ELEC 350 Communications Theory and Systems: I Review ELEC 350 Fall 007 1
Final Examination Saturday, December 15-3 hours Two pages of notes allowed Calculator Tables provided Fourier transforms Table.1 Bandpass to lowpass translation relations Table. Bessel function values Table 3.1 ELEC 350 Fall 007
Syllabus Overview of Communication Systems Review of Signal Analysis (ELEC 60,310) Analog Modulation Linear Modulation (DSB,AM,SSB,VSB) Angle Modulation (FM,PM) Random Processes System Performance in Noise 3
Course Content Text sections in Proakis and Salehi ( nd Edition) Chapter 1 Chapter Chapter 3 (except 3.4.3 and 3.5) Chapter 4 (except 4.5) Chapter 5 (except 5.5.4) Chapter 7 (only 7.7. link budget analysis) All slides are on the website www.ece.uvic.ca/~agullive/materials350.html Link Budgets http://www.ece.uvic.ca/~agullive/350link3.pdf ELEC 350 Fall 007 4
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Signals and Systems Signal used to transmit the information over the channel Information Bearing Signal The communication channel is modelled as a Linear System Main analysis tool: Fourier Transform ELEC 350 Fall 007 6
Power Spectral Density x( t) A cos( f t) c o R X Ac ( ) cos f0 R X (0) A c Ac SX ( f ) F{cos f0} j f0 j f0 A c e e j f e d Ac Ac ( f f0) ( f f0) 4 4 ELEC 350 Fall 007 7
Objectives of Modulation Convert a lowpass signal to bandpass Accommodate the simultaneous transmission of signals from several sources Expand the signal bandwidth to increase noise immunity ELEC 350 Fall 007 8
Amplitude Modulation Double-sideband suppressed carrier (DSB-SC) Conventional AM Single-sideband (SSB) AM Vestigal-sideband (VSB) AM ELEC 350 Fall 007 9
Conventional AM ELEC 350 Fall 007 10
Suppose that the nonlinear device is approximated by a second order polynomial ( ) 1 ( ) ELEC 350 Fall 007 11
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AM Modulation Summary Modulation Power Efficiency Spectral Efficiency (xw) Modulation Complexity Demodulation Conventional AM low low simple DSB-SC high low complex SSB high 1 high complex VSB high 1- medium complex ELEC 350 Fall 007 14
Angle Modulation Angle modulation Frequency modulation (FM): Frequency is changed by the message m(t). Phase modulation (PM): Phase is changed by the message m(t). Angle modulated signals have a high degree of noise immunity, but require larger bandwidth than AM signals. They are widely used in high-fidelity music broadcasting. They have a constant envelope, which is beneficial when using nonlinear amplifiers. ELEC 350 Fall 007 15
The message signal ( ) cos( ) is used with either FM or PM for the carrier A cos( f t). Find the modulated signal in each case. c Solution: PM FM ( t) k m( t) k a cos(f t) p p c m ( ) ( ) sin( ) we have ( ) cos( cos( cos( sin( )) )) / Modulation index for a general m(t) max max ( ) max ( ) / / max Modulation index ELEC 350 Fall 007 16
Varactor Diode Angle Modulator ELEC 350 Fall 007 17
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Phase-Locked Loop FM Demodulator ELEC 350 Fall 007 0
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Bandpass Processes ELEC 350 Fall 007
Def 4.6.1: X(t) is a bandpass or narrowband process if for f f W, where W f0 0 S ( f) 0 X Let X(t) be a bandpass process. Then R is a deterministic X () bandpass signal whose Fourier transform SX ( f) is nonzero in the neighborhood of. X(t) and its Hilbert transform have the form X ( t) and X ( t) are lowpass processes c f 0 X ( t) X ( t)cos( f t) X ( t)sin( f t) c 0 s 0 Xˆ ( t ) X ( t )sin( f t ) X ( t )cos( f t ) s c 0 s 0 ELEC 350 Fall 007 3
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Narrowband Noise Properties 1. X c( t) and X s( t) are zero-mean, lowpass, jointly stationary and jointly Gaussian random processes. If the power in X(t) is P X P P P S f df c s X X X X 3. X c( t) and X s( t) have common PSDs obtained by shifting the positive frequencies in SX ( f) to the left by f 0 and the negative frequencies in S to the right by X ( f) f 0 and adding the two spectra 5 ELEC 350 Fall 007
Noise in Analog Systems Most analog continuous-wave systems are bandpass -> suffer from bandpass noise Design the BP filter just wide enough to pass u(t) without distortion Minimize the noise power input to the demodulator Figure of Merit SNR at demodulator output Reference baseband SNR ELEC 350 Fall 007 6
AM Signal to Noise Ratio (SNR) S P P o Ac Pm R S N P N W N W N odsb ossb n n o o 0 0 S P P o Ac Pm R N P N W N W 0 0 S A / 1 a P mn N P N W a P N W P Ac a Pm a P o c n mn oam n 0 1 m 0 o a P P a P S S 1a P N W 1a P N N mn R mn m 0 m n n n b b b 7 ELEC 350 Fall 007
Angle Modulation The modulated signal ( ) cos( ( )) A c A c cos( f t k cos( f t k c c f p t m( t)) m( ) d ) PM FM ELEC 350 Fall 007 8
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Angle Modulation Noise PSD S n 0 ( f) N A N A 0 c 0 c f PM FM P n 0 WN A c 0 3 W N0 3Ac PM FM 30 ELEC 350 Fall 007
Noise PSD for PM and FM 31 ELEC 350 Fall 007
FM Signal to Noise Ratio (SNR) S ppmn S N b N o S PM 3 fpm FM n N b 1 S PM b PM max m(t) N S N o 1 3 S PM b FM max m(t) N 3 ELEC 350 Fall 007
Observations The output SNR is proportional to the square of the modulation index Angle modulation allows a tradeoff between SNR and bandwidth The relationship between the output SNR and the bandwidth expansion factor is quadratic Increasing too much results in the threshold effect where the signal is lost in noise Compared with AM, increasing the transmitted power increases the output SNR but the mechanisms differ In FM, noise affects higher frequencies more than lower frequencies ELEC 350 Fall 007 33
Threshold Effect in FM At threshold S N Carson s rule b, th 0( 1) B c f ( 1) W f Assume P M n P 1 M (max mt ( ) ) then S 3 S N f N o b ELEC 350 Fall 007 34
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Pre-emphasis and De-emphasis The phase of the transmitted signal is k t) k f p ( t m( t) m( ) d PM FM At high frequencies use PM At the transmitter, a differentiator followed by an FM modulator At the receiver, an FM demodulator followed by an integrator ELEC 350 Fall 007 36
Pre-emphasis and De-emphasis Filters In order to produce an undistorted version of the original message at the receiver output, we must have H ( f ) H ( f ) 1 for W f W p d ELEC 350 Fall 007 37
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Noise PSD and SNR Gain The noise power at the demodulator output 3 W N0f 0 W W Pn S ( ) arctan PD W n f df PD Ac f0 f0 The ratio of output SNRs is S W N o P PD n f o 0 S P W W 3 arctan nd N o f0 f 0 3 ELEC 350 Fall 007 39
Comparison of Analog Modulation Linear modulation DSB-SC SSB-SC VSB Conventional AM Nonlinear modulation PM FM ELEC 350 Fall 007 40
Comparison Criteria Bandwidth efficiency Power efficiency SNR at demodulator output Simplicity of the transmitter and receiver implementation Receiver complexity is most important ELEC 350 Fall 007 41
Bandwidth Efficiency SSB-SC is best VSB Bc W B W c W DSB-SC and Conventional AM FM is worst using Carson s rule: B 6W f c Bc W 5 B 1W f c ELEC 350 Fall 007 4
Power Efficiency Output SNR for a given received signal power Angle modulation and in particular FM provides the highest SNR gain Conventional AM and VSB+carrier are worst ELEC 350 Fall 007 43
Implementation Complexity Conventional AM and VSB+C demodulators have extremely simple receiver structures envelope detector FM also has a simple structure discriminator + AM demodulator To obtain better FM performance use a PLL SSB-SC and DSB-SC require coherent detectors (Squaring Loop or a Costas Loop) ELEC 350 Fall 007 44
Final Comments SSB modulation provides optimum noise performance and bandwidth efficiency with amplitude modulation Conventional AM provides the simplest receiver structure making it the most common wireless communication technique FM improves the noise performance at the expense of increased transmission bandwidth ELEC 350 Fall 007 45