EE104: Lecture 25 Outline

Announcements

Review of Last Lecture

Probability of Bit Error in ASK/PSK

Course Summary

Hot Topics in Communications

Next-Generation Systems

Announcements HW 7 due Monday at 9 pm (no late HWs)

Solutions will be posted then.

Final Exam is Th., 3/20, 8:30am in Gates B03 (basement) Exam is open book/notes, covers through today’s lecture. Emphasis is on material after midterm, similar to practice

finals SCPD student must make remote arrangements w/me by this

Friday

Practice finals posted on class website 10 bonus points if turned in by 3/20 at 8:30am (Joice has

solutions)

Final Review: Monday 7-8pm (room 380-380Y) Extra Office Hours

My extra hours: M 4:30-6:30, TW 12-2, and by appointment Jaron: W 4-6 (Bytes), Nikola: after review and T 5-7pm (110

Packard)

will be done at end of class (10 bonus points)

Review of Last Lecture

Passband Digital ModulationASK/PSK special cases of DSBSCFSK special case of FM

ASK/PSK Demodulator:

Decision devices finds if r(iTb) is closer to r0 or r1

Noise immunity N is half the distance between r0 and r1

Bit errors occur when noise exceeds this immunity

s(t)

cos(2fct)

bT

dt0

)(

nTb

Decision Device

“1” or “0” r(nTb)

r0

r1

N

r0+N

Noise in ASK/PSK

Probability of bit error: Pb=p(|N(nTb)|>N=.5|r1-r0|)

N(nTb) is a Gaussian RV: N~N(=0,2=.25NoTb)

For x~N(0,1), Define Q(z)=p(x>z)

ASK:

PSK:

s(t)

cos(2fct)

bT

0

nTb

r(nTb)+N(nTb) “1” or “0” +

N(t)

ChannelN

r1

r0

00

225.)25.( NE

NTA

bcbbbc QQTANpP

00

2 2)5.( NE

NTA

bcbbbc QQTANpP

Eb is averageenergy per bit

Course Summary

Communication System Block Diagram Fourier Series and Transforms Sampling Power Spectral Density and

Autocorrelation Random Signals and White Noise AM Modulation FM Modulation Digital Modulation

Communication System Block Diagram

Source encoder converts message into a message signal or bits. Source decoder converts back to original format.

Transmitter converts message signal or bits into a transmitted signal at some carrier frequency. Modulation, may also include SS, OFDM, precoding.

Channel introduces distortion, noise, and interference.

Receiver converts back to message signal or bits. Demodulation (for SS and OFDM too), may also include equalization.

SourceDecoderChannel ReceiverTransmitter

TextImagesVideo

)(ts )(ˆ ts)(ˆ...ˆˆ

21

tmbb

)(...21

tmbb

SourceEncoder

Main Focus of This Class

Modulation encodes message or bits into the amplitude, phase, or frequency of carrier signal.

Channel filters signal and introduces noise

Demodulator recovers information from carrier

Analog or DigitalModulator

)(ts )()(ˆ tnts )(ˆ...ˆˆ

21

tmbb

)(...21

tmbb

Transmitter

Channel

h(t)

+Analog or Digital

Demodulator

Receiver

n(t)

Need tools for manipulating and filtering signals and noise

Fourier Series

Exponentials are basis functions for periodic signals Can represent periodic signal in terms of FS coefficients Complex coefficients are frequency components of signal

tnfj

nnp ectx 02)(

dtetxT

c tnfj

T

pn0

0

2

0

)(1

0 T0 2T0-T0

.5T-.5T

c1 c2

c0

c3

c4

xp(t)

t f1/T0 2/T00-1/T0

c-4

c-3

c-2

c-1

Fourier Transform Represents spectral components of a signal Signal uniquely represented in time or frequency

domain These coefficients are frequency components of signal

dtetxfX nftj 2)()(

dfefXtx ftj 2)()(

.5T-.5T

A

tf

Timelimited signals have infinite frequency contentBandlimited signals are infinite duration

Key Properties of FTs

Frequency shifting (modulation)Multiplying signal by cosine shifts it by fc in

frequency.

Multiplication in time Convolution in Frequency

Convolution in time Multiplication in

Frequency

Filtering

Convolution defines output of LTI filters

Convolution (time) Multiplication (freq.)

Easier to analyze filters in frequency domainFilters characterized by time or freq.

responseExponentials are eigenfunctions of LTI

filters x(t) h(t) y(t)=h(t)*x(t)

X(f) H(f) Y(f)=H(f)X(f)

LTI Filter

ej2fct H(fc)ej2fct

Sampling

Sampling (Time):

Sampling (Frequency)

xs(t)

0 0 0

x(t) =n(t-nTs)

Xs(f)

0 0 0

X(f) =n(t-n/Ts)*

Nyquist Sampling Theorem

A bandlimited signal [-B,B] is completely described by samples every .5/B secs.Nyquist rate is 2B samples/sec

Recreate signal from its samples by using a low pass filter in the frequency domainSinc interpolation in time domainUndersampling creates aliasing

Xs(f)X(f)

B-B B-B

X(f)

Power Spectral Density

Distribution of signal power over frequency

PSD/autocorrelation FT pairs:

Rx(Sx(f)

Useful for filter and modulation analysis

Sx(f) dffSdttxT

P xT )(|)(|2

1lim 2

f

Sx(f) |H(f)|2Sx(f)H(f)

Sx(f) .25[Sx(f-fc)+ Sx(f+fc)]X

cos(2fct)

Assumes Sx(f) bandlimited [-B,B], B << fc

Random Signals Not deterministic (no Fourier transform)

Signal contained in some set of possible realizations

Characterize by average PSD Sn(f)

Autocorrelation Rn() Sn(f) is the correlation of the random signal after time .Measures how fast random signal changes

Experiment

Filtering and Modulation

Same PSD effect as for deterministic signals

Filtering

Modulation (no bandwidth

constraint on Sn)

Sn(f) |H(f)|2Sn(f)H(f)

Sn(f) .25[Sn(f-fc)+ Sn(f+fc)]X

cos(2fct)

White Noise

Signal changes very fastUncorrelated after infinitesimally

small delay Good approximation in practice Filtering white noise: introduces

correlation

.5N0() .5N0

f

Sn(f)Rn()

Sw(f)=.5N0 .5N0|H(f)|2

H(f)

Amplitude Modulation

Constant added to signal m(t)Simplifies demodulation if 1>|kam(t)|Constant is wasteful of power

Modulated signal has twice the BW of m(t)Simple modulators use nonlinear

devices

m(t)X

ka

X

cos(2fct)

+

1 s(t)=Ac[1+kam(t)]cos2fct

Detection of AM Waves

Entails tradeoff between performance and complexity (cost)

Square law detector squares signal and then passes it through a LPFResidual distortion proportional to m2(t)Noncoherent (carrier phase not needed in receiver)

Envelope detector detects envelope of s(t)Simple circuit (resistors, capacitor, diode)Only works when |kam(t)|<1 (poor SNR), no

distortion.Noncoherent

Double Sideband Suppressed Carrier

(DSBSC)

Modulated signal is

s(t)=Accos(2fct)m(t)

Generated by a product or ring modulator

Requires coherent detection (21)Costas Loop

m(t)

Accos(2fct+

ProductModulator

s(t) ProductModulator LPF

m´(t)

Accos(2fct+

Channel

Noise in DSBSC Receivers

Power in m´(t) is .25Ac2P

Sn´(f)=.25[Sn(f-fc)+Sn(f+fc)]|H(f)|2

For AWGN, Sn´(f)=.25[.5N0+.5N0], |f|<B.

SNR=Ac2P/(2N0B)

ProductModulator

m´(t)+ n´(t)

Accos(2fct+

s(t)=Accos(2fct+m(t)+

n(t)LPF

1

Single Sideband

Transmits upper or lower sideband of DSBSC

Reduces bandwidth by factor of 2Uses same demodulator as DSBSC

Coherent detection required.

USB LSB

FM ModulationInformation signal encoded in

carrier frequency (or phase)

Modulated signal is s(t)=Accos((t))(t)=f(m(t))

Standard FM: (t)=2fct+2kf m()dInstantaneous frequency: fi=fc+kfm(t)Signal robust to amplitude variationsRobust to signal reflections and

refractions

FM Bandwidth and Carson’s Rule

Frequency Deviation: f=kf max|m(t)|Maximum deviation of fi from fc: fi=fc+kfm(t)

Carson’s Rule:

B depends on maximum deviation from fc AND how fast fi changes

Narrowband FM: f<<BmB2Bm

Wideband FM: f>>Bm B2f

B2f+2Bm

Generating FM Signals

NBFMCircuit based on product modulator

WBFM

Direct Method: Modulate a VCO with m(t)

Indirect Method: Use a NBFM modulator, followed by a nonlinear device and BPF

FM Generation and Detection

Differentiator/Discriminator and Env. Detector

Zero Crossing DetectorUses rate of zero crossings to estimate fi

Phase Lock Loop (PLL)Uses VCO and feedback to extract m(t)

t

fcfcc dmktftmkfAts0

])(22sin[)](22[)(

ASK, PSK, and FSK

Amplitude Shift Keying (ASK)

Phase Shift Keying (PSK)

Frequency Shift Keying

0)(0

1)()2cos()2cos()()(

b

bcccc nTm

nTmtfAtfAtmts

1)()2cos(

1)()2cos()2cos()()(

bcc

bcccc nTmtfA

nTmtfAtftmAts

1)()2cos(

1)()2cos()(

2

1

bc

bc

nTmtfA

nTmtfAts

1 0 1 1

1 0 1 1

1 0 1 1

AM Modulation

AM Modulation

FM Modulation

m(t)

m(t)

ASK/PSK Demodulation

Probability of bit error: Pb=p(|N(nTb)|>N=.5|r1-r0|)

N(nTb) is a Gaussian RV: N~N(=0,2=.25NoTb)

For x~N(0,1), Define Q(z)=p(x>z)=.5erfc(z/2 )

ASK:

PSK:

s(t)

cos(2fct)

bT

0

nTb

r(nTb)+N(nTb) “1” or “0” +

N(t)

ChannelN

r1

r0

00

225.)25.( NE

NTA

bcbbbc QQTANpP

00

2 2)5.( NE

NTA

bcbbbc QQTANpP

Eb is averageenergy per bit

FSK Demodulation (HW 7)

Comparator outputs “1” if r1>r2, “0” if r2>r1

Pb=p(|N1-N2|>.5AcTb)=Q(Eb/N0) (same as PSK)

Minimum frequency separation required to differentiate |f1-f2|.5/Tb (MSK uses this minimum separation)

s(t)+n(t)

cos(2f1t)

bT

0

nTb r1(nTb)+N1

“1” or “0”

cos(2f2t)

bT

0

nTb

r2(nTb)+N2

Comparator

Megathemes in EE104

Fourier analysis simplifies the study of communication systems

Modulation encodes information in phase, frequency, or amplitude of carrier

Noise and distortion introduced by the channel makes it difficult to recover signal

The communication system designer must design clever techniques to compensate for channel impairments or make signal robust to these impairments.

Ultimate goal is to get high data rates with good quality and low cost.

Hot Topics in Communications

All-optical networksComponents (routers, switches) hard to

buildNeed very good lasersCommunication schemes very basicEvolving to more sophisticated techniques

Advanced RadiosAdaptive techniques for multimediaDirect conversion radiosSoftware radiosLow Power (last years on a battery)Ultra wideband

Wireless Communications

Future Wireless Systems

Nth Generation CellularWireless Internet (802.11)Wireless Video/Music Wireless Ad Hoc NetworksSensor Networks Smart Homes/AppliancesAutomated Vehicle NetworksAll this and more…

Ubiquitous Communication Among People and Devices

The End

Good luck on the final

Have a great spring break