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SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

Modulaciones de alta velocidad

QAM-OFDM- 1

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

1. Modulaciones de alta velocidad
Transmiten: voz, imagen y datos
Requieren alta eficiencia espectral
Han de ser robustas a las degradaciones que introduce elcanal
(ej: ecos y desvanecimientos)

Tx. Telefónica por
línea de abonado
Radiodifusión

QAM-OFDM- 2

- Modem V.34
- xDSL
- Modulación OFDM

Todas se apoyan en la modulación
QAM:
Buen compromiso EfBW
en canales AWGN

BER

Bastante robusta a errores de sincron.

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

Densidad espectralSeñal paso-banda:

{

s (t ) = Re Ac bs (t ) e j ( 2πf ct +θ c )

bs (t ) = is (t ) + jqs (t )

}

información

 b (t ) = i (t ) 2 + q (t ) 2
s
s
 s

bs (t ) = bs (t ) e jθ b (t ) 
θ b (t ) = tg −1 qs (t )

is (t )

s (t ) = Ac {is (t ) cos( wc t + θ c ) − qs (t ) sen(wc t + θ c )}

QAM-OFDM- 3

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY ANDCOMMUNICATIONS

Rs (τ ) =

Ac2

(R

is

(τ ) + Rqs (τ ) )cos( wcτ )

2
TF

S s (τ ) =

Ac2
4

QAM-OFDM- 4

(S

is

( f − f c ) + Sis ( f + f c ) + S qs ( f − f c ) + S qs ( f + f c ) )

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

s (t ) =

Modulación M-ASK:

∞

∑a

k = −∞

is (t ) =

∞

∑a

k = −∞

p(t − kT )

k

Sis ( f ) = σ r P( f ) + (ma r )

σ =
2
a

M 2 −1

ma =

12
Si

∞

2

∑

P (nr ) δ ( f − nr )
2

n = −∞

M −1

unipolar

2

t
  → P( f ) = sen πfT = T sinc( fT )
p (t ) = Π
 
πf
T 

Sis ( f ) =

M 2 −1
12r

QAM-OFDM- 5

p (t − kT ) cos( wc t + θ c )

Señal M-PAM

2

2
a

k

sinc ( fT ) +
2

( M − 1) 2
4

δ(f )Ef BW =

rb
BWs

(bits/s/Hz)

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

Modulación M-APK (QAM):

∞

jθ k
j ( wc t +θ c ) 
s(t ) = Re Ac ∑ ak e p(t − kT ) e

 k = −∞


ASK+PSK

I k + jQk

∞
 ∞

s(t ) = Ac  ∑ I k p(t − kT ) cos( wc t + θ c ) − ∑ Qk p(t − kT ) sen( wc t + θ c )
k = −∞
k = −∞


is (t ) =∞

k = −∞

qs (t ) =
Si

∑I
∞

∑Q

k = −∞

k

M1 = 2

QAM-OFDM- 6

I k = ±1,±3... ± ( M 1 − 1)

n

p (t − kT )

M2 = 2

m

M-APK

Qk = ±1,±3... ± ( M 2 − 1)

p (t − kT )

k

M=M1 M2

M =2

n+m

=2

b

r=

rb
b

baudios

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

QAM-OFDM- 7

SIGNAL PROCESSINGIN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

QAM-OFDM- 8

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

QAM-OFDM- 9

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

QAM-OFDM- 10

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONSBER
A igual eficiencia espectral que PSK y ASK, QAM permite mejor BER; ya que hay más grados
de libertad en su diseño

M
8

Mejora en SNR de QAM
sobre PSK para igual BER
1.65

16

4.20

32

7.02

64

9.95
Comparación argumentos
BER

QAM-OFDM- 11

SIGNAL PROCESSING IN COMMUNICATIONS GROUP
DEPARTMENT OF SIGNAL THEORY AND COMMUNICATIONS

El límite de Shannon paratransmisión libre de errores en canales limitados en banda y AWGN

C = BWc log 2 [1 + SNR ] (bits / seg )
Ej.: canal telefónico: BWc= 3KHz

SNR=30 dB (1000:1)

C=30 kbps

Para determinar la probabilidad de error de una modulación digital como M-QAM se ha
de recurrir a su constelación. La probabilidad de error pe viene determinada principalmente
por la distancia mínima entre ptos. de...