.09) −1
10
−2
BER
10
−3
10
theoretical Nu=Ns=64, Nu=Ns=16, Nu=Ns=16, Nu=Ns=64,
−4
10
6
8
known ch. known ch. Kalman (ωdT=10−2/4 ) Kalman (ωdT=10−2 )
10
12
14
16
SNR
)LJ X U H ,P S D F W R I ID G LQ J U D W H R Q W K H V H OH F W LR Q R I 1V 725 & G H W H F W R U W K D W E D OD Q F H V H [F H V V LYH P X OW LX V H U LQ W H U IH U H Q F H ZK H Q W R R P D Q \ V X E F K D Q Q H OV D U H U H MH F W H G W K U H V K R OG W R R OD U J H D Q G H [F H V V LYH W K H U P D O D Q G F K D Q Q H O H V W LP D W LR Q Q R LV H H Q K D Q F H P H Q W ZK H Q V X E F K D Q Q H OV ZLW K OR ZH U D P S OLW X G H V D U H LQ YH U W H G W K U H V K R OG W R R OR Z : H Q R W LF H LQ )LJ X U H W K D W D V W K H F K D Q Q H O ID G LQ J E H F R P H V ID V W H U W K H R S W LP D O W K U H V K R OG K7 +5 LQ F U H D V H V E H F D X V H R I W K H OD U J H U LP S D F W R I W K H F K D Q Q H O H V W LP D W LR Q Q R LV H H Q K D Q F H P H Q W $ Q R W K H U LP S OLF D W LR Q R I W K H F K D Q Q H O H V W LP D W LR Q S U R F H V V LV R Q W K H V H OH F W LR Q R I V \V W H P S D U D P H W H U V V X F K D V W K H OH Q J W K R I W K H V S U H D G LQ J V H TX H Q F H V 1V : H H [S H F W W K D W LQ F U H D V LQ J 1V ZLOO LP S U R YH W K H S H U IR U P D Q F H R I W K H V \V W H P E \ LQ W U R G X F LQ J D OD U J H U G H J U H H R I IU H TX H Q F \ G LYH U V LW \ 7K LV LV LQ G H H G W U X H LQ W K H F D V H ZK H Q W K H F K D Q Q H O LV S H U IH F W O\ H V W LP D W H G D W W K H U H F H LYH U > @ > @ + R ZH YH U IR U D p [H G E D Q G ZLG W K S H U V \P E R O : E \ D ID F W R U y) LP S OLH V W K D W c IQHZ E H 7E QHZ
c IQHZ
1V c I LQ F U H D V LQ J 1V
c I y) D Q G W K D W W K H Q H Z V \P E R O G X U D W LR Q V K R X OG
y) 7E 7K H U H IR U H W K H ID G LQ J U D W H G 7 H [S H U LH Q F H G E \ W K H V \V W H P
LV D OV R LQ F U H D V H G y) W LP H V W K X V D oH F W LQ J D G YH U V H O\ W K H S H U IR U P D Q F H R I W K H V \V W H P 7K LV
MMSE per Carrier vs TORC (Kalman Channel Estimation, Nu=Ns=8)
−1
BER
10
−2
10
MMSE TORC known chan. ωdT=10−3 ωdT=10−2 ωdT=10−1 −3
10
6
8
10
12
14
16
SNR
)LJ X U H &R P S D U LV R Q R I 006 ( S H U &D U U LH U D Q G 725 & K7 +5
G H W H F W R U V
S H U IR U P D Q F H OR V V F D Q H YH Q R YH U V K D G R Z W K H IU H TX H Q F \ G LYH U V LW \ J D LQ )LJ X U H V K R ZV W K D W D OW K R X J K LQ W K H F D V H R I S H U IH F W F K D Q Q H O NQ R ZOH G J H W K H V \V W H P W K H R Q H ZLW K 1V
ZLW K 1V
R X W S H U IR U P V
LQ W K H F D V H R I LP S H U IH F W F K D Q Q H O H V W LP D W LR Q LW S H U IR U P V ZR U V H
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r F LH Q W V ZLW K R X W H Q K D Q F LQ J W K H Q R LV H H [F H V V LYH O\ E \ P D NLQ J ? K D U G G H F LV LR Q V 21 R U 2) ) R Q ZK LF K V X E F K D Q Q H OV ZLOO E H LQ YH U W H G ZK LOH W K H 006 (
S H U &D U U LH U G H W H F W R U G R H V W K H V D P H E \ P D NLQ J ? V R IW G H F LV LR Q V
−1
MMSE per Carrier with LMS Channel Estimation (SNR=16 dB, Nu=8, Ns=8)
10
ω T=10−3 d ω T=10−2
BER
d
−2
10
−3
10
−3
10
−2
10
step size µ
)LJ X U H 3 H U IR U P D Q F H R I 006 ( S H U &D U U LH U D V D IX Q F W LR Q R I W K H V W H S V L] H z a D V H [S U H V V H G LQ LQ W K H R S W LP D O 06 (
P D Q Q H U ,Q W H U P V R I F R P S OH [LW \ E R W K G H W H F
W R U V K D YH W R F D OF X OD W H 1V V F D OD U V K R ZH YH U W K H 006 (
S H U &D U U LH U LV P R G H U D W H O\ P R U H
F R P S OH [ P D LQ O\ E H F D X V H LW U H TX LU H V D Q H V W LP D W H R I W K H 6 1 5
LQ 7K H 006 (
S H U
8 V H U G H W H F W R U LV V LJ Q Lp F D Q W O\ P R U H F R P S OH [ W K D Q E R W K R W K H U G H W H F W R U V D V F D Q E H V H H Q LQ : H F R Q W LQ X H E \ LQ YH V W LJ D W LQ J W K H S H U IR U P D Q F H R I W K H G LoH U H Q W IR U P V R I W K H 006 ( G H W H F W R U : H E H J LQ E \ H [D P LQ LQ J W K H H oH F W R I W K H D G D S W D W LR Q S D U D P H W H U V R Q W K H S H U IR U P D Q F H R I W K H G LoH U H Q W IR U P V R I W K H 006 ( G H W H F W R U :
K H Q / 06 D Q G 5 / 6 E D V H G F K D Q Q H O
H V W LP D W R U V D U H X V H G E \ W K H 006 ( G H W H F W R U W K H V H OH F W LR Q R I W K H V W H S V L] H z a D Q G W K H IR U J H W W LQ J ID F W R U y G H S H Q G V R Q W K H F K D Q Q H O ID G LQ J U D W H )R U H D F K ID G LQ J U D W H W K H U H LV D Q R S W LP D O V H OH F W LR Q R I W K H D G D S W D W LR Q S D U D P H W H U V D V G H S LF W H G LQ )LJ X U H V D Q G : H Q R W LF H W K D W W K H S H U IR U P D Q F H R I W K H 006 ( S H U &D U U LH U G H W H F W R U ZLW K / 06 F K D Q Q H O H V W LP D W LR Q LV
0
MMSE per Carrier and Adaptive MMSE Using RLS (SNR=16 dB, Nu=8, Ns=8)
10
ωdT=10−3 ω T=10−2 d
MMSE per Carrier with RLS ch. est. Adaptive MMSE using RLS −1
BER
10
−2
10
−3
10
0.1
0.2
0.3
0.4
0.5 0.6 forgetting factor λ
0.7
0.8
0.9
1
)LJ X U H 3 H U IR U P D Q F H R I 006 ( G H W H F W R U V D V D IX Q F W LR Q R I W K H IR U J H W W LQ J ID F W R U y P X F K P R U H V H Q V LW LYH W R W K H V H OH F W LR Q R I W K H V W H S V L] H z a W K D Q W K H S H U IR U P D Q F H R I W K H F R U U H V S R Q G LQ J 5 / 6 E D V H G G H W H F W R U W R W K H YD U LD W LR Q V R I W K H IR U J H W W LQ J ID F W R U y )X U W K H U P R U H )LJ X U H V K R ZV W K D W W K H 5 / 6 E D V H G 006 ( S H U 8 V H U G H W H F W R U ZLW K R X W H [S OLF LW F K D Q Q H O H V W LP D W LR Q LV D OV R U H OD W LYH O\ P R U H V H Q V LW LYH W R W K H V H OH F W LR Q R I W K H IR U J H W W LQ J ID F W R U y 6 LQ F H W K H . D OP D Q p OW H U J LYH V W K H R S W LP D O H V W LP D W H V LQ W K H 006 ( V H Q V H LW LV H [S H F W H G W K D W W K H S H U IR U P D Q F H R I W K H 006 (
G H W H F W R U X V LQ J W K H . D OP D Q p OW H U S U H V H Q W V D OR ZH U
E R X Q G R Q W K H S U R E D E LOLW \ R I H U U R U ZK H Q R W K H U F K D Q Q H O H V W LP D W R U V V X F K D V W K H / 06 D Q G 5 / 6 D U H X V H G 7K H U H IR U H LQ
)LJ X U H V ZH X V H W K H S H U IR U P D Q F H R I W K H
006 ( S H U &D U U LH U G H W H F W R U ZLW K . D OP D Q F K D Q Q H O H V W LP D W LR Q D V D U H IH U H Q F H D J D LQ V W ZK LF K P R U H U H D OLV W LF LP S OH P H Q W D W LR Q V R I W K H 006 (
G H W H F W R U ZK LF K G R Q R W U H TX LU H NQ R ZOH G J H
R I W K H F K D Q Q H O P R G H O D U H F R P S D U H G )LJ X U H V D Q G LOOX V W U D W H W K H S H U IR U P D Q F H R I W K H 006 (
S H U &D U U LH U G H W H F W R U ZLW K / 06 D Q G 5 / 6 F K D Q Q H O H V W LP D W LR Q U H V S H F W LYH O\
,W F D Q E H V H H Q W K D W W K H S H U IR U P D Q F H R I W K H G H W H F W R U ZK H Q 5 / 6 F K D Q Q H O H V W LP D W LR Q LV
MMSE per Carrier with LMS Channel Estimation (Nu=8, Ns=8)
0
10
−1
BER
10
−2
10
−3
ωdT=10 ω T=10−2 d −1 ωdT=10
−3
10
LMS estim. ( µ=0.002) Kalman estimation known channel
−4
10
6
8
10
12
14
16
SNR
)LJ X U H 3 H U IR U P D Q F H R I W K H 006 ( S H U &D U U LH U G H W H F W R U ZLW K / 06 F K D Q Q H O H V W LP D W LR Q X V H G LV P X F K F OR V H U W R W K D W R I W K H . D OP D Q p OW H U W K D Q ZK H Q / 06 H V W LP D W LR Q LV X V H G D W W K H H [S H Q V H R I LQ F U H D V H G F R P S OH [LW \ : H D OV R Q R W LF H W K D W W K H S H U IR U P D Q F H R I W K H 006 ( G H W H F W R U G H W H U LR U D W H V ZLW K LQ F U H D V LQ J F K D Q Q H O ID G LQ J U D W H LQ D V LP LOD U P D Q Q H U D V LW ZD V S U H YLR X V O\ R E V H U YH G IR U W K H 725 & G H W H F W R U $ V LW ZD V G H V F U LE H G LQ 6 H F W LR Q W K H 006 ( G H W H F W R U F D Q E H LP S OH P H Q W H G D G D S W LYH O\ ZLW K R X W H [S OLF LW F K D Q Q H O H V W LP D W LR Q ,Q > @ W K H W U D Q V LH Q W S H U IR U P D Q F H D Q G F R Q YH U J H Q F H R I W K H 006 (
S H U 8 V H U G H W H F W R U X V LQ J / 06 S U R S R V H G LQ > @ ZD V H [D P LQ H G LQ D V W D W LF
F K D Q Q H O D Q G LW ZD V V K R ZQ W K D W H YH Q W K H Q LW V F R Q YH U J H Q F H LV YH U \ V OR Z E H F D X V H R I W K H OD U J H H LJ H Q YD OX H V S U H D G R I W K H R E V H U YD W LR Q D X W R F R U U H OD W LR Q P D W U L[ 2X U F R P S X W H U H [S H U LP H Q W V LQ G LoH U H Q W ID G LQ J U D W H V V K R ZH G
W K D W W K H / 06
YH U \ V OR Z F R Q YH U J H Q F H D Q G LV X Q D E OH W R S H U IR U P F K D Q Q H OV G 7
b
D G D S W LYH G H W H F W R U LQ G H H G ZH OO %(5
b
G H P R Q VWUD WH V
H YH Q IR U V OR ZO\ ID G LQ J
IR U D Q \ YD OX H R I W K H V W H S V L] H z a $ OW K R X J K LQ W K H F D V H R I S H U IH F W O\
NQ R ZQ F K D Q Q H O W K H 006 ( S H U 8 V H U G H W H F W R U S H U IR U P V V OLJ K W O\ E H W W H U W K D Q W K H 006 ( S H U
MMSE per Carrier with RLS Channel Estimation (Nu=8, Ns=8)
0
10
−1
BER
10
−2
10
−3
ωdT=10 ω T=10−2 d ω T=10−1 d
−3
10
RLS estim. (λ=0.7) Kalman estimation known channel
−4
10
6
8
10
12
14
16
SNR
)LJ X U H 3 H U IR U P D Q F H R I W K H 006 ( S H U &D U U LH U G H W H F W R U ZLW K 5 / 6 F K D Q Q H O H V W LP D W LR Q &D U U LH U G H W H F W R U > @ LQ W K LV F D V H W K H D G D S W D W LR Q H U U R U V G R P LQ D W H W K H S H U IR U P D Q F H R I W K H 006 ( S H U 8 V H U G H W H F W R U 7K H 5 / 6 D G D S W LYH 006 ( S H U 8 V H U G H W H F W R U P D Q D J H V W R W U D F N W K H F K D Q Q H O YD U LD W LR Q V X S W R D F H U W D LQ S R LQ W D OW K R X J K LW V W LOO S H U IR U P V ZR U V H W K D Q W K H 006 (
S H U &D U U LH U G H W H F W R U H P S OR \LQ J H [S OLF LW F K D Q Q H O H V W LP D W LR Q D V LW LV V K R ZQ LQ
)LJ X U H 7K H D E R YH U H V X OW V V X J J H V W W K D W W K H D G D S W LYH 006 (
S H U &D U U LH U G H W H F W R U ZLW K 5 / 6
F K D Q Q H O H V W LP D W LR Q LV D YH U \ D W W U D F W LYH 0&&' 0$ G H W H F W R U ZK LF K F R P E LQ H V J R R G S H U IR U P D Q F H ZLW K U H OD W LYH O\ OR Z F R P S OH [LW \ % H F D X V H R I W K H V H IH D W X U H V LW LV X V H IX O W R H [D P LQ H W K H S H U IR U P D Q F H R I W K H G H W H F W R U ZK H Q D P R U H S U D F W LF D O F K D Q Q H O P R G H O LH W K H ZLG H O\ D F F H S W H G -D NH V P R G H O LV X V H G 7K H S R ZH U V S H F W U X P
R I W K H p U V W R U G H U F K D Q Q H O G H V F U LE H G
LQ K D V Q R G LV F R Q W LQ X LW LH V D Q G G H F U H D V H V ZLW K IU H TX H Q F \ D F F R U G LQ J W R G G ZK H U H G VS H F WUX P
b
}IG F R U U H V S R Q G V W R W K H G% IU H TX H Q F \ IG 2Q W K H R W K H U K D Q G W K H S R ZH U G H U LYH G IU R P
W K H -D NH V F K D Q Q H O P R G H O K D V G LV F R Q W LQ X LW LH V D Q G G H S H Q G V R Q W K H
Adaptive MMSE per User with RLS Algorithm (Nu=8, Ns=8)
0
10
−1
BER
10
−2
10
ωdT=10−3 ωdT=10−2 ωdT=10−1
−3
10
Adaptive MMSE with RLS (λ=0.93) MMSE with Kalman chan. estim. known channel −4
10
6
8
10
12
14
16
SNR
)LJ X U H 3 H U IR U P D Q F H R I W K H 5 / 6 E D V H G 006 ( S H U 8 V H U D G D S W LYH G H W H F W R U IU H TX H Q F \ D F F R U G LQ J W R ' b
b
ZK H U H '
}I' F R U U H V S R Q G V W R W K H P D [LP X P
' R S S OH U V K LIW I' 7K H U H IR U H W K H ID G LQ J U D W H V R I W K H W ZR F K D Q Q H O P R G H OV D V P H D V X U H G E \ W K H S U R G X F W V G 7 D Q G ' 7 D U H Q R W G LU H F W O\ F R P S D U D E OH 7K H S H U IR U P D Q F H R I W K H 006 ( S H U &D U U LH U G H W H F W R U ZLW K 5 / 6 F K D Q Q H O H V W LP D W LR Q ZK H Q W K H -D NH V F K D Q Q H O P R G H O LV X V H G LV G H S LF W H G LQ )LJ X U H ,W LV F OH D U W K D W W K H 5 / 6 H V W LP D W R U P D Q D J H V W R W U D F N W K H F K D Q Q H O YD U LD W LR Q G H V F U LE H G E \ -D NH V P R G H O ZH OO H YH Q IR U K LJ K ID G LQ J U D W H V ' 7
c
b
D OW K R X J K W K H S H U IR U P D Q F H G H W H U LR U D W H V V LJ Q Lp F D Q W O\ D IW H U W K D W S R LQ W ,Q W K H U H P D LQ G H U R I W K LV V H F W LR Q ZH S U H V H Q W D G LV F X V V LR Q ZK LF K F R P S D U H V W K H G H F LV LR Q G LU H F W H G
D Q G
S LOR W D LG H G
D S S UR D F K H V D Q G
H [S OR U H V W K H W U D G H R oV E H W ZH H Q
F K D Q Q H O H V W L
P D W LR Q R YH U K H D G D Q G S H U IR U P D Q F H 7K H F K D Q Q H OV R X Q G LQ J P H W K R G S U R S R V H G LQ > @ X V H V H Q W LU H 2)' 0 V \P E R OV IR U S H U LR G LF F K D Q Q H O H V W LP D W LR Q 7K H U H IR U H D OW K R X J K LQ W K H 2)' 0 V \P E R OV ZLW K G D W D W K H S U R F H V V LQ J J D LQ 1V D Q G W K H Q X P E H U R I V \P E R OV z D U H Q R W U H G X F H G W K LV P H W K R G E H F R P H V YH U \ LQ H r F LH Q W H YH Q IR U P R G H U D W H O\ ID G LQ J F K D Q Q H OV 7K LV LV S R LQ W H G
MMSE per Carrier with RLS Channel Estimation (λ=0.7, N =N =8) u
0
s
10
−1
BER
10
−2
10
known channel ω T=5*10−3 D −2 ωDT=5*10 −1 ωDT=10 ω T=3*10−1
−3
10
D
−4
10
6
8
10
12
14
16
SNR
)LJ X U H 3 H U IR U P D Q F H R I 006 ( S H U &D U U LH U G H W H F W R U ZLW K -D NH V F K D Q Q H O P R G H O R X W LQ > @ > @ ZK H U H LW LV V X J J H V W H G W K D W
R I W K H 2)' 0 V \P E R OV E H X V H G IR U F K D Q Q H O
H V W LP D W LR Q H YH Q IR U YH U \ V OR ZO\ ID G LQ J F K D Q Q H OV 3 H U IR U P D Q F H U H V X OW V LQ V W D W LF F K D Q Q H OV > @ V K R Z LW LV V OLJ K W O\ E H W W H U W K D Q W K H ? S LOR W F D U U LH U V P H W K R G 7K H S LOR W V \P E R OD LG H G P H W K R G R I > @ > @ U H TX LU H V W K H P LQ LP D O S LOR W R YH U K H D G D P R Q J S LOR W D LG H G V F K H P H V ( YH Q ZLW K R YH U V D P S OLQ J E \ D ID F W R U R I D W \S LF D O R YH U K H D G R I R Q O\
1
1W
LV U H S R U W H G LQ > @ > @ ZK LF K LP S OLH V D
U H G X F W LR Q LQ
W K H S U R F H V V LQ J J D LQ R U W K H G D W D U D W H LQ H YH U \ W K LU G 2)' 0 V \P E R O 7K H ? S LOR W F D U U LH U V P H W K R G U H G X F H V W K H Q X P E H U R I V X E F K D Q Q H OV D YD LOD E OH IR U G D W D LQ H D F K 2)' 0 V \P E R O OR ZH U 1V D Q G R U z ,W V R YH U K H D G LV LQ F U H D V H G ZLW K G H F U H D V LQ J F R K H U H Q F H E D Q G ZLG W K D Q G W \S LF D O R YH U K H D G R I
WR
LV U H S R U W H G LQ > @ > @ 7K H G H F LV LR Q G LU H F W H G D S S U R D F K
LV W K H R Q O\ D S S U R D F K W K D W G R H V Q R W U H TX LU H U H J X OD U LQ V H U W LR Q R I NQ R ZQ V \P E R OV LQ W K H W U D Q V P LW W H G G D W D D Q G D OO D YD LOD E OH V X E F K D Q Q H OV D U H X V H G W R W U D Q V P LW G D W D 7K H U H IR U H H YH Q ZLW K R F F D V LR Q D O U H W U D LQ LQ J W K D W P D \ R F F X U LQ D S U D F W LF D O V \V W H P
E H F D X V H R I V H U LR X V
G LV U X S W LR Q V LQ W K H F K D Q Q H O W K H R YH U K H D G LV F R P S D U D W LYH O\ W K H OR ZH V W R Q W K H R U G H U R I LQ LW LD O 2)' 0 W U D LQ LQ J V \P E R OV 7K LV U H G X F H G R YH U K H D G F R P H V ZLW K D S H Q D OW \ V LQ F H W K H G H W H F W R U V F D Q Q R W W U D G H LQ F U H D V H G R YH U K H D G IR U E H W W H U S H U IR U P D Q F H LQ YH U \ ID V W ID G LQ J F K D Q Q H OV D Q G W K H S H U IR U P D Q F H G H W H U LR U D W H V V LJ Q Lp F D Q W O\ IR U K LJ K ID G LQ J U D W H V ' 7 !
b
D V F D Q E H V H H Q LQ )LJ X U H V D Q G 2Q O\ W K H S LOR W D LG H G D S S U R D F K R I > @ > @ LV D E OH W R D G MX V W LW V R YH U K H D G W R LP S U R YH LW V S H U IR U P D Q F H LQ YH U \ ID V W ID G LQ J F K D Q Q H OV 6 LQ F H W K H G H V LJ Q LV E D V H G R Q W K H ZR U V W F D V H V F H Q D U LR LQ V OR ZH U ID G LQ J U D W H V W K H ? H [F H V V R YH U V D P S OLQ J LQ
W K H W LP H G R P D LQ
V \V W H P
LQ K H U H Q W O\ S U H V H Q W D OV R LQ
S H U IR U P D Q F H 7K LV LV G H P R Q V W U D W H G LQ > @ > @ D V G H S LF W H G LQ )LJ X U H ZK H U H
W K H S LOR W J U LG LV G H V LJ Q H G IR U D X V H U V S H H G R I Y LQ F U H D V H V R Q O\ ZK H Q Y
NP K ' 7
V D P S OLQ J W K H R U H P
NP K 7K H F K D Q Q H O H V W LP D W LR Q 06 (
c
IR U D OO V S H H G V E H W ZH H Q D Q G NP K c '
? S LOR W F D U U LH U V G R H V Q R W LP S U R YH W K H
b
b
D Q G U H P D LQ V S U D F W LF D OO\ W K H V D P H
x ' 7 x c
LV V D W LV p H G > @ 7K LV H [S OD LQ V ZK \ W K H % ( 5
V \V W H P V LQ > @ > @ LV P R U H W K D Q G % IR U YH U \ V OR Z ID G LQ J U D W H V ' 7 x
b
b
IR U ZK LF K W K H
S H U IR U P D Q F H R I W K H
ZR U V H W K D Q ZLW K S H U IH F W O\ NQ R ZQ F K D Q Q H OV H YH Q $ V LW F D Q E H V H H Q LQ )LJ X U H V D Q G W K H
P R U H F R P S OH [ G H F LV LR Q G LU H F W H G P H W K R G X V LQ J z1V 5 / 6 H V W LP D W R U V H [S H U LH Q F H V V P D OOH U S H U IR U P D Q F H G H J U D G D W LR Q F R P S D U H G W R W K H F D V H R I NQ R ZQ F K D Q Q H O IR U OR Z W R P R G H U D W H ID G LQ J U D W H V ' 7 x
b
10
0
Channel Estimation MSE
ωDT=1.3 •10-1
10
ωDT=5 •10-2
-1
ωDT=6.7 •10-1
10
ωDT=10-2
-2
Decision-directed, RLS, λ=0.7 Pilot-aided, 2x 1-D Filtering 10
ωDT=2.6 •10-3
-3
5
10
15
20
SNR
)LJ X U H 06 ( YV 6 1 5 IR U 5 / 6 D Q G 3 LOR W D LG H G H V W LP D W LR Q 1X 1V -D NH V P R G H O
&KDSWHU &RQFDWHQDWHG &RGLQJ DQG , WHU DWLYH 'HFRGLQJ LQ &'0
$ % :, 61
% DFNJU RXQG
7K H Q H D U R S W LP D O S H U IR U P D Q F H R I S D U D OOH O F R Q F D W H Q D W H G
LQ W H U OH D YH G
7X U E R F R G H V LQ
$ : *1 F K D Q Q H OV > @ > @ K D V S U R P S W H G D Q LQ W H Q V H U H V H D U F K D F W LYLW \ R Q G LoH U H Q W F R Q F D W H Q D W H G F R G LQ J V F K H P H V H P S OR \LQ J LQ W H U OH D YH U V > @ > @ 7K H H P H U J H Q F H R I Q H [W J H Q H U D W LR Q % :
,6 1
V \V W H P V V X F K
D V W K R V H V S H F Lp H G
LQ
W K H ,07 LQ LW LD W LYH R oH U LQ J V H U YLF H V
ZK LF K F D Q W R OH U D W H U H OD W LYH O\ OR Q J G H OD \V P D NH V W K H X V H R I F R Q F D W H Q D W H G LQ W H U OH D YH G F R G LQ J V F K H P H V YH U \ S U R P LV LQ J 5 H F H Q W O\ S D U D OOH O 7X U E R F R G H V K D YH E H H Q D G R S W H G D V D Q :
R S W LR Q LQ W K H ,6 D Q G :
&' 0$ V W D Q G D U G V ( [D P S OH V R I U H V H D U F K R Q ,6 E D V H G D Q G
&' 0$ V \V W H P V H P S OR \LQ J 7X U E R F R G H V F D Q E H IR X Q G LQ > @ > @ > @ > @ > @ 5 H V H D U F K R Q W K H D S S OLF D W LR Q R I F R Q F D W H Q D W H G LQ W H U OH D YH G F R G H V W R &' 0$
K D V V R ID U
IR F X V H G R Q V \V W H P V X V LQ J S D U D OOH O F R Q F D W H Q D W H G F R G H V 3 && ,Q W K LV G LV V H U W D W LR Q ZH H [D P LQ H W K H S H U IR U P D Q F H R I ' 6 &' 0$ V \V W H P V ZK LF K X V H G LoH U H Q W F R Q F D W H Q D W H G LQ W H U OH D YH G F R G LQ J V F K H P H V D Q G LW H U D W LYH G H F R G LQ J : H F R Q V LG H U D E D V H OLQ H V \V W H P
ZK LF K LV E D V H G
R Q W K H IR U ZD U G OLQ N R I W K H ,6 > @ V W D Q G D U G D Q G LW V * H YR OX W LR Q D Q G R S H U D W H V LQ D
P X OW LS D W K 5 D \OH LJ K ID G LQ J F K D Q Q H O : H H [D P LQ H W K U H H G LoH U H Q W H Q F R G LQ J V F K H P H V D 3 D U D OOH O &R Q F D W H Q D W H G &R G LQ J 3 && V F K H P H > @ ZLW K W ZR F R P S R Q H Q W F R Q YR OX W LR Q D O F R G H V LQ S D U D OOH O D 6 H U LD OO\ &R Q F D W H Q D W H G &R G LQ J 6 && V F K H P H > @ ZLW K W ZR F R P S R Q H Q W F R Q YR OX W LR Q D O F R G H V LQ V H U LH V D Q G D + \E U LG 6 H U LD OO\ &R Q F D W H Q D W H G &R G LQ J + 6 && V F K H P H ZLW K D F R Q YR OX W LR Q D O R X W H U F R G H D Q G D 7X U E R LQ Q H U F R G H V LP LOD U W R W K H R Q H S U R S R V H G LQ > @ ZK H U H W K H R X W H U F R G H ZD V D E OR F N % &+ F R G H : H F R P S D U H W K H LU S H U IR U P D Q F H W R W K D W R I 5
W K H ,6 ,6 F R Q YR OX W LR Q D O H Q F R G H U IR U R YH U D OO F R G H U D W H V 5
U D W H , R S W LR Q D Q G
U D W H ,, R S W LR Q D Q G IR U G LoH U H Q W F R Q V W U D LQ W OH Q J W K V R I W K H F R P S R Q H Q W F R G H V : H D OV R LQ YH V W LJ D W H W K H H oH F W R I YD U \LQ J W K H F K D Q Q H O ID G LQ J U D W H D Q G W K H Q X P E H U R I ZLU H OH V V IU D P H V F R Q W D LQ LQ J R Q H LQ W H U OH D YH G G D W D E OR F N : H H [W H Q G R X U U H V H D U F K W R LQ F OX G H V \V W H P V X V LQ J 0X OW L&R G H &' 0$ 0&' &' 0$ > @ D q H [LE OH P X OW LS OH D F F H V V V F K H P H W K D W D OOR ZV IR U P X OW LU D W H G D W D W U D Q V P LV V LR Q X V LQ J ' 6 6 6 ZLW K F R Q V W D Q W S U R F H V V LQ J J D LQ 0&' &' 0$
LV D W W U D F W LYH E H F D X V H LW F R P E LQ H V
E D F NZD U G V F R P S D W LE LOLW \ ZLW K H [LV W LQ J ' 6 &' 0$ V \V W H P V q H [LE LOLW \ LQ W U D Q V P LV V LR Q G D W D UD WH V D Q G
E D Q G ZLG W K
D 0&' &' 0$ V \V W H P
R Q
G H P D Q G
IH D W X U H V 8 V LQ J 3 && LQ
D V S H F Lp F F R Q p J X U D W LR Q
R I
ZD V p U V W H [D P LQ H G LQ > @ ZK LOH D V F K H P H D OOR ZLQ J IR U LW H U D W LYH
G H F R G LQ J ZD V S U R S R V H G LQ > @ ,Q W K LV G LV V H U W D W LR Q ZH H [D P LQ H D J H Q H U D OL] H G 0&' &' 0$ V \V W H P
H P S OR \LQ J D V H U LD OO\ F R Q F D W H Q D W H G V F K H P H ZLW K D Q R X W H U H Q F R G H U K D YLQ J D V LQ S X W
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)( 5 S H U IR U P D Q F H ZLW K W K H 3 && V F K H P H D OW K R X J K LW V S H U IR U P D Q F H LP S U R YH V G U D P D W LF D OO\ IR U K LJ K H U 6 1 5 V 7K LV R E V H U YD W LR Q LV LQ OLQ H ZLW K ZK D W ZD V R E V H U YH G LQ $ : *1 F K D Q Q H OV > @ ZK H U H LW ZD V V K R ZQ W K D W D OW K R X J K LQ J H Q H U D O 6 && S H U IR U P V ZR U V H W K D Q 3 && D W OR ZH U 6 1 5 V LW R X W S H U IR U P V LW LQ K LJ K H U 6 1 5 V D Q G G R H V Q W G LV S OD \ W K H H U U R U q R R U W K D W LV W \S LF D O LQ S D U D OOH O 7X U E R V F K H P H V 2Q H OD V W F R Q F OX V LR Q G U D ZQ IU R P W K H 3 && F R G H ZLW K / D Q LW H U D W LYH 0$ 3
LV R Q O\ V OLJ K W O\ ZR U V H W K D Q W K D W ZLW K /
)LJ X U H LV W K D W
P D NLQ J W K H X V H R I
G H F R G H U ZLW K R Q O\ V W D W H V D ID YR U D E OH D OW H U Q D W LYH W R X V LQ J D V W D W H
,Q JHQHUDO D ODUJHU EORFN RI GDWD FDQ EH HQFRGHG LQWHUOHDYHG DQG WKHQ WUDQVPLWWHG LQ 0, VXFFHVVLYH PVHF ZLUHOHVV IUDPHV
9 LW H U E L G H F R G H U 7K H H oH F W R I W K H F K D Q Q H O ID G LQ J U D W H ' 7 R Q W K H S H U IR U P D Q F H R I W K H F R Q YR OX W LR Q D O D Q G W K H 3 && 6 && V F K H P H V LV G H S LF W H G LQ )LJ X U H IR U 6 1 5
G % D Q G F R G H UD WH 5
: H
Q R W LF H W K D W D OW K R X J K W K H S H U IR U P D Q F H R I D OO V F K H P H V LP S U R YH V ZLW K K LJ K H U ID G LQ J U D W H V D V H [S H F W H G IR U D S H U IH F W O\ NQ R ZQ F K D Q Q H O W K H LP S U R YH P H Q W IR U E R W K F R Q F D W H Q D W H G F R G H V LV P R U H G U D P D W LF H V S H F LD OO\ IR U K LJ K ID G LQ J U D W H V ,Q )LJ X U H ZH F R Q V LG H U W K H F D V H W K D W D OD U J H E OR F N R I G D W D LV H Q F R G H G LQ W H U OH D YH G D Q G W K H Q W U D Q V P LW W H G LQ P X OW LS OH 0, IU D P H V E OR F N PVHF ZLU H OH V V IU D P H V )R U PVHF IU D P H V W K LV P H D Q V W K D W W K H G H F R G LQ J G H OD \ LV PVHF ZK LF K LV D F F H S W D E OH IR U P D Q \ D S S OLF D W LR Q V ,Q )LJ X U H ZH D OV R S OR W W K H V X E )U D P H ( U U R U 5 D W H IR U W K H F R Q YR OX W LR Q D O F R G H D V V X P LQ J W K D W H D F K G D W D E OR F N LV G LYLG H G LQ 0, V X E IU D P H V H D F K ZLW K D V H S D U D W H &5 & 2X U H [S H U LP H Q W V V K R ZH G W K D W W K H % OR F N ( U U R U 5 D W H % O( 5 LP S U R YH P H Q W LQ F R Q F D W H Q D W H G LQ W H U OH D YH G F R G H V E \ D G G LQ J &5 & V LV P X F K V P D OOH U D Q G G R H V Q R W MX V W LI\ W K H H [W U D R YH U K H D G 7K LV G LoH U H Q F H F D Q E H H [S OD LQ H G E H F D X V H H U U R U S D W W H U Q V D IW H U LW H U D W LYH G H F R G LQ J ZH U H IR X Q G W R E H P X F K P R U H E X U V W \ LH W K H U H ZH U H IH Z IU D P H V ZLW K H U U R U V D Q G P R U H E LW H U U R U V W K U R X J K R X W H D F K H U U R Q H R X V IU D P H W K D Q LQ F R Q YR OX W LR Q D O F R G H V LH W K H U H ZH U H P R U H IU D P H V ZLW K H U U R U V D Q G IH Z E LW H U U R U V S H U H U U R Q H R X V IU D P H ,Q )LJ X U H ZH D OV R S U H V H Q W S H U IR U P D Q F H U H V X OW V R I W K H + 6 && V F K H P H ZK H U H W K H S X Q F W X U H G U D W H R I W K H R X W H U F R G H ZD V F K R V H Q 5 J LYLQ J LW S R R U H U % ( 5
RXW
% LW H U U R U V LQ W K LV V \V W H P
D S S H D U H G YH U \ F OX V W H U H G
S H U IR U P D Q F H ZK H Q F R P S D U H G ZLW K W K H 3 && D Q G 6 && V F K H P H V D O
W K R X J K V W LOO U H OD W LYH O\ E H W W H U W K D Q W K H F R Q YR OX W LR Q D O V F K H P H : W K H S H U IR U P D Q F H R I + 6 && LV W K D W W K H % O( 5
K D W LV U H P D U ND E OH D E R X W
V OR S H LV P X F K V W H H S H U W K D Q E R W K R I W K H R W K H U
F R Q F D W H Q D W H G V F K H P H V 7K LV LV S D U W LF X OD U O\ D S S D U H Q W ZK H Q F R P S D U H G W R W K H 3 && V F K H P H ZK LF K LP S OLH V W K D W D OR ZH U H U U R U q R R U LV D W W D LQ H G 7K LV U H V X OW LV D OV R R E V H U YH G IR U $ : *1 F K D Q Q H OV LQ > @ )LJ X U H V K R ZV W K H % O( 5 S H U IR U P D Q F H R I W K H 3 && D Q G + 6 && V F K H P H V IR U H D F K LW H U D W LR Q R X W H U OR R S LW H U D W LR Q V IR U + 6 &&
BER vs SNR, 1 Frame Interleaving, ω T=0.027 d
0
10
−1
10
−2
BER
10
−3
10
Uncoded R=3/4 R=1/2 Conv. L=9 SCC, L=5 PCC, L=4 PCC, L=5
−4
10
−5
10
2
3
4
5
Average γ
6
7
8
7
8
b
FER vs SNR, 1 Frame Interleaving, ω T=0.027 d
0
10
−1
FER
10
−2
10
Uncoded R=3/4 R=1/2 Conv. L=9 SCC, L=5 PCC, L=4 PCC, L=5
−3
10
−4
10
2
3
4
5
Average γ
6
b
)LJ X U H % ( 5 X S S H U D Q G )( 5 IU D P H LQ W H U OH D YLQ J
OR ZH U S H U IR U P D Q F H F R P S D U LV R Q V IR U V LQ J OH 0,
BER vs Fading Rate, γ =4 dB, R=1/2, N=192 b
−1
10
−2
BER
10
−3
10
Convolutional, L=9 SCC, L=5 PCC, L=5 −4
10
−3
10
−2
−1
10
10
Fading rate ω T D
FER vs Fading Rate, γ =4 dB, R=1/2, N=192 b
0
10
−1
FER
10
−2
10
Convolutional, L=9 SCC, L=5 PCC, L=5 −3
10
−3
10
−2
−1
10
Fading rate ω T
10
D
)LJ X U H ( oH F W R I W K H ID G LQ J U D W H ' 7 R Q % ( 5
X S S H U D Q G )( 5
OR ZH U
BER vs SNR, 5 Frame Interleaving, R=1/2, ω T=0.027 d
−1
10
−2
10
−3
BER
10
−4
10
−5
10
Conv. L=9 H−SCC., L=4 SCC, L=4 PCC, L=4
−6
10
−7
10
2
2.5
3
3.5
4
Average γ
4.5
5
5.5
6
5.5
6
b
BlER vs SNR, 5 Frame Interleaving, R=1/2, ω T=0.027 d
0
10
−1
Block Error Rate
10
−2
10
−3
10
Conv. L=9 H−SCC., L=4 SCC, L=4 PCC, L=4 subFER
−4
10
2
2.5
3
3.5
4
Average γ
4.5
5
b
)LJ X U H % ( 5 X S S H U D Q G % O( 5 IU D P H LQ W H U OH D YLQ J
OR ZH U S H U IR U P D Q F H F R P S D U LV R Q V IR U P X OW LS OH 0,
PCC, L=4, 5 Frame Interleaving, R=1/2, ω T =0.027 D s
0
10
−1
Block Error Rate
10
−2
10
−3
10
−4
10
2
2.2
2.4
2.6
2.8
3
Average γ
3.2
3.4
3.6
3.8
4
b
H−SCC, L=4, 5 Frame Interleaving, R=1/2, ω T =0.027 D s
0
10
−1
Block Error Rate
10
−2
10
−3
10
−4
10
2
2.5
3
Average γ
3.5
4
4.5
b
)LJ X U H ( oH F W R I Q X P E H U R I LW H U D W LR Q V R Q % O( 5
IR U 3 && X S S H U D Q G + 6 && OR ZH U
0
&'&'0
$ 5HVXOWV
,Q D OO 0&' &' 0$ U H V X OW V W K H R YH U D OO F R G H U D W H LV 5 W K H U H IR U H W K H X Q F R G H G E OR F NV D U H 1E
d 0 V \P E R OV OR Q J 7K H F R P S R Q H Q W F R Q YR OX W LR Q D O F R G H V R I W K H F R Q F D W H Q D W H G
LQ W H U OH D YH G V F K H P H V K D YH F R Q V W U D LQ W OH Q J W K / R I W K H S R V W 6 3 D Q G S U H 6 3
7K H % LW ( U U R U 5 D W H % ( 5 S H U IR U P D Q F H
V F K H P H V LV G H S LF W H G LQ )LJ X U H : H Q R W LF H W K D W W K H % ( 5
S H U IR U P D Q F H R I W K H S U H 6 3 V F K H P H V LV E H W W H U W K D Q W K H S R V W 6 3 IR U D OO H Q F R G LQ J V F K H P H V D OW K R X J K W K H LP S U R YH P H Q W F D X V H G E \ OD U J H U LQ W H U OH D YLQ J OH Q J W K V LV U H OD W LYH V P D OO 7K H V F K H P H V X V LQ J 3 && F R G H V G LV S OD \ W K H E H V W S H U IR U P D Q F H H V S H F LD OO\ IR U OR ZH U 6 1 5 V &R P S D U LQ J W K H S H U IR U P D Q F H E H W ZH H Q W K H S R V W 6 3
D Q G W K H S U H 6 3
V F K H P H V U H YH D OV
D G LoH U H Q W V LW X D W LR Q ZK H Q W K H % OR F N ( U U R U 5 D W H % O( 5 LV W K H F K R V H Q p J X U H R I P H U LW 7K LV LV G H S LF W H G S U H 6 3
LQ
)LJ X U H ,Q
W K LV F D V H ZH Q R W LF H W K D W W K H S H U IR U P D Q F H R I W K H
V F K H P H V LV P X F K E H W W H U ZLW K D OO V \V W H P V E H Q H p W LQ J E \ W K H OR Q J H U LQ W H U OH D YLQ J
OH Q J W K R I W K H R X W H U LQ W H U OH D YH U }RXW 7K H LP S U R YH P H Q W LQ K LJ K 6 1 5 V LV H YH Q OD U J H U IR U W K H F R Q F D W H Q D W H G LQ W H U OH D YH G V F K H P H V ZK LF K V H H P
W R E H Q H p W IU R P
W K H OR Q J H U LQ W H U OH D YH U V
E H W ZH H Q W K H LU F R P S R Q H Q W F R G H V ,W K D V W R E H Q R W H G K R ZH YH U W K D W V LQ F H J U R X S V R I 0 H Q F R G H G V \P E R OV R I H D F K E OR F N D U H V X E MH F W W R W K H V D P H ID G LQ J Q R LV H V W D W LV W LF V W K H J D LQ E \ LQ F U H D V LQ J W K H 7X U E R LQ W H U OH D YH U OH Q J W K V E \ 0
W LP H V LV V P D OOH U W K D Q LI D OO H Q F R G H G
V \P E R OV R I H D F K E OR F N K D G E H H Q W U D Q V P LW W H G LQ 0,
V X F F H V V LYH LQ G H S H Q G H Q W O\ ID G H G
ZLU H OH V V IU D P H V &R P S D U LQ J )LJ X U H V D Q G ZH V H H W K D W IR U D % O( 5 W K H 7X U E R LQ W H U OH D YH U R I W K H 3 && V F K H P H 0,
b
LQ F U H D V LQ J
W LP H V LP S U R YH V S H U IR U P D Q F H E \ P R U H
W K D Q G % ZK LOH IR U W K H F R U U H V S R Q G LQ J V F K H P H LQ )LJ X U H W K H LP S U R YH P H Q W LV D E R X W G % $ Q R W K H U LQ W H U H V W LQ J U H P D U N G U D ZQ IU R P
)LJ X U H LV W K D W W K H % O( 5
W K H 0&6 H U LD O V F K H P H LV E H W ZH H Q W K H S U H 6 3
D Q G W K H S R V W 6 3
S H U IR U P D Q F H R I
V F K H P H V ZLW K LW V V OR S H
V LP LOD U W R W K H S R V W 6 3 6 && V F K H P H ,Q )LJ X U H V D Q G ZH Q R W LF H W K D W W K H S U H 6 3
V F K H P H V G H P R Q V W U D W H D E X U V W LH U
$OWKRXJK WKH 0&6HULDO VFKHPH LQFXGHV ERWK SRVW63 DQG SUH63 HQFRGHUV IRU LOOXVWUDWLYH SXUSRVHV LQ DOO pJXUHV ZH VKRZ LW DV SDUW RI WKH SUH63 VFKHPHV
H U U R U E H K D YLR U ZK H Q W K H U H V X OW V D U H F R P S D U H G W R W K H S R V W 6 3
V F K H P H V LH P X F K IH ZH U
E OR F NV F R Q W D LQ D OD U J H U Q X P E H U R I H U U R U V 7K H V D P H W U H Q G LV R E V H U YH G LQ E R W K 6 &&' 0$ D Q G 0&' &' 0$
ZK H Q D F R P S D U LV R Q LV P D G H E H W ZH H Q W K H F R Q YR OX W LR Q D O F D V H D Q G W K H
S D U D OOH O D Q G V H U LD OO\ F R Q F D W H Q D W H G LQ W H U OH D YH G V F K H P H V 7K LV R E V H U YD W LR Q P R W LYD W H G X V W R H [D P LQ H W K H H U U R U V W D W LV W LF V D W W K H IU D P H OH YH O ,Q D S U D F W LF D O V \V W H P
W K LV ZR X OG P H D Q W K D W
D &5 & F R G H ZR U G ZR X OG E H LQ V H U W H G LQ D OO 0 IU D P H V F R U U H V S R Q G LQ J W R H D F K X V H U E OR F N 7K H )U D P H ( U U R U 5 D W H )( 5 S H U IR U P D Q F H R I W K H G LoH U H Q W V F K H P H V LV V K R ZQ LQ )LJ X U H &R P S D U LQ J )LJ X U H V D Q G ZH R E V H U YH W K D W D V H [S H F W H G D OO S R V W 6 3 W K H 0&6 H U LD O D Q G W K H S U H 6 3 F R Q YR OX W LR Q D O V F K H P H V E H Q H p W W K H P R V W ZK H Q W K H )( 5 F K R V H Q p J X U H R I P H U LW 7K H % O( 5
D Q G )( 5
S H U IR U P D Q F H R I E R W K W K H S U H 6 3
6 && V F K H P H V LV S U D F W LF D OO\ W K H V D P H D Q G U H P D LQ V W K H E H V W D P R Q J D OO V F K H P H V
LV W K H
3 && D Q G
Post−S/P Schemes, M=5 codes/user, N =5x192 b
0
10
−1
Bit Error Rate
10
−2
10
−3
10
Uncoded Conv, L=9 SCC, L=5 PCC, L=5
−4
10
−5
10
2
3
4
5
Average γ
6
7
8
7
8
b
Pre−S/P Schemes, M=5 codes/user, N =5x192 b
0
10
−1
Bit Error Rate
10
−2
10
−3
10
Uncoded Conv, L=9 MC−Serial, L=5 SCC, L=5 PCC, L=5
−4
10
−5
10
2
3
4
5
Average γ
6
b
)LJ X U H % LW ( U U R U 5 D W H S H U IR U P D Q F H F R P S D U LV R Q V IR U ? 3 R V W 6 3 X S S H U D Q G ? 3 U H 6 3 OR ZH U V F K H P H V ZLW K 0 F R G H V X V H U
Post−S/P and Pre−S/P Schemes, M=5 codes/user, N =5x192 b
0
10
−1
Block Error Rate
10
−2
10
Post−S/P Pre−S/P Uncoded Conv, L=9 MC−Serial, L=5 SCC, L=5 PCC, L=5
−3
10
−4
10
2
3
4
5
Average γb
6
7
8
)LJ X U H % OR F N ( U U R U 5 D W H S H U IR U P D Q F H F R P S D U LV R Q V ZLW K 0 F R G H V X V H U
Post−S/P Schemes, M=5 codes/user, N =5x192 b
0
10
−1
Frame Error Rate
10
−2
10
Uncoded Conv, L=9 SCC, L=5 PCC, L=5
−3
10
−4
10
2
3
4
5
Average γ
6
7
8
7
8
b
Pre−S/P Schemes, M=5 codes/user, N =5x192 b
0
10
−1
Frame Error Rate
10
−2
10
Uncoded Conv, L=9 MC−Serial, L=5 SCC, L=5 PCC, L=5
−3
10
−4
10
2
3
4
5
Average γ
6
b
)LJ X U H )U D P H ( U U R U 5 D W H S H U IR U P D Q F H F R P S D U LV R Q V IR U ? 3 R V W 6 3 X S S H U D Q G ? 3 U H 6 3 OR ZH U V F K H P H V ZLW K 0 F R G H V X V H U
&KDSWHU /RZ 6SU HDGLQJ *DLQ 96*&'0
$
IRU % :, 61
% DFNJU RXQG
9 D U LD E OH 6 S U H D G LQ J *D LQ &' 0$ 9 6 *&' 0$ > @ K D V E H H Q D G R S W H G LQ Q H [W J H Q H U D W LR Q &' 0$ V \V W H P V H J ,6 :
&' 0$ LQ R U G H U W R D F F R P P R G D W H G LoH U H Q W G D W D U D W H V
ZK LOH NH H S LQ J F R Q V W D Q W W K H V LJ Q D O H Q YH OR S H D Q G E D Q G ZLG W K $ ' 6 &' 0$
V \V W H P V ZLW K 5 $ . (
F R P P R Q D V V X P S W LR Q LQ
U H F H LYH U V LV W K D W E H F D X V H R I W K H OD U J H 6 * W K H H oH F W R I
W K H ,Q W H U 3 D W K ,Q W H U IH U H Q F H ,3 , F D Q E H Q H J OH F W H G > @ ,Q K LJ K G D W D U D W H D S S OLF D W LR Q V K R ZH YH U W K H 6 * F D Q E H D V OR Z D V F K LS V S H U W U D Q V P LW W H G F R G H G V \P E R O ZK LF K P D NH V W K H H oH F W R I ,3 , LP S R U W D Q W LQ W K H G H V LJ Q R I % :
,6 1 V \V W H P V X V LQ J 9 6 *&' 0$
6 LQ J OH X V H U U H F H LYH U G H V LJ Q D Q G H TX D OL] D W LR Q LQ ' 6 &' 0$
V \V W H P V K D YH U H F H Q W O\ D W
W U D F W H G D Q LQ W H Q V H U H V H D U F K LQ W H U H V W 7ZR F D V H V D U H F R Q V LG H U H G G H S H Q G LQ J R Q ZK H W K H U V K R U W R U OR Q J V S U H D G LQ J F R G H V D U H X V H G E H F D X V H R I W K H G LoH U H Q W H oH F W R I W K H P X OW LS D W K G H OD \ V S U H D G R Q W K H V \V W H P
S H U IR U P D Q F H :
LQ J J D LQ ' 6 6 6 V \V W H P V S H U IR U P
K H Q V K R U W V S U H D G LQ J V H TX H Q F H V D U H X V H G OR Z V S U H D G
V LP LOD U O\ W R Q D U U R ZE D Q G Q R Q V S U H D G V \V W H P V E H F D X V H
,6 , D U LV LQ J IU R P
S D W K D U U LYD OV ZLW K G H OD \V OD U J H U W K D Q R Q H V \P E R O S H U LR G E H F R P H V W K H OLP
LW LQ J ID F W R U LQ W K H LU S H U IR U P D Q F H )R U W K LV U H D V R Q P R V W H TX D OL] D W LR Q D Q G 6 H OI,Q W H U IH U H Q F H &D Q F H OD W LR Q 6 ,& V F K H P H V D U H D S S OLH G W R V \V W H P V ZLW K V K R U W V S U H D G LQ J V H TX H Q F H V > @ > @ > @ > @ 7K H S U R E OH P
R I V H YH U H ,6 , F D Q E H D OOH YLD W H G ZLW K W K H X V H R I OR Q J V S U H D G LQ J
V H TX H Q F H V ,Q W K LV F D V H S D W K D U U LYD OV ZLW K G H OD \V OH V V W K D Q R Q H V \P E R O S H U LR G D S S H D U W R E H W K H OLP LW LQ J ID F W R U LQ W K H S H U IR U P D Q F H R I X Q F R G H G V \V W H P V ZLW K 5 $ . ( > @ ZK LF K U H D F K D Q H U U R U q R R U LQ W K H K LJ K 6 1 5
U H F H LYH U V > @
U H J LR Q ( TX D OL] D W LR Q D Q G 6 ,& V F K H P H V
K D YH E H H Q S U R S R V H G LQ > @ > @ D Q G > @ W R V X S S U H V V ,3 , D Q G H OLP LQ D W H W K H H U U R U q R R U R E V H U YH G LQ K LJ K 6 1 5 V ,Q S U D F W LF D O % :
,6 1
D S S OLF D W LR Q V H J ,6 :
&' 0$ 9 6 *&' 0$
V \V W H P V
X V H F R Q F D W H Q D W H G V K R U W R U W K R J R Q D O F R G H V IR U F K D Q Q H OL] D W LR Q D Q G OR Q J S V H X G R U D Q G R P
VH
TX H Q F H V IR U V H F W R U L] D W LR Q S U LYD F \ &K D Q Q H O F R G LQ J LV D OV R X V H G W R U H G X F H W K H U H TX LU H G 6 1 5
W R D W W D LQ W K H G H V LU H G S H U IR U P D Q F H )X U W K H U P R U H YH U \ K LJ K G D W D U D W H D S S OLF D W LR Q V
ZK LF K U H TX LU H OR Z 6 * P R V W S U R E D E O\ LQ YR OYH R Q O\ R Q H W U D Q V P LW W LQ J X V H U S H U V H F W R U D W D Q \ W LP H ( YH Q W K R X J K &' 0$ W U D Q V P LV V LR Q LV X V H G P X OW LS OH D F F H V V R I K LJ K G D W D U D W H X V H U V LV F R Q W U R OOH G LQ W K H 0$ & OD \H U D Q H [D P S OH R I W K LV F D V H LV W K H [( 9 ' 2 S U R S R V D O E D V H G R Q + ' 5
> @ ,Q W K LV F K D S W H U ZH H [D P LQ H W K H S H U IR U P D Q F H R I V X F K V \V W H P V LH K LJ K
G D W D U D W H OR Z 6 * F R G H G 9 6 *&' 0$
V \V W H P V ZLW K 5 $ . (
U H F H LYH U V 7K LV S H U IR U P D Q F H
F D Q E H X V H G D V D E H Q F K P D U N D J D LQ V W ZK LF K 6 ,& D Q G H TX D OL] D W LR Q V F K H P H V D U H F R P S D U H G : H LQ YH V W LJ D W H W K H H oH F W R I 6 * D V OR Z D V F K LS V S H U F R G H G V \P E R O R Q W K H S H U IR U P D Q F H R I V \V W H P V H P S OR \LQ J &R Q YR OX W LR Q D O D Q G 7X U E R F R G H V : H S U H V H Q W D V H OILQ W H U IH U H Q F H D Q D O \V LV D Q G ZH LQ YH V W LJ D W H W K H LP S D F W R I ,3 , R Q F R G H G V \V W H P V X Q G H U G LoH U H Q W P X OW LS D W K F K D Q Q H O S U R p OH V
6\VWHP 'HVFU LSWLRQ
: H F R Q V LG H U D E D V H OLQ H V \V W H P
ZK LF K F R U U H V S R Q G V W R W K H IR U ZD U G R U U H YH U V H OLQ N R I D F R
K H U H Q W 9 6 *&' 0$ V \V W H P $ E OR F N R I 1E V R X U F H E LQ D U \ G D W D V \P E R OV EL N Ih J N 1E b R I X V H U L D U H S D V V H G W K U R X J K W K H F K D Q Q H O H Q F R G H U D Q G W K H H Q F R G H G E LQ D U \ V \P E R OV GL N N
1I b D U H S OD F H G LQ W R IU D P H V R I OH Q J W K 1I ZK H U H 1I
1E 5 D Q G 5
LV W K H R YH U D OO F R G H U D W H 7K H V H IU D P H V D U H W K H Q S D V V H G W K U R X J K D F K D Q Q H O E OR F N LQ W H U OH D YH U R I W K H V D P H OH Q J W K D Q G W K H V \P E R OV D U H V S U H D G E \ X V LQ J R Q H R I W K H D YD LOD E OH F K D Q Q H OL] D W LR Q 2U W K R J R Q D O 9 D U LD E OH 6 S U H D G LQ J )D F W R U 29 6 ) V H TX H Q F H V ZL Q Q
1V b
R I OH Q J W K 1V W K H 6 * LV H TX D O W R 1V )R U V LP S OLF LW \ R I Q R W D W LR Q ZH F R Q V LG H U W K D W W K H U H V X OW LQ J V LJ Q D O LV W K H Q % 3 6 . W X D O * V \V W H P V 43 6 .
V S U H D G E \ X V LQ J D OR Q J 3 1 V H TX H Q F H S Q D OW K R X J K LQ D F
V S U H D G LQ J LV X V H G 7K H V LJ Q D OV R I R W K H U X V H U V D U H W K H Q D G G H G LQ
D V \Q F K U R Q R X V R U D V \Q F K U R Q R X V P D Q Q H U F R U U H V S R Q G LQ J W R W K H IR U ZD U G D Q G U H YH U V H OLQ N U H V S H F W LYH O\ : H D V V X P H W K D W R Q O\ R Q H K LJ K G D W D U D W H OR Z6 * X V H U W U D Q V P LW V D W H D F K W LP H D Q G W K D W W K H U H V W R I W K H X V H U V D U H OR ZG D W D U D W H K LJ K 6 * 7K H U H IR U H ZH D V V X P H W K D W W K H LU H oH F W F D Q E H LQ F R U S R U D W H G LQ W K H E D F NJ U R X Q G Q R LV H D Q G LQ W K H U H V W R I W K H F K D S W H U ZH G U R S W K H X V H U LQ G H [ L 7K H U H V X OW LQ J E D V H E D Q G W U D Q V P LW W H G V LJ Q D O V W K D V W K H IR OOR ZLQ J IR U P T
V W ZK H U H
(F G W F W
;
G W
G N 57 W b N7
Z P S Q 57F W b Q7F
N b
F W P
Q PRG 1V 7F D Q G 7
; Q b
1V 7F D U H W K H F K LS D Q G V \P E R O G X U D W LR Q V U H V S H F W LYH O\ 57 W
57F W D U H X Q LW U H F W D Q J X OD U S X OV H V R I G X U D W LR Q 7 D Q G 7F U H V S H F W LYH O\ D Q G (F LV W K H H Q H U J \ S H U W U D Q V P LW W H G F K LS 7K H E OR F N G LD J U D P
R I W K H W U D Q V P LW W H U LV G H S LF W H G LQ W K H X S S H U S D U W
R I )LJ X U H
wi(n) CHANNEL ENCODER
CHANNEL INTERLEAVER
p(n)
x
Σ
x
ORTHOGONAL SPREADING
Data of User i
LONG PN SPREADING
OTHER USERS
CHANNEL ESTIMATOR
MULTIPATH FADING CHANNEL
wi(n) Data Estimates
Ns
CHANNEL DECODER
Σ
CHANNEL DEINTERLEAVER
1 Ns n=1
x
RAKE RECEIVER AND LONG PN DESPREADER
ORTHOGONAL DESPREADING
)LJ X U H % D V H E D Q G 9 6 *&' 0$ E OR F N G LD J U D P 7K H ZLU H OH V V F K D Q Q H O LV D V V X P H G W R E H D P X OW LS D W K ID G LQ J F K D Q Q H O ZLW K 1S S D W K V D V G H V F U LE H G LQ 7K H LQ G H S H Q G H Q W ] H U R P H D Q F R P S OH [ *D X V V LD Q S U R F H V V H V DO W oO W HbMO W O
1S b D U H P R G H OH G X V LQ J -D NH V P R G H O 7K H Q W K H U H F H LYH G
V LJ Q D O D W W K H LQ S X W R I W K H U H F H LYH U K D V W K H IR OOR ZLQ J IR U P U W
1S b
;
DO W V W b O Y W
O
ZK H U H x 1S b x 7P D U H W K H S D W K G H OD \V 7P LV W K H P D [LP X P
G H OD \
V S U H D G R I W K H F K D Q Q H O D Q G Y W LV ] H U R P H D Q F R P S OH [ $ : *1 ZLW K S R ZH U V S H F W U D O G H Q V LW \ 1 : H D V V X P H W K D W W K H U H D U H 1S S D W K G H OD \V ZK LF K D U H LQ W H J H U P X OW LS OH V R I W K H F K LS G X U D W LR Q LH O
rO 7F ZK H U H rO I E7P 7F FJ
$ W W K H U H F H LYH U W K H V LJ Q D O LV p U V W S D V V H G W K U R X J K D F K LS P D W F K H G p OW H U D Q G V D P S OH G D W W K H F K LS LQ W H U YD O D Q G W K H V D P S OH V D U H IH G LQ W R D 5 $ . (
U H F H LYH U ZLW K 1S p Q J H U V ,Q
H D F K p Q J H U W K H V D P S OH V D U H P X OW LS OLH G E \ W K H F R P S OH [ F R Q MX J D W H R I W K H F R U U H V S R Q G LQ J F K D Q Q H O F R H r F LH Q W V 05 & F R P E LQ LQ J D Q G W K H Q W K H \ D U H F R U U H OD W H G ZLW K D S S U R S U LD W H O\ G H OD \H G YH U V LR Q V R I W K H 3 1
V H TX H Q F H S Q 7K H R X W S X W R I W K H 5 $ . (
U H F H LYH U LV IR U P H G
E \ D G G LQ J W K H R X W S X W V R I D OO p Q J H U V D Q G W D NLQ J W K H U H D O S D U W 7K H V \P E R O R E V H U YD W LR Q V \ N N
1I b D W W K H LQ S X W R I W K H G H F R G H U D U H R E W D LQ H G D IW H U S H U IR U P LQ J R U W K R J R Q D O
G H V S U H D G LQ J ZLW K W K H V H TX H Q F H Z Q 7K H E OR F N G LD J U D P
R I W K H U H F H LYH U LV G H S LF W H G LQ W K H
OR ZH U S D U W R I )LJ X U H
6HOI, QWHU IHU HQFH $QDO\VLV
6 H OILQ W H U IH U H Q F H F D Q E H D V V X P H G Q H J OLJ LE OH R Q O\ LQ ' 6 &' 0$ V \V W H P V ZLW K OD U J H 6 * ,Q W K D W F D V H W K H % ( 5 S H U IR U P D Q F H R I W K H ? LG H D O 5 $ . ( U H F H LYH U LV W K D W R I D Q 1S W K G LYH U V LW \ F R P E LQ H U X V LQ J 05 & > @
1S
> b z @
3E
1S b
;
N
ZK H U H E \ G H p Q LW LR Q
V
zu D Q G qz F LV W K H D YH U D J H 6 1 5
1S b N > z @N N
qz F qz F
S H U p Q J H U ZK LF K LV D V V X P H G LG H Q W LF D O IR U D OO 1S p Q J H U V $ V
V X J J H V W H G LQ > @ W K H H oH F W R I Q R Q Q H J OLJ LE OH ,3 , ZLW K D Q R Q LG H D O 5 $ . ( F D Q E H H [D P LQ H G X V LQ J D *D X V V LD Q D S S U R [LP D W LR Q LQ X Q F R G H G V \V W H P V ZLW K U D Q G R P
V H TX H Q F H V > @ 7K LV
D S S U R [LP D W LR Q K R ZH YH U ZD V V K R ZQ LQ D S S U R S U LD W H IR U V \V W H P V ZLW K OR Z 6 * > @ > @ :
LW K R X W W K LV D S S U R [LP D W LR Q D Q H [D F W F OR V H G IR U P
H [S U H V V LR Q IR U W K H S U R E D E LOLW \ R I H U U R U
LV LQ W U D F W D E OH H YH Q IR U X Q F R G H G V \V W H P V 7K H U H IR U H LQ W K H U H V W R I W K LV V H F W LR Q ZH H [D P LQ H W K H IR U P
R I WK H F R G H G
V \P E R O R E V H U YD W LR Q V D Q G
ZH P D NH R E V H U YD W LR Q V ZK LF K
K H OS
X V
X Q G H U V W D Q G W K H S H U IR U P D Q F H R I F R G H G V \V W H P V 7K H R E V H U YD W LR Q R I W K H F R G H G V \P E R O G N D W W K H LQ S X W R I W K H G H F R G H U K D V W K H IR OOR ZLQ J IR U P \ N
HI
1S b
; O
,Q
D V ZH OO D V LQ
DeO N
=
1V 7F
N 7 O
N7 O
U W F W b O GWJ
W K H U H V W R I W K H F K D S W H U ZH D V V X P H W K D W W K H F R P S OH [ F K D Q Q H O
F R H r F LH Q W V DO N D U H F R Q V W D Q W G X U LQ J R Q H V \P E R O LQ W H U YD O D OW K R X J K W K H \ P D \ F K D Q J H R YH U V X F F H V V LYH LQ W H U YD OV D Q G IR U V LP S OLF LW \ ZH G U R S W K H LQ G H [ N 6 X E V W LW X W LQ J D Q G
LQ ZH F D Q U H ZU LW H W K H R E V H U YD W LR Q D V D V X P \ N 7K H p U V W W H U P
\V N \Q N \,3 , N
1S b
;
oO
O
7K H V H F R Q G W H U P
T
(F G N
\Q N LQ LV W K H $ : *1 Q R LV H \Q N
HI
1S b
; O
DeO
1S b
; oO 1V O
=
1V 7F
N 7 O
N7 O
N 1V rO
;
Y W F W b O GWJ
Z P S Q b rO u Q
Q N1V rO
Q b rO PRG 1V D Q G u Q
FRVvO HIY Q J VLQvO PIY Q J LV ] H U R P H D Q
$ : *1 ZLW K YD U LD Q F H 1 $ V V X P LQ J NQ R ZQ S D W K J D LQ V W K H Q R LV H W H U P D Q G YD U LD Q F H YDUI\Q N J
1S b
; O
7K H W K LU G W H U P \,3 , N
\V N LQ LV W K H X V H IX O V LJ Q D O \V N
ZK H U H P
R IWK UH H WH UP V
T
oO
1 1V
K D V ] H UR P H D Q
\,3 , N LQ F R U U H V S R Q G V W R W K H ,3 ,
HI (F
1S b
; O
DeO
1S b
;
O
DO
1V 7F
=
N 7 O
N7 O
G W b O F W b O F W b O GWJ
O O
7K H ,3 , LQ F D Q E H U H ZU LW W H Q D V W K H V X P
R I 1S 1S b W H U P V R I P X W X D O V X P
R I
LQ W H U IH U H Q F H N7 O N 7 O @ D V LW F D Q E H V H H Q LQ )LJ X U H ( D F K R I W K H Q R Q R YH U OD S S LQ J D U H D V D Q G W K H R YH U OD S S LQ J D U H D LI D Q \ LQ W K H F R U U H V S R Q G LQ J LQ W H J U D O R I U H V X OW W R D V X P
R I QX D Q G QF E LQ D U \ h H TX LS U R E D E OH LLG 5 9 V
U H V S H F W LYH O\ ZK H U H W K H Q X P E H U R I F K LS V F R U U H V S R Q G LQ J W R W K H Q R Q R YH U OD S S LQ J D U H D V LV QX
PLQ 1V MrO b rO M x 1V
D Q G W K H Q X P E H U R I F K LS V F R U U H V S R Q G LQ J W R W K H R YH U OD S S LQ J D U H D LI D Q \ LV x QF )U R P
1V b QX 1V
D Q G E D V H G R Q W K H D E R YH W K H P X W X D O LQ W H U IH U H Q F H E H W ZH H Q p Q J H U V O O
F D Q E H ZU LW W H Q D V ' ' ' ' @ 7K H LW H U D W LYH G H F R G H U
X V H V W K H / R J 0$ 3 D OJ R U LW K P
D Q G D P D [LP X P
8QFRGHG 96*&'0
Q X P E H U R I LW H U D W LR Q V
$
)LJ X U H S U H V H Q W V W K H S H U IR U P D Q F H R I D Q X Q F R G H G V \V W H P
D Q G W K H F R U U H V S R Q G LQ J S H U IR U
P D Q F H R I D Q 05 & F R P E LQ H U ZLW K 1S G H J U H H V R I G LYH U V LW \ > @ : H H [S H F W IU R P IR U D OD U J H 6 * W K H S H U IR U P D Q F H R I W K H V \V W H P W K H ? LG H D O 5 $ . ( )R U 1V
W K D W
ZLW K ,3 , ZLOO E H F OR V H W R W K H S H U IR U P D Q F H R I
W K H S H U IR U P D Q F H R I W K H V \V W H P
LV D S S U R [LP D W H O\ W K H V D P H
W R W K D W R I W K H ? LG H D O 5 $ . ( 7K H U H IR U H LQ W K H U H V W R I W K LV V H F W LR Q ZH ZLOO X V H 1V D E H Q F K P D U N R I ? ,3 ,IU H H S H U IR U P D Q F H :
K H Q W K H 6 * J H W V V P D OOH U D Q G W K H 6 1 5
D V K LJ K H U
Uncoded, Np=2 and Np=4 paths, longer delays
-1
10
-2
10
Ns=2 -3
BER
10
Ns=4 -4
10
Ns=8 -5
Ideal RAKE RAKE with IPI Np=2 paths
10
Ns=64
Np=4 paths -6
10
5
10
15
20
25
30
γb
)LJ X U H 3 H U IR U P D Q F H R I X Q F R G H G 9 6 *&' 0$ V \V W H P V ZLW K OR Q J H U G H OD \V : K H Q 1S W K H G H OD \V D U H r r : K H Q 1S W K H G H OD \V D U H r r r r W K H H oH F W R I W K H ,3 , E H F R P H V G R P LQ D Q W D Q G W K H V \V W H P
U H D F K H V D Q H U U R U q R R U 7K LV
H U U R U q R R U LV X V X D OO\ F LW H G D V W K H P R W LYD W LR Q E H K LQ G 6 ,& V F K H P H V )LJ X U H D OV R V K R ZV W K D W LQ W K H OR Z 6 1 5
U H J LR Q ZK H U H $ : *1
LV G R P LQ D Q W W K H S H U IR U P D Q F H ZLW K S D W K V
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p OH ZLW K OR Q J H U G H OD \V LV F K R V H Q ' H S H Q G LQ J R Q W K H 6 * W K H V H G H OD \V F D Q E H OR Q J H U W K D Q R Q H V \P E R O G X U D W LR Q 7 % D V H G R Q ZH H [S H F W W K D W W K H LQ F U H D V H G G H OD \V ZLOO Q R W G H W H U LR U D W H W K H S H U IR U P D Q F H R I W K H V \V W H P
F R P S D UH G
W R G H OD \V ZK LF K
D U H V P D OOH U
W K D Q R Q H V \P E R O S H U LR G ,Q G H H G F R P S D U LQ J W K H U H V X OW V G H S LF W H G LQ )LJ X U H V D Q G ZH V H H W K D W W K H S H U IR U P D Q F H ZK H Q
W K H G H OD \V D U H OR Q J H U LV V LP LOD U R U V OLJ K W O\ E H W W H U
Convolutional Encoding, Np=2 and Np=4 paths
-1
10
-2
10
Ns=2
-3
BER
10
Ns=4 -4
10
Ns=8 -5
10
Np=2 paths Np=4 paths Ns=64
-6
10
2
3
4
5
6
7
8
9
10
11
12
13
γb
)LJ X U H ( oH F W R I 6 * R Q W K H S H U IR U P D Q F H R I 9 6 *&' 0$ ZLW K &R Q YR OX W LR Q D O F R G LQ J 7K LV G H P R Q V W U D W H V W K H ID F W W K D W LQ V \V W H P V ZLW K OR Q J 3 1 V H TX H Q F H V ,3 , U D W K H U W K D Q ,6 , D U LV LQ J IU R P
OR Q J G H OD \V LV W K H ID F W R U OLP LW LQ J W K H S H U IR U P D Q F H 7K LV R E V H U YD W LR Q D OV R
LP S OLH V W K D W OR Q J 3 1
V H TX H Q F H V V K R X OG E H X V H G LQ V \V W H P V R S H U D W LQ J LQ YH U \ G LV S H U V LYH
F K D Q Q H OV &R Q F D W H Q D W LQ J OR Q J 3 1
V H TX H Q F H V G H D OV H oH F W LYH O\ ZLW K W K H S U R E OH P
ZLW K R X W V LJ Q Lp F D Q W O\ LQ F U H D V LQ J W K H V \V W H P
&RGHG 96*&'0
R I ,6 ,
F R P S OH [LW \
$
7K H H oH F W R I OR Z 6 * R Q W K H S H U IR U P D Q F H R I F R G H G V \V W H P V ZLW K &R Q YR OX W LR Q D O F R G LQ J LV G H S LF W H G LQ )LJ X U H ,W LV NQ R ZQ W K D W LQ ID G LQ J F K D Q Q H OV F R G LQ J LQ F U H D V H V W K H G H J U H H R I H oH F W LYH G LYH U V LW \ R I W K H V \V W H P W K X V U H G X F LQ J W K H U H TX LU H G 6 1 5 ,Q F R Q W U D V W W R W K H F D V H ZK H U H W K H Q X P E H U R I 5 $ . (
IR U D J LYH Q S H U IR U P D Q F H
p Q J H U V 1S LV LQ F U H D V H G LQ F R G H G
V \V W H P V K LJ K H U G LYH U V LW \ LV D F K LH YH G ZLW K R X W LQ F U H D V LQ J W K H S R ZH U U D W LR R I ,3 , R YH U $ : *1 LQ $ V ZH Q R W LF H LQ )LJ X U H ZLW K &R Q YR OX W LR Q D O F R G LQ J W K H G H V LU H G S H U IR U P D Q F H
Turbo Encoding, Np=2 and Np=4 paths
-1
10
-2
10
-3
10
BER
Ns=2 Ns=64
-4
10
Ns=4 -5
10
Ns=8
Np=2 paths Np=4 paths -6
10
2
3
4
5
6
7
8
9
10
γb
)LJ X U H ( oH F W R I 6 * R Q W K H S H U IR U P D Q F H R I 9 6 *&' 0$ ZLW K 7X U E R F R G LQ J %(5 y
b
LV D F K LH YH G
LQ
W K H P H G LX P
W R OR Z 6 1 5
U H J LR Q :
:
K H Q 1S
G H S LF W H G LQ )LJ X U H :
W K H S H U IR U P D Q F H R I F R G H G
V \V W H P V ZLW K
7X U E R F R G LQ J LV
LW K 7X U E R F R G LQ J W K H G H V LU H G S H U IR U P D Q F H %(5 y
D F K LH YH G IR U H YH Q OR ZH U 6 1 5 ZK H U H ,3 , K D V D Q H YH Q V P D OOH U LP S D F W : W K H S H U IR U P D Q F H G H J U D G D W LR Q LV OH V V W K D Q G % 1S
WK H
W K H S H U IR U P D Q F H G H J U D G D W LR Q LV
H YH Q V P D OOH U $ J D LQ D Q H U U R U q R R U LV R E V H U YH G R Q O\ IR U 1V 7K H H oH F W R I OR Z 6 * R Q
1S
IR U 1V y D Q G D Q H U U R U q R R U
S H U IR U P D Q F H G H J U D G D W LR Q F D X V H G E \ ,3 , LV OH V V W K D Q G % G X H W R ,3 , LV R E V H U YH G R Q O\ IR U 1V
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