EE140 Introduction to Communication Systems Lecture 4

EE140 Introduction to

Communication Systems

Lecture 4

Instructor: Prof. Hua Qian

ShanghaiTech University, Spring 2019

Architecture of a (Digital) Communication System

©2019 Hua Qian EE140: Introduction to Communication Systems 2

SourceA/D

converterSourceencoder

Channelencoder

Modulator

Channel

DetectorChanneldecoder

Sourcedecoder

D/Aconverter

User

Transmitter

Receiver

Absent if

source isdigital

Noise

Contents

• Analog Modulation

– Amplitude modulation

• DSB

• SSB

• VSB

– Pulse modulation

– Angle modulation (phase/frequency)


Examples of Analog Modulation


Modulation

• What is modulation?

– Transform a message into another signal to facilitate transmission over a communication channel

• Generate a carrier signal at the transmitter

• Modify some characteristics of the carrier with the information to be transmitted

• Detect the modifications at the receiver

• Why modulation?

– Frequency translation

– Frequency-division multiplexing

– Noise performance improvement


Analog Modulation

• Characteristics that can be modified in the carrier

– Amplitude

– Frequency

– Phase


Amplitude modulation

Angle modulation

AMPM

( ))t(t)t(fcos)t(A)t(C θπ += 2

Amplitude Modulation

• Double-sideband suppressed-carrier AM (DSB-SC)

– Baseband signal (modulating wave):

– Carrier wave

– Modulated wave


)t(m

( )02 θπ += ftcosA)t(C

( )02 θπ +== ftcos)t(Am)t(C)t(m)t(S

DSB-SC Spectrum


)ff(M)ff(MA)f(S cc ++−=2

1

Demodulation of DSB-SC Signals

• Phase-coherent demodulation


24

2 2 2

tfcos)t(m)t(mA

tfcosA)t(mtfcosA)t(s)t(r

c

cc

π

ππ

+=

==

s(t) v(t) vo(t)Product modulator

Low-pass filter

cos(2πfct)

PLL (phase-locked loop)

Local oscillator

Demodulation of DSB-SC Signals

• DSB-SC demodulation: graphic interpretation


Question: not Phase Coherent?

• Phase error 𝜗


)t(m)tfcos(A)t(mcosA

)tfcos(tfcos)t(Am)tfcos()t(s)t(r

c

ccc

θπθ

θππθπ

++=

+=+=

42

1

2

1

22 2

( ) 42

1

2

1)t(mtfcosA)t(Am)t(r cπ+=

Uncertainty in the amplitude

Another Way to Generate DSB-SC Signals


A signal

spectrum can

be translated

an amount

by multiplying

the signal with

any periodic

wave form

whose

fundamental

frequency is

cω

cω

Double-sideband, Large-carrier (DSB-LC)

• DSB-LC signal (conventional AM signal) = DSB-SC signal + a carrier term


tcosAtcos)t(m)t(s cc ωω +=

Graphic Interpretation

• DSB-LC signal


Tim

e d

om

ain

Fre

quency d

om

ain

DSB-LC Properties

• The role played by parameter A

– If A is larger enough, say , the envelope of the modulated waveform will be proportional to .

• The DC response of the signal has been lost in the demodulation as a result of the addition of the carrier.


)t(mminA

)t(m

)t(m

Modulation Index

• Modulation index m is a dimensionless scale factor and used to represent the relative magnitudes of the sideband and carrier portion of the modulated signal.

• When m<1, and we also have


0

amplitude carrier peak

amplitude SC-DSB peak==

A

)t(mmaxm

)t(mmin)t(m)t(m)t(mmax −=−

magnitude) (min.magnitude) (max.

magnitude) (min.-magnitude) (max.

+=m

Modulation Index (cont’d)


Demodulation of DSB-LC Signals

• Coherent demod: possible, but not easy.

– Phase and frequency synchronizations are required;

• Noncoherent demod: envelope detection

– The RC circuit can perform low pass filtering

– Condition: or


The simplicity of envelop

detector has made

Conventional AM a practical

choice for AM-radio

broadcasting

RC too large

Correct RC

RC too small

)t(mminA 1m

Transmission Efficiency

• Transmission (modulation) efficiency:

• If , we have . The transmission efficiency

– Because , the transmission efficiency of a DSB-LC system is at best 33.3%. That is, at least 67% of the total power is expended in the carrier and wasted as the carrier term does not contain any information.

– For comparison, the transmission efficiency of a DSB-SC system is 100%.


)t(mA

)t(m

P

P

t

s

22

2

+==μ

tcosmA)t(m cω= ( ) 222 mA)t(m =

2

2

2 m

m

+=η

1m

Single-sideband (SSB) Modulation

• DSB modulation results in a doubling of the bandwidth of a given signal.

• Each pair of sidebands (i.e. upper or lower) contains the complete information of the original signal.

• The original signal can be recovered again from either the upper or lower pair of sidebands by an appropriate frequency translation. ➔ single-

sideband modulation


SSB

• Advantage: SSB modulation is efficient because it requires no more bandwidth than that of the original signal and only half that of the corresponding DSB signal.


Generation of SSB-SC Signals

• Generation of SSB-SC signals

• Method 1: filtering

– generate a DSB-SC signal;

– filter out one pair of sidebands (upper or lower).

• Requirement of method 1:

– does not contain significant low-frequency components;

– the sideband filter is usually built at a dictated frequency.


Generation of SSB-SC Signals (Cont’d)

• Method 2: phase-shift

– generate the quadrature function by shifting the phase of by 90 degrees at each frequency component.

– Upper (SSB+) sideband and lower (SSB-) sideband are given by

• Requirement:

– phase shifted by

exactly 90 degrees.

– used in low-freq

SSB generation and

in digital


)t(m)t(m̂

tsin)t(m̂tcos)t(m)t( ccSSB ωωφ =

SSB-SC Demodulation

• Synchronous detection

– Received SSB-SC signal:

– Local generated carrier signal:

– Through a low-pass filter (LPF), the output is given by:

– If no error


tsin)t(m̂tcos)t(m)t(s cc ωω =

]t)cos[()t(C c θωω ++= Δ

]}t)sin[(]t){sin[()t(m̂

]}t)cos[(]t){cos[()t(m

]t)cos[(]tsin)t(m̂tcos)t(m[)t(C)t(s

c

c

ccc

θωωθω

θωωθω

θωωωω

++−+

++++=

++=

ΔΔ

ΔΔ

Δ

2

2

21

21

]t)sin[()t(m̂]t)cos[()t(m)t(me θωθω ++= ΔΔ 21

21

21 )t(m)t(me =

SSB-SC Demodulation (Cont’d)

• Frequency domain graphic interpretation


Single-sideband, Large-carrier (SSB-LC)

• SSB-LC signal: SSB-SC signal + a carrier term

• In time domain:

– The frequency response at DC is NOT desired.

• Synchronous detection: √

• Envelope detection, not straightforward

– Requirement of envelope detection: the carrier is much larger than the SSB-SC envelope, i.e.


tsin)t(m̂tcos)t(mtcosA)t(s ccc ωωω +=

)t(mAA

)t(mA

A

)t(m̂

A

)t(m

A

)t(mA)]t(m̂[)]t(mA[)t(r

++

+++=++=

21

21

2

2

2

222

)t(m̂)t(mA 22 +

Comments on SSB

• Good:

– Save spectrum

– Save energy

• Bad:

– Complex implementation


Vestigial-sideband (VSB) Modulation

• The generation of SSB signals may be quite difficult when the modulating signal bandwidth is wide or where one cannot disregard the low-frequency components.

• In Vestigial-sideband (VSB) modulation, a portion of one sideband is transmitted.

• VSB is a compromise between SSB and DSB.

• Generation of VSB-SC signals: in frequency domain

– where filter passes some of the lower (or upper) sideband and most of the upper (or lower) sideband.


)(H)(M)(M)(S VccSCVSB ωωωωωω 2

1−++=−

)(HV ω

VSB Modulation (Cont’d)

• Frequency domain graphic interpretation


Comparison of AM Techniques

• DSB-SC:

– more power efficient. Seldom used

• DSB-LC (AM):

– simple envelop detector

– Example: AM radio broadcast

• SSB:

– requires minimum transmitter power and bandwidth. Suitable for point-to-point and over long distances

• VSB:

– bandwidth requirement between SSB and DSBSC.

– Example: TV transmission


Performance of AM Demod

• Synchronous detection vs envelope detection


– In synchronous detection, the output signal and noise always remain additive and the curve-slope is a constant, independent of input SNR.

– The nonlinear behavior of envelope detection declines the SNR performance wheninput noise increases.

Contents






Analog Pulse Modulation


Pulse-Amplitude Modulation (PAM)

Pulse-Width Modulation (PWM)

Pulse-Position Modulation (PPM)

Modulating Signal

Analog Pulse Modulation (cont’d)

• PAM: constant-width, uniformly spaced pulses whose amplitude is proportional to the values of at the sampling instants.

• PWM: constant-amplitude pulses whose width is proportional to the values of the input at the sampling instants.

• PPM: constant-width, constant-amplitude pulses whose position is proportional to the values of the input at the sampling instants.



• Remarks

– PWM is a popular choice where the remote proportional control of a position or a position rate is desired.

– Disadvantages of PWM include the necessity for detection of both pulse edges and a relatively large guard time is needed.

– Only the trailing edges of the PWM waveforms contain the modulating information. PPM conveys only the timing marks of the trailing edges.

– PAM and PWM are “self-clocking” (the waveform presents clock timing), while the use of PPM requires a method of regenerating clock timing.

– PWM and PPM are nonlinear, Fourier analysis cannot be used directly.


Pulse-code Modulation (PCM)

• Quantization: the sampled analog signal is quantized into a number of discrete levels.

• Digitization: assign a digit to each level (one-to-one mapping) so that the waveform is reduced to a set of digits at the successive sample times.

• Code: the digits are expressed in a coded form. Binary code (i.e. a code using only two possible pulse levels) is the most popular choice.


(3-bit code) Representations

of PCM code(8 levels)

PCM (cont’d)

• Advantages of PCM systems

– In long-distance communications, PCM signals can be completely regenerated (noise-free) at intermediate repeater stations because all the information is contained in the code. The effects of noise do not accumulate and only the transmission noise between adjacent repeaters need be concerned.

– Modulating and demodulating circuitry is all digital, thus affording high reliability and stability.

– Signals may be stored and time scaled efficiently.

– Efficient codes can be utilized to reduce unnecessary repetition (redundancy) in message. (source coding)

– Appropriate coding can reduce the effects of noise and interference. (channel coding)


Contents






Analog Pulse Modulation


Pulse-Amplitude Modulation (PAM)

Pulse-Width Modulation (PWM)

Pulse-Position Modulation (PPM)

Modulating Signal


• PAM: constant-width, uniformly spaced pulses whose amplitude is proportional to the values of at the sampling instants.

• PWM: constant-amplitude pulses whose width is proportional to the values of the input at the sampling instants.

• PPM: constant-width, constant-amplitude pulses whose position is proportional to the values of the input at the sampling instants.



• Remarks

– PWM is a popular choice where the remote proportional control of a position or a position rate is desired.

– Disadvantages of PWM include the necessity for detection of both pulse edges and a relatively large guard time is needed.

– Only the trailing edges of the PWM waveforms contain the modulating information. PPM conveys only the timing marks of the trailing edges.

– PAM and PWM are “self-clocking” (the waveform presents clock timing), while the use of PPM requires a method of regenerating clock timing.

– PWM and PPM are nonlinear, Fourier analysis cannot be used directly.


Pulse-code Modulation (PCM)

• Quantization: the sampled analog signal is quantized into a number of discrete levels.

• Digitization: assign a digit to each level (one-to-one mapping) so that the waveform is reduced to a set of digits at the successive sample times.

• Code: the digits are expressed in a coded form. Binary code (i.e. a code using only two possible pulse levels) is the most popular choice.


(3-bit code) Representations

of PCM code(8 levels)

PCM (cont’d)

• Advantages of PCM systems

– In long-distance communications, PCM signals can be completely regenerated (noise-free) at intermediate repeater stations because all the information is contained in the code. The effects of noise do not accumulate and only the transmission noise between adjacent repeaters need be concerned.

– Modulating and demodulating circuitry is all digital, thus affording high reliability and stability.

– Signals may be stored and time scaled efficiently.

– Efficient codes can be utilized to reduce unnecessary repetition (redundancy) in message. (source coding)

– Appropriate coding can reduce the effects of noise and interference. (channel coding)


Contents






Analog Modulation

• Characteristics that can be modified in the carrier

– Amplitude

– Frequency

– Phase


Amplitude modulation

Angle modulation

AMPM

( ))t(t)t(fcos)t(A)t(C θπ += 2

Angle Modulation

• Either phase or frequency of the carrier is varied according to the message signal

• General form

– time-varying phase

– Instantaneous frequency


)]t(tfcos[A)t(s c θπ += 2

)t(θ

dt

)t(d)t(f

θ=

PM and FM

• Phase modulation

– Overall output

• Frequency modulation

– Overall output


constant a is and deviation phase is where pp K),t(mK)t( =θ

)]t(mKtfcos[A)t(s pc += π2

constant a is and deviation frequency is where ff K),t(mKdt

)t(d=

θ

]d)(mKtfcos[A)t(st

fc 0

0

2 θττπ ++=

PM and FM: Graphic Interpretation


AM and PM

• Amplitude modulation (AM) is linear

–

• Angle modulation (PM and FM) is nonlinear


m(t))t(dm

)t(ds of tindependen is

( ) tfcos)t(mA)t(s cπ2 +=

( ) ( ) ( ) ( )

++−−=

+−−+=

=+=

23

22

22

3

1

2

11

2

32

322

2

tfsin!

)t(tfcos

!

)t(tfsin)t(tfcosA

)t(!

j)t(!

)t(j A eRe

eA eRe)t(tfcosA)t(s

cccc

tfj

)t(jtfj

c

c

c

πθ

πθ

πθπ

θθθ

θπ

π

θπ

“Linear” Angle Modulation

• Nonlinear angle modulation: the sidebands arising in angle modulation do not obey the principle of superposition.

• However, if , the high-order terms in 𝑠(𝑡) can be ignored


1)t(θ

( ) ( ) tfsin)t(tfcosA)t(s cc πθπ 22 −

Approximately linear!

Narrowband FM (NBFM)

• Narrowband FM (NBFM) – sinusoidal modulating signal

• Given

– where is the peak frequency deviation, and is the modulation index


]d)(mKtfcos[A)t(st

fc 0

0

2 θττπ ++=

0 and 2 0 == θtfcosa)t(m mπ

tfsintfsinf

ftfsin

f

aKd)(mK)t( mm

m

m

m

f

t

f πβπππ

ττθ 2222

0

==== Δ

fΔ β

NBFM (Cont’d)

• If (i.e. ), the narrowband FM signal is given by

• Compared with DSB-LC (AM)


1)t(θ10 β

−+=

−=

− tfjtfjtfj

cmc

mmc eeAeRe

tfsintfsinAtfcosA)t(s

πππ ββ

ππβπ

222

221

2 2 2

++=

+=

− tfjtfjtfj

cmc

mmc em

em

AeRe

tftfmAtfcosA)t(s

πππ

πππ

222

221

2cos 2cos 2

Narrowband PM (NBPM)

• Narrowband PM (NBPM) – sinusoidal modulating signal

• Given

• If , s(t) is approximately linear.

• DSB-LC(AM), NBPM and NBFM are examples of linear modulation.

• If the modulating signal bandwidth is , the narrowband angle-modulated signal will have a bandwidth of .


)]t(mKtfcos[A)t(s pc += π2

0 and 2 0 == θtfcosa)t(m mπ

tfcostfcosaK)t(mK)t( mmpp πβπθ 22 ===

10 β

mf

mf2

Wideband FM

• If modulation index is NOT small, the spectral density of a general angle-modulated signal cannot be obtained by Fourier transform.

• Wideband FM

– Modulation index


]d)(mKtfcos[A)t(st

fc 0

0

2 θττπ ++=

tfsinjtfj

mcm

m

fc

mc eAeRe

tfsintfcosAtfsinf

KtfcosA)t(s

πβπ

πβπππ

π

22

2222

2

=

+=

+=

m

f

m f

K

f

f

πβ

2==

Δ

Wideband FM

• is a periodic function of time with a fundamental frequency of 𝑓𝑚. Its Fourier series

representation is

– Bessel functions of the first kind


tfsinj meπβ 2

−

−

−=

==2

2

2222 1 where

T

T

tnfjtfsinj

n

n

tnj

n

tfsinjdtee

TFeFe mmmm ππβωππβ ，

)(JF nn β=

Spectra of FM Signal

• Total average power in an FM signal is a constant.


constant mf constant fΔ

Bandwidth of FM Signals

• Bandwidth of FM signals, theoretically unlimited.

• Significant sideband

– For large : diminish rapidly for . Assume there are significant sidebands, .

– For small : only and have significant magnitude. Assume , .

• Carson’s rule:

– An approximation of the bandwidth.


mfnW 2=

β )(Jn β βnfffnW mm Δ 2 2 2 == ββ=n

β )(J β0 )(J β1

mfW 21=n

( ) ( )β+=+ 1 2 2 mm fffW Δ

Example

• A 10 MHz carrier is frequency-modulated by a sinusoidal signal such that the peak frequency deviation is 50 kHz. Determine the approximate bandwidth of the FM signal (a) 500 kHz; (b) 500 Hz; (c) 10 kHz.

• Solution:

– (a) ➔

• Carson’s rule gives:

– (b) ➔


– (c) . Check Bessel function table, we have



1100500

50=== .

f

f

m

Δβ MHzfB m 12 =

MHz.)(fB m 1112 =+ β

1100500

50000===

mf

fΔβ kHzfB 100 2 = Δ

kHz)(fB m 10112 =+ β

51050 ==

kHz)(fB m 12012 =+ β

kHznfB m 1602 ==8=n

Wideband PM

• Wideband PM:

– Instantaneous phase:

– Peak phase deviation:

– Instantaneous frequency:

– Peak frequency deviation:

• Wideband PM – sinusoidal modulating signal

– Let and


])t(mKtfcos[A)t(s pc 02 θπ ++=

02 θπθ ++= )t(mKtf)t( pc

)t(mKmax p =θΔ

= )t(mdt

dKmaxf pΔ

)t(mdt

dKf)t(

dt

d)t(f pc +== θ

tfcosa)t(m mπ2 = 00 =θ

tfcosjtfj

mpcmc eAeRetfcosKatfcosA)t(s

πβπππ 222 2 =+=

Generation of Wideband FM Signals

• Direct method: vary the carrier frequency directly with the modulating signal by using the voltage-controlled oscillator (VCO).

– The oscillation frequency of a simple tuned electronic oscillator is given by , where L: inductance; C: capacitance.

– For very small variations (i.e. ), the square-root relationship can be approximated by a linear term.

• Requirement of direct method:

– The long-term frequency stability is not as good as the crystal-stabilized oscillators so that frequency stabilization is needed.

– The percentage frequency deviation that can be attained in this method is quite small. (say 𝛽 < 0.2 in theory)


)t(m

( )LC/f π210 =

cff Δ

Generation of Wideband FM Signals (Cont’d)

• Indirect method: Armstrong indirect FM transmitter

– produce a narrowband FM signal.

– use frequency multiplier to increase the value of β.

• Frequency multiplier is a nonlinear device designed to multiply the frequencies of the input signal by a given factor, say .

• Frequency converter is often used to control the value of the carrier frequency. It translates the spectrum of a signal by a given amount but does not alter its spectral content.


lawnth −

Frequency multiplier Frequency converter

mf mnf

cn 1 −cn

Generation of Wideband FM Signals (Cont’d)

• Indirect method: Armstrong indirect FM transmitter

– As a result of the multiplication and heterodyne operations, it is difficult in this system to maintain the correct magnitude of carrier to sidebands, and thus it could not be used for an information signal with DC content.


Demodulation of Wideband FM Signals

• Demodulation: to provide an output signal whose amplitude is linearly proportional to the instantaneous frequency of the input FM signal.

• Direct method: use frequency discriminator

– Frequency discriminator is the system that has a linear frequency-to-voltage transfer characteristic.

– Ideal differentiator has a linear amplitude versus frequency characteristic and therefore is a frequency discriminator.

Input:

Output:

– If , the modulating signal can then be detected by an envelope detector.


]d)(mktfcos[A)t(st

fc 00

2 θττπ ++=

+++−= 0

0 2 ]2[ θττ d)(mKtπfsin)t(mKπfA)t(s

dt

d t

fcfc

cf f)t(mK π2

Demodulation of Wideband FM Signals (Cont’d)

• Examples of frequency discriminator



• Indirect method: use phase-locked loop (PLL)

– Phase comparator detects the timing difference between the two periodic signals (with the same fundamental frequency) and produces an output voltage that is proportional to this difference.

– Loop filter controls the dynamic response of the PLL. We have

– Voltage-controlled oscillator (VCO) generates a constant-amplitude periodic waveform whose instantaneous frequency is proportional to the input voltage, i.e., .


Phasecomparator

)(tsi

Loop

filter

Voltage-controlled

oscillator (VCO)

)(tso

)(tsc

)(ts f

)t(h)t(s)t(s co =

)t(sKf)t(s ofcf += π2


• Indirect method: output of PLL

– Assume and

the phase comparator output is then

– If is small and we have .


)]t(tfcos[A)t(s ici νπ += 21 )],t(tfsin[A)t(s fcf νπ += 22

)]t()t(sin[AA

)]t(tfsin[A)]t(tfcos[A)t(s

if

LPfcicc

νν

νπνπ

−

++

21

21

2

1

2 2

)t()t( if νν − )]t()t([k)t(s ifcc νν −

Phasecomparator

)(tsi

Loop

filter

Voltage-controlled

oscillator (VCO)

)(tso

)(tsc

)(ts f


• Indirect method: output of PLL


)t(h)]t()t(sin[kk)t(h)t(sk)t(sk)t(dt

difcfcfoff −=== ννν

Phasecomparator

)(tsi

Loop

filter

Voltage-controlled

oscillator (VCO)

)(tso

)(tsc

)(ts f

0=+− )t(kk)t(kk)t(dt

dicffcff ννν

1=

)t(h

x)xsin(No PLL loop


• Indirect method: output of PLL (with loop)

– Output voltage is proportional to the instantaneous frequency (referred to the carrier) of the input wideband FM signal.

– The PLL demodulates the input wideband FM signal!


ττνν d)(sk)t()t(t

offi =0

)t(dt

d

k)t(s i

f

o ν1

Signal-to-noise Ratio (SNR) in FM Reception

• Input signal and input noise of the FM detector

• Output signal of the FM detector

• For convenience, assume

• Output noise of the FM detector

– Unmodulated carrier with additive bandpass noise

where and


2 2 2

00

/AS]d)(fktfcos[A)t(s i

t

fc =++= θττπ

)t(fk)t(dt

d)t()t(s fcco =−=− ωθωω

)t(fkS)t(fk)t(s fofo

22 ==

)]t(tcos[)t(r

tsin)t(ntcos)t(ntcosA)t(ntcosA

c

cscccc

γω

ωωωω

+=

−+=+

)t(n)t(n)t(nNtfsin)t(ntfcos)t(n)t(n scicscc

222 22 ===−= ππ

22 )]t(n[)]t(nA[)t(r sc ++= .)t(nA

)t(ntan)t(

c

s 1

+= −γ

SNR in FM Reception (cont’d)


– Assume the noise is small, i.e. , we have

– Output noise: .


A)t(n&)t(n sc

A

)t(n

A

)t(ntan

)t(nA

)t(ntan)t( ss

c

s

+= −− 11γ

)t(ndt

d

A)t(

dt

d)t(n so

1= γ

Power Spectral Density / Mean Power of Noise

• Input noise 𝑛(𝑡) of the FM detector

Bandwidth:

• Quadrature noise component

Bandwidth:


Hzwatts)(Sn 2ηω =

π

η

πω

2

2 2 2 WW

)(S)t(nN ni ===mnW ω 2=

0 2W2W−

)(snS

)t(ns

ηωωω =++−=LPcncnn )ω(S)ω(S)(S

s

π

η

πω

2

2

2 22 WW

)(S)t(nsns ==

mnW ω 2 =

Power Spectral Density / Mean Power of Noise


– where is the

frequency response of the

time differentiator (recall

• The discriminator output is limited by a low-pass filter (LPF) with a cutoff frequency of , the bandwidth of output noise is .


)t(no

2

2

2

22

2

1

A)(S

A)(H)(S

A)(S

sso nnn

ηωω

ωωωω ===

ωω j)(H =

)(Fj)t(fdt

dFT ωω =

mω

mω

2

3

0

2

2

2

3

2

1

Ad

Ad)(S)t(nN m

noo

mm

mo π

ωηωω

π

ηωω

π

ωω

ω==== −

SNR in FM Reception (cont’d)

• Signal-to-noise ratios (SNR) in FM reception

– For wideband FM, the output signal-to-noise ratio increases as the square of the bandwidth, which is proportional to .


W

A

N

SSNR

i

ii

2

η

π==

3

222

3

m

f

o

oo

)t(fKA

N

SSNR

ωη

π==

fK

SNR in PM Reception

• Input signal of the PM detector

• Output signal of the PM detector

• For convenience, assume

• Input noise of the PM detector

• Output noise of the PM detector

– Assume the noise is small,


2 2

0 AS])t(fKtcos[A)t(s ipc =++= θω

)t(fkt)t()t(s pco =−− 0θωθ

)t(fkS)t(fk)t(s popo

22 ==

)t(n

π

η

πωηω

2

2 2 2 2 WW

)(S)t(nNHzwatts)(S nin ====

)t(no

)t(nA)t(ntan)t()t(n cso += −1γ

.A

)t(n)t( sγ

22

2

22

22

1

AA)t(nN

A)(S

A)(S mm

oonn so π

ωη

π

ωηηωω =====

SNR in PM Reception (cont’d)

• Signal-to-noise ratios (SNR) in PM reception

• For sinusoidal modulating signal, i.e. , we have


W

A

N

SSNR

i

ii

2

η

π==

m

p

o

oo

)t(fkA

N

SSNR

ωη

π

222

==

mmm

p

o

o A)(AakA

N

S

ωη

βπ

ωη

θπ

ωη

π

2

2

2

2222222

===Δ

i

i

o

o

N

Sn

N

S 2β=

tωcosa)t(m m =

SNR in PM Reception (cont’d)

• Compared to the AM signal with 100% modulation, we have

– Conclusion: the output SNR can be made much higher in PM than in DSB-LC (AM) by increasing the modulation index .

– Assumption: (1) ; (2) .

– Expense: an increase in also increases the signal bandwidth.


AMo

o

AMi

c

PMo

o

N

S

N

S

N

S

=

=

22 ββ

β

A)t(n&)t(n sc 1ββ

Comparison of CW Modulation Systems


EE140 Introduction to Communication Systems Lecture 4

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Transcript of EE140 Introduction to Communication Systems Lecture 4