PDF Mobile Radio Communications

Session 4: Modulation & transmission

Mobile Radio Communications

Mobile Radio Communications

Why modulation ? Why modulation ?

• RF carrier as transmission medium

• spectral efficiency

• robustness on radio path

• analog versus digital information

Carrier modulation Carrier modulation

• amplitude/phase

• phasor / complex baseband representation

• I and Q modulation:

cos and sin

in-phase and quadrature component

AM PM

I Q

I

Q real complex

AM

Constant-envelope modulation Constant-envelope modulation

• RF amplitude constant

• class C amplification (efficiency)

• limiting receiver

• non-linear TX-RX operations

• information in phase only (but be careful …)

PA

s(t) VCO

Analog modulation Analog modulation

• Information is analog

• AM, PM, and FM

( ) ^{t A} [ ^m ( ) ^t ] ^{f t}

s

_AM

=

_c

¹ + ^{cos 2} π

_c

f _c -f _c

S

( ) ^{f t}

A t A

m A if

k A

_c

c m c

m

= ^{cos 2} π

=

AM

SSB modulation SSB modulation

• AM: redundant information (two side bands)

• Remove one side band → Single Side Band

• Complex !

( ) ^{t A} ( ^m ( ) ^{t f t m} ( ) ^{t f t} )

s

_SSB

=

_c

^{cos 2} π

_c

_m ^{ˆ sin 2} π

_c

f _c -f _c

S SSB

( ) ^t

m ˆ Hilbert transform

SSB generation SSB generation

HS _m S _m

H j

HS _m

j

f _c -f _c

Q

j

-j

* -f _c f _c

I

S _m

f _c -f _c

I

* -f _c f _c

I

SSB generation SSB generation

f _c -f _c

I

( ) ^{t f t}

m

A

_c

^{cos 2} π

_c

f _c -f _c

I

( ) ^{t f t}

m

A

_c

^{ˆ sin 2} π

_c

• Addition: lower side bands

• Subtraction: upper side bands

SSB features SSB features

• Amplitude and phase modulation

• Bandwidth efficient but poor performance in radio channel

• Needs accurate frequency tuning

• Pilot tone required

Angle modulation Angle modulation

• Frequency or phase

• Constant envelope

( ) ( ) _



 



 +

= ∫

∞

− t f c

c

FM

t A f t k m d

s ^{cos 2} π ² π τ τ

( ) ^{t A f t}

m

if =

_m

^{cos 2} π

_m

FM

( ) _



 



 +

= f t

f A t k

f A

t

s

_m

m m f c

c

FM

^{cos 2} π ^{sin 2} π

k

_f

frequency deviation in V/Hz

W f W

A k

_{f m}

f

= ∆

β =

Angle modulation Angle modulation

( ) ^{t A} [ ^{f t k m} ( ) ^t ]

s

_FM

=

_c

cos 2 π

_c

+ _θ PM

k

_θ

phase deviation in rad/Hz

∂ / ∂ t

m(t)

PM

FM

m(t)

FM

∫ PM

θ

β

_p

= k _θ A

_m

= ∆

FM modulation FM modulation

f _c -f _c

I

m f

T

f

B = 2 ( β + 1 ) β

_f

< ¹ f

B

_T

= 2 ∆ β

_f

>> 1

Carson’s rule:

FM SNR performance FM SNR performance

FM

detector LPF

( ) ^W

N SNR A

f c

in

2 1

2

0 2

= +

β ( ) ^{( )}

ⁱⁿ

p f

f

out

SNR

V t SNR m

2

1

2

6  





 

 + 

= β β

(

^f

¹ ) ^W

2 β + _{2 W}

FM SNR performance FM SNR performance

W N

SNR _{out f} P ^carrier

0

3 β 2

=

2

2 c carrier

P = A

Digital modulation Digital modulation

• Information is digital

• binary modulation: bit b _i → symbol s _k

• m-ary modulation: {b _i ,b _i+1 …b _i+N-1 } → s _k log ₂ m bits/symbol

m → η b ( η _b ^{= R} _b ^/W)

• E _b energy per bit: P _carrier × T _b

• E _s energy per symbol: P _carrier × T _s

• N ₀ noise spectral density: P _noise /W

Digital modulation Digital modulation

• symbol duration T _s ; symbol rate R _s = 1/T _s symbol rate = baud rate

• bit duration T _b ; bit rate R _b = 1/T _b

R _b = R _s log ₂ m

Shannon’s channel capacity Shannon’s channel capacity

) 1

(

log ₂ SNR W

C = +

W R N

E W

N

T E

P

SNR P ^{b b b b}

N

s = ⋅

= ⋅

=

0 0

R b

C =

Maximum capacity:

Shannon’s channel capacity Shannon’s channel capacity

) 1

( log

0

2 W

R N

E W

R _{b b b}

⋅ +

=

b b

W R b

b b

W R

N E

η

η 1

2 1

2

0

= −

= −

η spectral efficiency b/s/Hz

Power-bandwidth trade-off Power-bandwidth trade-off

η _b ^[dB]

-25 -20 -15 -10 -5 0 5 10

0

-5

E b /N 0 [dB]

5 10 15 20 25

BW limited

power limited

GSM

IS-95

DECT Bluetooth

Power spectral density Power spectral density

( ) v ( ) ^τ

v f R

G ↔ ^F

( ) ^{τ = E} ( ^v ( ) ( ) ^{t v t + τ} )

R _v

autocorrelation:

Wiener-Kinchine theorem:

Bandwidth definitions Bandwidth definitions

-60 -50 -40 -30 -20 -10 0

-3dB BW

null-to-null BW

G(f) ↑

→ f

absolute BW: freq. range for which G(f) > 0

99% BW: freq. range where 99% of power is

Digital transmission chain Digital transmission chain

Information bits Symbol mapping I/Q mapping

Line coding Pulse Shaping RF upconversion

011000110001101101110010 s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ s ₇ s ₈

} } } } } } } }

Constellation diagram Constellation diagram

I Q

E s

E s

−

Normalize by 2 T _s d _ij

Orthogonal:

( ) ( ) ⁰

0

∫ ^{t j t dt} =

T

i φ

φ

j

i ≠

Error probability Error probability

0 d _ij /2 d _ij

) ( )

2 2 exp(

) 1

Pr(

₀ ² ₀

0

z Q dz

z z

z P

z

e

= ≥ = ∫

^∞

_π − =

Error probability Error probability

 





 



= 

 

 

=

≥

=

2 0

2 )

Pr( N

Q d Q A

z d

P ^ij

norm ij norm

e σ

σ z = A

s

s

E

T

A = 2 ⋅ A

_norm

= E

_s

B N

₀

σ = σ

_norm

= ^N

₀

²

BPSK BPSK

I Q

E b

E b

−

b

ij E

d = 2

 

 

=

0 ,

2 N Q E

P _{e BPSK} ^b 2

A 2

E

E _s = _b =

QPSK QPSK

I Q

E b

2

b

ij E

d = 2

 

 

=

0 ,

2 N Q E

P _{e QPSK} ^b 4

2

A 2

E _b = E ^s =

Offset-QPSK Offset-QPSK

QPSK

OQPSK

π π /4 QPSK /4 QPSK

I Q

I

Q

π π /4 QPSK /4 QPSK

I Q

11 01 00 10

π/4 3π/4

−3π/4

−π/4

b _k , b _k-1 φ _k

Minimum Shift Keying Minimum Shift Keying

I

Q

I

Q

1 1 0 1 0 0 0 1 1 0

0 0 1 0 1 0 1 1 1

1 1 0 1 0 0 0 1 1 0

0 0 1 0 1 0 1 1 1

MSK is

MSK is cos cos -shaped OQPSK -shaped OQPSK

Minimum Shift Keying Minimum Shift Keying

( ) _ ^ _ ^ ( ) ⁺

= f t

T t t

m

S _c

b I

MSK π π

2 2 cos

cos

( ) ( ^{f t} )

T t t

m _c

b

Q π π

2 2 sin

sin  

 

[ ( ) ]

( ^{f m t f t} )

S _MSK = ^{cos 2} π _c + ∆ _{FSK with ∆ f=1/4T b}

Continuous phase FSK (CPFSK) Continuous phase FSK (CPFSK)

Continuous phase modulation (CPM)

Continuous phase modulation (CPM)

Minimum Shift Keying Minimum Shift Keying

Orthogonal frequency keying Orthogonal frequency keying

s

c T

f

f 4

: 1

1 = +

s

c T

f

f 4

: 1

0 = −

T _s

0

Minimum Shift Keying Minimum Shift Keying

90

^o

-90

^o

-270

^o

270

^o

360

^o

-360

^o

1

1 0 1 0

0

0 1 0 1

PHASE TRELLIS PHASE TRELLIS

s

c

T

f

f 4

: 1

1 = +

s

c

T

f

f 4

: 1

0 = −

FSK:

T 2T 3T 4T

Symbol

Symbol transistions transistions

I Q

OQPSK MSK

QPSK

A

φ

0 T_s

π 2T_s

A

φ

0 T_s/2

π T_s A

φ

0 T_s

π 2T_s

Power spectral densities Power spectral densities

-40 -30 -20 -10 0 10

-50

f

_c

-70

-60

f

_c

+R

_b

f

_c

-R

_b

f

_c

-2R

_b

f

_c

+2R

_b

BPSK QPSK

MSK

GMSK GMSK

• Gaussian shaping of phase signal

PA

b(t) ^LPF VCO

 

 

=

0 ,

2 N Q E

P _{e GMSK} α ^b ₌

a ^{0 . 68} 85 . 0

25 .

= 0 BT

∞

→

{ BT

FSK FSK

• logical “1”: positive frequency shift

• logical “0”: negative frequency shift

PA

b(t) ^LPF VCO

 

 

=

0

, N

Q E

P _{e FSK} ^b

0 1

f

_c

- ∆ ^{f f}

_c

⁺ ∆ ^f

( ^{f R} )

B _T = 2 ∆ +

Other modulation schemes Other modulation schemes

M-ary PSK:

I Q

η M

_b

E

_b

/N0

2 0.5 10.5

4 1 10.5

8 1.5

14

16 2 18.5

32 2.5 23.4

64

3

28.5

Other modulation schemes Other modulation schemes

M-ary QAM:

I Q

η M

_b

E

_b

/N0

4 1 10.5

16 2 15

64 3 18.5

256 4 24

1024 5 28

4096

6

33.5

Digital transmission chain Digital transmission chain

Information bits Symbol mapping I/Q mapping

Line coding Pulse Shaping RF upconversion

011000110001101101110010 s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ s ₇ s ₈

} } } } } } } }

Line coding Line coding

impulse train → pulse train

→

• Spectral widening

• bit synchronization

• DC component

• return-to-zero (RZ)

• non-return-to-zero (NRZ)

• Manchester

• unipolar

• bipolar

Line coding formats Line coding formats

unipolar bipolar NRZ

RZ

Manchester NRZ

1 0 0 1 0 1 1 0 0 1 0 1

Digital transmission chain Digital transmission chain

Information bits Symbol mapping I/Q mapping

Line coding Pulse Shaping RF upconversion

011000110001101101110010 s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ s ₇ s ₈

} } } } } } } }

Pulse shaping Pulse shaping

TX filter

δ ^{(t) RX filter}

h _tx (t)=p(t) h _rx (t)

h _c (t)

h _eff (t)

( ) ( ) ( ) ( ) ^{t t h t h t h} ( ) ^t

h _eff = δ ∗ _tx ∗ _c ∗ _rx

( ) s ⁼ eff nT

h

Nyquist criterion: { ^K _{0 n} ⁿ _≠ ⁼ ₀ ⁰

Inter-symbol interference

Inter-symbol interference

Eye diagram Eye diagram

-2 -1 0 1 2

0.0 0.5T

_s

eye opening

-0.5T

_s

Inter-symbol interference

Inter-symbol interference

Eye diagram Eye diagram

-2 -1 0 1 2

0.0 0.5T

_s

eye opening

-0.5T

_s

Pulse shaping Pulse shaping

• spectral efficiency is optimized (minimal BW, low leakage)

• bit synchronization is facilitated

• ISI effects are minimized

Choose optimal h _tx (t) such that:

• bit synchronization is optimized

• ISI effects are minimized

Choose optimal h _eff (t)=h _tx (t)*h _rx (t) such that:

Sinc Sinc pulse pulse

( ) ( )

( ) s s

eff t T

T t t

h π

π

= sin ( ) ^{= Π} _ ^ _ ^

s s

eff f

f f f

H 1

↔ ^F

T_s 1/2T_s

t f

↔ ^F

Shaping Shaping

( ) ( )

( ) ^z ( ) ^t

T t

T t t

h

s s

eff = •

π π sin

T_s t

Nyquest criterion remains satisfied for z(t):

Shaping Shaping

-4 -3 -2 -1 0 1 2 3 4

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

t

Shaping Shaping

-3dB BW

=

=

*

.

z(t)

Z(f)

t

f

Raised cosine shaping Raised cosine shaping

s

eff f T

H ( ) =

 





 





 

 

 



 

 − −

+

=

s s

s

f T T

T

2 cos 1

2 1

α α

π

= 0

( ) T

s

f 1 2

0 ≤ ≤ − α

( ) T

s

f ≥ 1 + α 2

rest

( )

( ) ( )

 

 



⋅ 

 

 





= −

s s s

s

eff t T

T t T

t

T t t

h π

π α

πα ^sin 4

1

2 ) cos

( ₂

Raised cosine shaping Raised cosine shaping

α =0 α =0.3 α =0.5 α =0.9

1/T

t

f

RRC shaping RRC shaping

h _eff (t)=h _tx (t)*h _rx (t) Raised Cosine

h _tx (t)=h _rx (t)=sqrt(h _eff (t)) Root Raised Cosine

Gaussian

Gaussian shaping shaping

) exp(

)

( ^{2 2} _s ²

eff f f T

H = − α

) exp(

) (

2 2 2

2

s

eff T

t t

h α

π α

π ₋

=

s

dB T

B α

2 ) 2 ln(

3 =

−

Gaussian

Gaussian shaping shaping

α =2.0 α =1.0 α =0.5

T_s/2 T_s 3T_s/2 0

t

1/T_s 2/T_s 3/T_s

0

f

Spectral effect Spectral effect

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-60

-50

-40

-30

-20

-10

0

10

Digital transmission chain Digital transmission chain

Information bits Symbol mapping I/Q mapping

Line coding Pulse Shaping RF upconversion

011000110001101101110010 s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ s ₇ s ₈

} } } } } } } }

RF RF upconversion upconversion ( ) ^t ( ^t ( ) ^t )

A t

s ( ) = cos ω _c + φ

( ) ^t [ ( ) ( ) ( ) ^{t t} ( ) ( ) ( ) ^{t t} ]

A t

s ^{( )} = ^cos φ ^sin ω _c − ^sin φ ^cos ω _c

A(t)cos( φ ^(t))

LO

A(t)sin( φ ^(t))

sin( ω _c ^t)

cos( ω _c ^t) Σ ^s(t)

Via I and Q modulation:

RF RF upconversion upconversion ( ) ^t ( ^t ( ) ^t )

A t

s ( ) = cos ω _c + φ

( ) ^t ( ( ) ^t )

s LPF

t

s ( ) = { 2 ⋅ _IF ⋅ cos ω _c + ω _IF

Via IF stage: ^s IF ( ^t ) = ^A ( ) ^t cos ( ω IF ^t − φ ( ) ^t )

( ) [ ^cos ( ( ) ) ( ) ( ^cos ( ² ) ( ) ) ] ^}

{ A t t t A t t t

LPF ω _c + φ + ω _c + ω _IF − φ

=

RF RF upconversion upconversion

A(t)cos( ω _IF ^t- φ ^(t))

LO

cos( ω _c ⁺ ω _IF ^)t)

s(t) LPF

Via IF stage:

RF RF downconversion downconversion

S

f _lo -f _lo

LO

f _c -f _c

image

RF RF downconversion downconversion

• High IF: f _lo -f _c >> W _band

• Low IF: f _lo -f _c ≈ ^W _band

• Zero IF: f _lo -f _c =0

Coherent versus non-coherent Coherent versus non-coherent

reception reception

• phase reference

• phase and frequency are retrieved

Coherent:

• energy detection

• differential detection (previous symbol is reference)

Non-coherent:

r(t)

f, φ

r(t)

τ f 1

f 2

m

a

x

r(t)

• Read:

Chapter 5: §5.11

Chapter 6: §6.1-6.10, 6.12-6.17 (not 6.14.2)

• Solve problems:

Chapter 5: 5.1, 5.5, 5.6, 5.12

FOR NEXT WEEK

FOR NEXT WEEK

Inter-symbol interference Inter-symbol interference

0

Inter-symbol interference

Inter-symbol interference