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C = W log2
(1 +
S
N
)(1)
M = 2m o m = log2 M (2)
m
TS=
log2 M
TS[bits/s] (3)
Tb =1R
=TS
m=
1mRS
(4)
RS =R
log2 M(5)
R
W=
log2 M
WTS=
1WTb
[bits/s/Hz] (6)
W =1TS
= RS (7)
R
W= log2 M [bits/s/Hz] (8)
W =M
TS= MRS (9)
R
W=
log2 M
M[bits/s/Hz] (10)
S
N0=
Eb
N0R (11)
Eb
N0(dB) =
S
N0(dB −Hz)−R(dB − bit/s) (12)
S
N0=
Eb
N0R =
ES
N0RS (13)
PE(M) = 2Q
[√2ES
N0sin( π
M
)]M > 2 (14)
Q(x) =1√2π
ı́nf∫x
exp[− u2
2
]du (15)
Q(x) ∼=1
x√
2πexp
[− x2
2
](16)
ES
N0= (log2 M)
Eb
N0(17)
PB∼=
PE
log2 M=
PE
mPE << 1 (18)
Eb
N0(dB) (19)
PE(M) ≤ M − 12
exp(− ES
2N0
)(20)
ES
N0= (log2 M)
Eb
N0(21)
PB =2m−1
2m − 1PE (22)
G(dB) =(Eb
N0
)uncoded
(dB)−(Eb
N0
)coded
(dB)
(23)
RC =
(n
k
)R (24)
RS =RC
log2 M(25)
EC
N0=
(n
k
)Eb
N0(26)
ES
N0= (log2 M)
EC
N0(27)
S
N0=
Eb
N0R =
EC
N0RC =
ES
N0RS (28)
ES
N0= (log2 M)
EC
N0= (log2 M)
(k
n
)Eb
N0(29)
PE(M) ∼= 2Q
[√2ES
N0sin( π
M
)](30)
pc∼=
PE
log2 M=
PE
m(31)
PB∼=
1n
n∑j=l+1
j(n
j
)pj
c(1− pc)n−j (32)
PB =PE
log2 M=
2Q
[√2ES
N0sin(
πM
)]log2 M
(33)
Gp =WSS
R(34)
Gp =RCH
R(35)
S
N0=
Eb
N0R =
EC
N0RS =
ECH
N0RCH (36)
ECH
N0=
S
N0
( 1RCH
)=
S
N0
( 1GpR
)=( 1
Gp
)Eb
N0
(37)
ECH
N0(dB) =
Eb
N0(dB)−Gp(dB) (38)
ES
N0=
EC
N0=(k
n
)Eb
N0(39)
pc = PE = Q
(√2EC
N0
)(40)
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