EE104: Lecture 25 Outline

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

3. DN r0+N 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 “1” or “0” r(nTb) s(t)  r0 cos(2pfct)

4. DN Noise in ASK/PSK N(t) nTb r1 “1” or “0” • 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: r(nTb)+N(nTb) s(t) +  r0 Channel cos(2pfct) 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. Source Decoder Channel Receiver Transmitter Communication System Block Diagram Text Images Video • 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. Source Encoder

7. + 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 n(t) Analog or Digital Modulator Analog or Digital Demodulator h(t) Transmitter Channel Receiver 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 f 0 2/T0 1/T0 -1/T0 -T0 0 T0 2T0 c4 c-4

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

12. 0 Sampling • Sampling (Time): • Sampling (Frequency) = x(t) nd(t-nTs) xs(t) 0 0 = X(f) nd(t-n/Ts) * Xs(f) 0 0 0

13. X(f) 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) 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) |H(f)|2Sx(f) Sx(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) |H(f)|2Sn(f) Sn(f) H(f) cos(2pfct) Sn(f) .25[Sn(f-fc)+ Sn(f+fc)] X

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

18. Amplitude Modulation cos(2pfct) • 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 ka s(t)=Ac[1+kam(t)]cos2pfct 1 m(t) + X X

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) m´(t) Product Modulator Product Modulator Channel LPF Accos(2pfct+f1) Accos(2pfct+f2)

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

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

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 fcAND how fast fi changes • Narrowband FM: Df<<BmB2Bm • Wideband FM: Df>>BmB2Df B2Df+2Bm

25. Generating FM Signals • NBFM • Circuit 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

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 1 0 1 1 • Amplitude Shift Keying (ASK) • Phase Shift Keying (PSK) • Frequency Shift Keying m(t) AM Modulation 1 0 1 1 m(t) AM Modulation 1 0 1 1 FM Modulation

28. DN ASK/PSK Demodulation N(t) nTb r1 “1” or “0” • 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: r(nTb)+N(nTb) s(t) +  r0 Channel cos(2pfct) Eb is average energy per bit

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

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