Week9a, Digital Modulation

8/7/2019 Week9a, Digital Modulation

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EE 580

Wire less Com m unic at ions Syst em s

Fal l 2004

Dig i t a l Modulat ion

Richard S. Wolff, Ph. D.

[email protected] 994 7172

509 Cobleigh Hall



Modu la t ion and w i re less syst em s

• Analog:– used in early radio systems,

– first generation cellular• Digital:

– more efficient use of spectrum

– Better noise immunity (regeneration)

– inter-works better with other system elements and data applications,

– typical in second generation cellular

– Supports complex signal conditioning and processing techniques

• Source coding

• Encryption

• Equalization

– DSPs used to implement modulators and demodulators in software

– Software radio: alterations and improvements easy to implement!!



Represent a t ion o f m odula t ing

s ignal

• Message is a time sequence of symbols• Each symbol can have m states

• Each symbol represents n bits of information

lbits/symbolog2 mn =



Represent a t ion o f m odula t ing

s ignal : ex am ple

Number of

states, m

log2

m n bits/symbol

1 0 0

2 1 1

4 2 2

8 3 3

16 4 4

Transmit m symbols/sec

Results in n bits/sec



Choos ing a m odula t ion t ec hn ique:

des i rab le feat ures

• Low bit error rate at low received signal tonoise ratio

• Performs well under multipath and fading

conditions

• Occupies minimum bandwidth

• Easy and inexpensive to implement

Numerous trade offs implied by these attributes!!



K ey issues in selec t ing a

m odulat ion t ec hnique

• Power efficiency• Bandwidth efficiency



Pow er e f f ic ienc y

• Power efficiency ηp

: ability of modulation technique to

preserve the fidelity of the digital message at low power

levels

• Increase in signal power can raise noise immunity (forthermal noise)

• Trade off between fidelity (low errors) and signal power

• Metric: signal energy per bit/noise power spectral density:Eb /N0 needed to achieve a a certain probability of error

(BER)



BER versus EB/N0 for d i f feren t PSK

and FSK m odula t ion t ec hn iques



Ex am ple : BER versus Eb/N0

Ef fec t s o f Rayleigh fad ing



Bandw idt h ef f i c ienc y

• bandwidth efficiency : ability of modulation technique to

accommodate data within a limited bandwidth

• Increase in signal rate will decrease pulse width of digital

symbol, which increases the signal bandwidth (think of

Fourier transform: ∆T~1/ ∆f)

• Result is a trade off between symbol rate R and bandwidth

occupancy B

• Metric: ηB=R/B bps/Hz• System capacity of digital mobile system directly related to

bandwidth efficiency of the modulation technique



Bandw idt h ef f i c ienc y : ex am ples

• Occupied bandwidth B ~ 1/R, R=symbol rate

• BPSK: 2 states (m=2), n=1bit/symbol,

η=R/B=1/1=1 bps/Hz

• DPSK: 4 states (m=4), n=2 bits/symbol η=R/B=2/1=2 bps/Hz• 8PSK: 8 states (m=8), n=3 bits/symbol

η=R/B=3/1=3 bps/Hz



Channel c apac i t y : Shannon l im i t

• Upper bound on achievable bandwidth efficiency– Assumes non-fading channel

– Assumes additive white Gaussian noise (AWGN)

rationoisetosignal /

bandwidthRF

bpscapacity,channel

)1(log 2max

=

=

=

+==

N S

B

C

N

S

B

C

Bη



Shannon l im i t , ex am ples

• AMPS channel, B = 30kHz. Assume SNR=20dB.

What is maximum channel capacity C?

kbpsC

N

S BC

7.199

)1001(log000,30)1(log 22

=

+=+=

Note that data rate actually used in an AMPS channel is well

below the Shannon limit!

Voice message signal = 64kbpsVoice band data signal = 48kbps



Shannon l im i t , ex am ples

• Deep space link, B = 30kHz. Assume SNR=0.1dB.

What is maximum channel capacity C?

kbpsC N

S BC

ratio N S

ratio N

SdB

N

S dB N

S

49.30

)023.11(log000,30)1(log

023.11010

10,1.0

22

01.010 / 1.0

10 /

=

+=+=

===

==

Earth-space links are typically power limited: low SNR do to:1. Limited spacecraft transmit power

2. Large path loss



Ot her fac t o rs af fec t ing c ho ic e of

m odulat ion t ec hnique

• In addition to power and bandwidthefficiency, must consider:

– Cost and complexity of subscriber equipment

– A modulation that is simple to detect– Performance under Ricean and Rayleigh fading

– Performance under multipath conditions

– Interference environment

– Effects of timing jitter



Bandw idt h and pow er spec t ral

dens i ty

• Signal spread in frequency inversely proportional tosymbol rate R

• Narrow pulses (high symbol rate) lead to large spectralBW

• Define absolute bandwidth of signal as frequencyrange over which the signal has a non-zero powerspectral density PSD

rangefrequencyoverextends

/ )(sin~

shape,pulserrectangulawithsymbolsFor

22

∞

f f PSD



PSD for rec t angula r pulses

Time

A m

p l i t u d e

Tp



Def in i t ions o f signa l bandw idt h

• Null-to-null bandwidth: width of main spectral

lobe

• Half-power bandwidth: frequency where PSD has

dropped to half (3dB) of its peak value• Occupied bandwidth: defined by FCC as band

which leaves 0.5% of power below lower and

above upper band limit. 99% of power in occupied

bandwidth



L ine c od ing

• Line coding is the scheme used to representsuccessive zeros and ones

• Return to zero (RZ): pulse returns to zero

within each symbol period

1 1 0 1



Line c od ing I I• Non-return to zero (NRZ): pulse does NOT return

to zero within each symbol period

• Manchester coding: special case of NRZ

– “1” represented by a positive pulse followed bya negative pulse (within a symbol period)

– “0” represented by a negative pulse followed bya positive pulse (within a signal period

• Line codes can be– unipolar (0 or +V)

– Bipolar(-V or +V)

L i di l



L ine c oding ex am ples

Unipolar NRZ

Bipolar NRZ

Unipolar RZ

Bipolar RZ.

Manchester code



L ine c od ing t rade of fs

• RZ: return to zero every symbol adds transitions

– Leads to spectral broadening

– Improves timing synchronization

• NRZ codes

– More spectral efficiency– Poorer synchronization

• Manchester code

– No DC component– Simple synchronization

– More spectral spreading than NRZ

P t f U i l NRZ



frequency is normalized with respect to the bit rate 1/ T b, and the

average power is normalized to unity

Pow er spec t ra o f Unipolar NRZ



Pow er spec t ra o f b ipo lar NRZ

frequency is normalized with respect to the bit rate 1/ T b, and theaverage power is normalized to unity.




average power is normalized to unity.

Pow er spec t ra o f unipo la r RZ

Pow er spec t ra of Bipo lar RZ



The frequency is normalized with respect to the bit rate1/ T b, and the average power is normalized to unity.

Pow er spec t ra o f Bipo lar RZ

P f M h d




average power is normalized to unity.

Pow er spec t ra o f Manc hes t e r c ode

C i f l i d i t



Unipolar NRZ

Bipolar RZ

Manchester NRZ

Com par ison o f l ine c od ing spec t ra



Ef fec t s of bandw idt h l im i t ing a

d ig i t a l s igna l

• Typically band pass limit the transmittedsignal

• Cutting off some of the energy in the

frequency domain leads to spreading in the

time domain

• Net effect is inter-symbol interference(ISI)!!



Graphic a l “ proof ” o f ISI due t o

band l im i t ing

Transmit rectangular pulses in time domain

time

Fourier transform of a pulse

frequency




band l im i t ing I I

Pass transmitted pulse through a band pass filter

frequency

Transmitted pulse is truncated in the frequency

domain

frequency




band l im i t ing I I I

Fewer frequency components result in wider pulse intime domain

Intersymbol interference results where received

pulses overlap in time domain

time



Pulse shaping

• Technique to limit the bandwidth of thereceived signal while at the same time

minimizing ISI

• Typical approaches: round off the “sharp

edges”

– Raised cosine roll-off filter– Gaussian filter



Raised Cosine t ransfer func t ion

ss

s RC

T

f

T

T f COS f H

2

)1(

2

)1(

2)12(1

21)(

α α

α

α π

+≤≤

−

⎥⎥⎦⎤

⎢⎢⎣⎡ ⎥

⎦⎤⎢

⎣⎡ +−+=

α +==

1

1 B

T

Rs

s

RF bandwidth increases with α, but ISI goes down



Spec t rum of Raised Cosine pu lse

Vi r t ue of pu lse shaping



Vi r t ue o f pu lse shap ing



Represent ing d ig i t a l s ignals in

vec t o r spac e

• Consider a set S of waveforms representing

discrete symbols

• For binary modulation, bit= symbol , S has two

symbols• For higher order modulation, S>2

symbolainedtransmittbecanthatbitsof numbern,log 2 == M n

Example: QPSK has 4 symbols (0, π /2,π,3π /2), log2(4)=2 bits/symbol



BPSK c onst e l la t ion d iagram

•Two symbols (0, π)

•Distance between the symbols represents how different the signals are

•Large symbol separation makes it easier for receiver to detect symbol

correctly



Noise e f fec t s on c ons t e l lat ion

As the noise increases, the symbol smears out, and can overlap

with another symbol, causing a symbol error

Week9a, Digital Modulation

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