10주차

10주차

M진 디지털 변조

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목표

Ÿ 대역통과 신호의 표현방법 이해

Ÿ M-ASK, M-FSK, M-PSK, MSK, QAM의 특성 비교 - Error probability

- Power spectrum

- Bandwidth efficiency (대역효율) - 그 외: implementation

내용

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Introduction

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대역통과 신호의 표현

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QPSK (Quaternary PSK)

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MSK (minimum shift keying)

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M-ary modulation

Ÿ M-ASK Ÿ M-FSK Ÿ M-PSK

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Combined amplitude and phase shift keying (QAM, APK)

Digital Modulations (from chap. 10)

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M-ary modulation

Ÿ  -bit symbol 사용 (



 ^가지의 signal) Ÿ M-ASK, M-PSK, M-FSK, M-QAM, ...

Ÿ Symbol rate



_ vs. Bit rate



_, Symbol duration



_ vs. Bit duration



_



_ ^



_,



_  



_ Ÿ 대역효율 배 증가 (FSK 제외)

Ÿ



이 커질수록 BER 성능은 악화 (QPSK, M-FSK 제외)

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Digital modulation에서 고려해야 할 요소

1) BER (or SER) à power에 의해 결정

2) Power spectral density

3) Bandwidth efficiency

data rate bandwidth

º

à modulation level, spectrum에 의해 결정

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Two factors of bandwidth efficiency

M진 디지털 변조

(1) 통과대역 신호의 표현

(2) Quadrature Phase Shift Keying (QPSK) (3) Minimum Shift Keying (MSK)

(4) M-ary Amplitude Shift Keying (M-ASK) (5) M-ary Frequency Shift Keying (M-FSK) (6) M-ary Phase Shift Keying (M-PSK)

(7) Quadrature Amplitude Modulation (QAM)

Three Representations for Bandpass Signals

(1) Magnitude & phase

{ }

( ) ( ) cos 2 _c ( )

s t = A t

p

f t +q t à bandpass signal

(2) In-phase & quadrature-phase

( )

( ) I t cos 2 _c Q( ) sin 2 _c

s t =

p

f t - t

p

f t à bandpass signal

(3) Complex envelope

( ) A t( ) ^j ( )^t

s t% = e ^q à lowpass signal

※ Complex envelope와 bandpass signal의 관계

{

²

} {

^{( ) 2}

}

( ) Re ( ) ^{j fct} Re ( ) ^{j t j f tc}

s t = %s t e ^p = A t e ^q e ^p

(1) Magnitude & Phase Representation

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Any bandpass signal

Ÿ can be represented as

{ }

( ) ( ) cos 2 _c ( ) s t = A t

p

f t +q t

․



 : real-valued baseband signal

․  : real-valued baseband signal

Ÿ This representation is easy to interpret physically, but often is not mathematically convenient.

A t( )

( )t

q

2

p

f_c

< phasor diagram >

(2) In-phase & Quadrature-phase Representation

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Bandpass signals

{ }

( ) ( )

( ) cos ( ) (

( ) cos 2

cos 2 sin 2

cos 2 sin

)sin ( )

( ) ( ) 2

c

c c

c c

s A t t

A t t A t t

I t Q

t f t

f t f

t t f t

t f

q

q q

p

p p

p p

= +

= -

= -

․ ( )I t = A t( ) cos ( )

q

t : in-phase component of





․ ( )Q t = A t( )sin ( )

q

t : quadrature-phase component of





․ A t( ) = I² +Q²

․ ¹ ( )

( ) tan

( ) t Q t

q

= ^{- æ}ç I t ^ö÷

è ø

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직교 좌표계 표현

( ) I t ( )

Q t

( ) A t

( )t

q

cos 2

p

f t_c sin 2

p

f t_c

-

(3) Complex Envelope Representation

( ) I t ( )

Q t

( ) A t

( )t

q

Re

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Complex envelope 표현 Im

( ) ( ) ^j ( )^t ( ) ( ) s t = A t e ^q = I t + jQ t

%

․ A t( ) = I² +Q²

․ ¹ ( )

( ) tan

( ) t Q t

q

= ^{- æ}ç I t ^ö÷

è ø

Ÿ Also called 'equivalent lowpass signal'

※ Complex envelope와 bandpass signal의 관계

{ } { }

{ }

2 (

2 )

( ) ( ) Re ( )

( ) cos 2 ( )

Re ^{j fc j t j f tc}

c

s t s t t A t e e

A t f t t

e ^{p q p}

p q

= =

= +

%

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Complex exponential 표현의 장점

Ÿ Compact

Ÿ 삼각함수 표현이 아닌 복소표현으로 다루기가 용이 Ÿ Baseband simulation of bandpass modulation

Frequency Band Relationship

f fc

- f_c

Spectrum of ( )s t%

^Re

(

^{´ ej2p f tc}

)

f fc

- f_c

2B

Spectrum of ( )s t

※ Note : What is the difference?

Ÿ

f vs. f Ans) Q(t) vs. conj(Q(t))

vs.