1. 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

2. 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 Y)
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)
tbp will be done at end of class (10 bonus points)

3. Review of Last Lecture Passband Digital Modulation
ASK/PSK special cases of DSBSC
FSK special case of FM
ASK/PSK Demodulator:
Decision devices finds if r(iTb) is closer to r0 or r1
Noise immunity DN is half the distance between r0 and r1
Bit errors occur when noise exceeds this immunity
Decision Device
nTb r1
r(nTb)
“1” or “0”
s(t)
r0+N  DN r0
cos(2pfct)

4. Noise in ASK/PSK
N(t)
nTb r1
“1” or “0”
r(nTb)+N(nTb)
s(t) +  DN
Channel r0
cos(2pfct)
Probability of bit error: Pb=p(|N(nTb)|>DN=.5|r1-r0|)
N(nTb) is a Gaussian RV: N~N(m=0,s2=.25NoTb)
For x~N(0,1), Define Q(z)=p(x>z)
ASK:
PSK:
Eb is average
energy per bit

5. 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

6. Communication System Block Diagram
Text
Images
Video
Source
Encoder
Transmitter
Channel
Receiver
Source
Decoder
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.

7. Main Focus of This Class
n(t)
Analog or Digital
Modulator
Analog or Digital
Demodulator
h(t) +
Transmitter
Channel
Receiver
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
Need tools for manipulating and filtering signals and noise

8. 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
xp(t) c0
c-1 c1
c-2 c2
c-3 c3
-.5T
.5T t
-1/T0
1/T0
2/T0 f
-T0 T0
2T0
c-4 c4

9. Fourier Transform Represents spectral components of a signal
Signal uniquely represented in time or frequency domain
These coefficients are frequency components of signal A
-.5T
.5T t f
Timelimited signals have infinite frequency content
Bandlimited signals are infinite duration

10. 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

11. Filtering Convolution defines output of LTI filters
Convolution (time) Multiplication (freq.)
Easier to analyze filters in frequency domain
Filters characterized by time or freq. response
Exponentials are eigenfunctions of LTI filters
LTI Filter
x(t)
y(t)=h(t)*x(t)
h(t)
H(fc)ej2pfct
ej2pfct
X(f)
H(f)
Y(f)=H(f)X(f)

12. Sampling Sampling (Time): = Sampling (Frequency) = * x(t) nd(t-nTs)
xs(t)
X(f) *
nd(t-n/Ts) =
Xs(f)

13. 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 domain
Sinc interpolation in time domain
Undersampling creates aliasing
X(f)
X(f)
Xs(f) -B B -B B

14. Power Spectral Density
Distribution of signal power over frequency
PSD/autocorrelation FT pairs: Rx(t) Sx(f)
Useful for filter and modulation analysis
Sx(f) f
cos(2pfct)
Sx(f)
|H(f)|2Sx(f)
Sx(f)
.25[Sx(f-fc)+ Sx(f+fc)]
H(f) X
Assumes Sx(f) bandlimited [-B,B], B << fc

15. Random Signals Not deterministic (no Fourier transform)
Signal contained in some set of possible realizations
Characterize by average PSD Sn(f)
Autocorrelation Rn(t) Sn(f) is the correlation of the random signal after time t.
Measures how fast random signal changes
Experiment

16. 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)
cos(2pfct)
Sn(f)
.25[Sn(f-fc)+ Sn(f+fc)] X

17. White Noise Signal changes very fast
Uncorrelated after infinitesimally small delay
Good approximation in practice
Filtering white noise: introduces correlation
Rn(t)
Sn(f)
.5N0d(t)
.5N0 f t
Sw(f)=.5N0
.5N0|H(f)|2
H(f)

18. Amplitude Modulation Simple modulators use nonlinear devices
cos(2pfct) ka 1
s(t)=Ac[1+kam(t)]cos2pfct
m(t) X + X
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

19. Detection of AM Waves
Entails tradeoff between performance and complexity (cost)
Square law detector squares signal and then passes it through a LPF
Residual 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

20. Double Sideband Suppressed Carrier (DSBSC)
Modulated signal is s(t)=Accos(2pfct)m(t)
Generated by a product or ring modulator
Requires coherent detection (f2f1)
Costas Loop
m(t)
s(t)
Product
Modulator
Product
Modulator
m´(t)
Channel
LPF
Accos(2pfct+f1)
Accos(2pfct+f2)

21. Noise in DSBSC Receivers
n(t)
LPF
s(t)=Accos(2pfct+f)m(t)
m´(t)+ n´(t)
Product
Modulator 1 +
Accos(2pfct+f)
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)

22. Single Sideband Transmits upper or lower sideband of DSBSC
Reduces bandwidth by factor of 2
Uses same demodulator as DSBSC
Coherent detection required.
USB
LSB

23. FM Modulation
Information signal encoded in carrier frequency (or phase)
Modulated signal is s(t)=Accos(q(t))
q(t)=f(m(t))
Standard FM: q(t)=2pfct+2pkf m(t)dt
Instantaneous frequency: fi=fc+kfm(t)
Signal robust to amplitude variations
Robust to signal reflections and refractions

24. FM Bandwidth and Carson’s Rule
Frequency Deviation: Df=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: Df<<BmB2Bm
Wideband FM: Df>>Bm  B2Df
B2Df+2Bm

25. Generating FM Signals NBFM WBFM Circuit based on product modulator
Direct Method: Modulate a VCO with m(t)
Indirect Method: Use a NBFM modulator, followed by a nonlinear device and BPF

26. FM Generation and Detection
Differentiator/Discriminator and Env. Detector
Zero Crossing Detector
Uses rate of zero crossings to estimate fi
Phase Lock Loop (PLL)
Uses VCO and feedback to extract m(t)

27. ASK, PSK, and FSK Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
m(t)
AM Modulation
m(t)
AM Modulation
FM Modulation

28. ASK/PSK Demodulation
N(t)
nTb r1
“1” or “0”
r(nTb)+N(nTb)
s(t) +  DN
Channel r0
cos(2pfct)
Probability of bit error: Pb=p(|N(nTb)|>DN=.5|r1-r0|)
N(nTb) is a Gaussian RV: N~N(m=0,s2=.25NoTb)
For x~N(0,1), Define Q(z)=p(x>z)=.5erfc(z/2 )
ASK:
PSK:
Eb is average
energy per bit

29. FSK Demodulation (HW 7)
nTb
r1(nTb)+N1 
“1” or “0”
s(t)+n(t)
cos(2pf1t)
Comparator
nTb
r2(nTb)+N2 
cos(2pf2t)
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)

30. 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.

31. Hot Topics in Communications
All-optical networks
Components (routers, switches) hard to build
Need very good lasers
Communication schemes very basic
Evolving to more sophisticated techniques
Advanced Radios
Adaptive techniques for multimedia
Direct conversion radios
Software radios
Low Power (last years on a battery)
Ultra wideband
Wireless Communications

32. Future Wireless Systems
Ubiquitous Communication Among People and Devices
Nth Generation Cellular
Wireless Internet (802.11)
Wireless Video/Music
Wireless Ad Hoc Networks
Sensor Networks
Smart Homes/Appliances
Automated Vehicle Networks
All this and more…

33. The End
Good luck on the final
Have a great spring break