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**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

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**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)

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**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)

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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

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**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

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**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.

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**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

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**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

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**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

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**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

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**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)

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**Sampling Sampling (Time): = Sampling (Frequency) = * x(t) nd(t-nTs)**

xs(t) X(f) * nd(t-n/Ts) = Xs(f)

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**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

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**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

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**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

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**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

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**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)

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**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

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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

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**Double Sideband Suppressed Carrier (DSBSC)**

Modulated signal is s(t)=Accos(2pfct)m(t) Generated by a product or ring modulator Requires coherent detection (f2f1) Costas Loop m(t) s(t) Product Modulator Product Modulator m´(t) Channel LPF Accos(2pfct+f1) Accos(2pfct+f2)

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**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)

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**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

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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

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**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<<BmB2Bm Wideband FM: Df>>Bm B2Df B2Df+2Bm

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**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

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**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)

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**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

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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

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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)

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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.

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**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

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**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…

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

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