fórmulas básicas de telecomunicaciones

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)

1