Communication Systems. Communication Systems

Transcription

1 Communicaion Sysems Analog communicaion Transmi and receive analog waveforms Ampliude Modulaion (AM Phase Modulaion (PM Freq. Modulaion (FM Quadraure Ampliude Modulaion (QAM Pulse Ampliude Modulaion (PAM Digial communicaion Trea ransmission and recepion as digiized Transmission and recepion wih analog waveforms Ampliude Shif Keying (ASK Phase Shif Keying (PSK Frequency Shif Keying (FSK QAM PAM Communicaion Sysems Basic srucure m( Signal Processing Carrier Circuis TRANSMITTER s( Transmission Medium r( Carrier Circuis RECEIVER Signal Processing mˆ ( Informaion sources Message signal m( is he informaion source o be sen Possible informaion sources include voice, music, images, video, and daa, which are baseband signals Baseband signals have power concenraed near DC

2 Transmier Signal processing condiions he message signal Lowpass filering o make sure ha he message signal occupies a specific bandwidh, e.g. in AM and FM radio, each saion is assigned a slo in he frequency domain. In a digial communicaions sysem, we migh add redundancy o he inpu bi sream m[n] Carrier circuis Conver baseband signal ino a frequency band appropriae for he channel Uses analog and/or digial modulaion 3 Channel Transmission media: Wireline (wised pair, coaxial, fiber opics Wireless (indoor/air, oudoor/air, underwaer, space Propagaing signals experience a gradual degradaion over disance Boosing improves signal and reduces noise, e.g. repeaers 4

3 Wireline Channel Impairmens Aenuaion: linear disorion ha is dependen on he frequency response of he channel. Spreading: he finie exen of each ransmied pulse increases, i.e. pulse widens Transmi pulse lengh T s Channel impulse response lengh T h Resuling waveform due o convoluion has duraion T s + T h Phase jier: he same sinusoid experiences differen phase shifs in he channel Addiive noise: arises from many sources in he ransmier, channel, and receiver 5 Wireless Channel Impairmens Same as wireline channel impairmens plus ohers Fading: muliplicaive noise Example: alking on a cellular phone while driving a car when he recepion fades in and ou Muliple propagaion pahs Muliple ways for ransmied signal o arrive a receiver 6 3

4 Receiver and Informaion Sinks Receiver Carrier circuis undo effecs of carrier circuis in ransmier, e.g. demodulae from a bandpass signal o a baseband signal Signal processing subsysem exracs and enhances he baseband signal Informaion sinks Oupu devices such as compuer screens, speakers, and TV screens 7 Hybrid Communicaion Sysems Mixed analog and digial signal processing in he ransmier and receiver Ex: message signal is digial bu broadcas over an analog channel (compressed speech in digial cell phones Signal processing in he ransmier m( Signal processing in he receiver A/D A/D Converer Equalizer Error Correcing Codes digial sequence Deecion digial sequence Digial Signaling Decoder code D/A Converer Waveform Generaor baseband signal D/A 8 4

5 Power Specra Deerminisic signal x( w/ Fourier ransform X(f Power specrum is square of absolue value of magniude response (phase is ignored P x ( f = X ( f = X ( f X ( f Muliplicaion in Fourier domain is convoluion in ime domain Conjugaion in Fourier domain is reversal and conjugaion in ime X ( f X { x( τ ( τ } ( f = F x Auocorrelaion of x( R x ( τ = x( τ x ( τ Maximum value a R x (0 R x (τ is even symmeric, x( i.e. R x (τ = R x (-τ 0 T s R x (τ T s -T s T s τ 9 Power Specra Power specrum for signal x( is P x ( f = F R x ( τ Auocorrelaion of random signal n( R n R n For zero-mean Gaussian n( wih variance σ R ( τ = E n( n ( + τ = σ δ ( τ P ( f = σ n { } Esimae noise power specrum in Malab N = 6384; % number of samples gaussiannoise = randn(n,; plo( abs(ff(gaussiannoise.^ ; n { } { n( n ( + τ } = n( n ( + τ { n( n ( τ } = n( n ( τ d = n( τ n ( τ ( τ = E d ( τ = E noise floor 0 5

6 Transmi One Bi Transmission over communicaion channel (e.g. elephone line is analog Here is one way o do i -level digial PAM -A A x ( 0 0 bi x ( Τ b Τ b bi inpu x( Communicaion Channel Model channel as LTI sysem wih impulse response h( Assume ha T h < T b oupu h( y( Τ h -A T h A T h y ( 0 Τ h y ( Τ h receive 0 bi Τ h +Τ b receive bi Τ h +Τ b Transmi Two Bis (Inerference Transmiing wo bis (pulses back-o-back will cause overlap (inerference a he receiver A x( Τ b h( = Τ b Τ h y( Τ h +Τ b Τ b -A T h bi 0 bi Assume ha T h < T b Sample y( a T b, T b,, and hreshold wih hreshold of zero How do we preven inersymbol inerference (ISI a he receiver? bi 0 bi inersymbol inerference 6

7 Transmi Two Bis (No Inerference Preven inersymbol inerference by waiing Th seconds beween pulses (called a guard period x( h( A Τ h +Τ b Τ b Τ h bi 0 bi Disadvanages? = Assume ha T h < T b -A T h Τ b y( Τ h +Τ b Τ h bi 0 bi 3 Mached Filer Deecion of a pulse in presence of addiive noise, ignoring channel memory Receiver knows wha pulse shape i is looking for p( x( h( y( y(t Pulse signal w( AWGN zero mean S(f = N 0 / Mached filer = T y( = p( h( + w( h( = g ( + n( 0 4 7

8 Mached Filer Derivaion Design of mached filer Maximize signal power, i.e. power of g 0 ( a = T Minimize noise, i.e. power of n( Combine design crieria max η, where η is peak pulse SNR g ( T η = E{ n ( } 0 = insanane ous power average power 5 Mached Filer Given ransmier pulse shape p( of duraion T, mached filer is given by h op ( = k p(t- for all k Duraion and shape of impulse response of he opimal filer is deermined by pulse shape p( h op ( is scaled, ime-reversed, and shifed version of p( Opimal filer maximizes peak pulse SNR Eb ηmax = ( ( SNR P f df = = = p d σ σ σ Does no depend on pulse shape p( Proporional o signal energy E b Inversely proporional o power specral densiy of noise 6 8

9 Digial -level PAM Sysem a k {-,} s( x( y( y( i b i bis PAM p( h( Σ c( Clock T b pulse shaper AWGN w( Sample a Decision Maker =it b mached filer Threshold λ Clock T b 0 Transmier Channel Receiver Transmied signal = a p( s ( k k T b k Requires synchronizaion of clocks beween ransmier and receiver 7 Eliminaing ISI in PAM One choice for P(f is a recangular pulse W is he bandwidh of he sysem Inverse Fourier ransform of a recangular pulse is is a sinc funcion p( = sinc (π W P( f = W 0 P( f = W This is called he Ideal Nyquis Channel, W < f, f > W f rec( W I is no realizable because he pulse shape is no causal and is infinie in duraion < W 8 9

10 Eliminaing ISI in PAM Anoher choice for P(f is a raised cosine specrum P( f = W π ( f W sin 4W W f 0 0 f < f f f < W f W f f W Roll-off facor gives bandwidh in excess of bandwidh W for ideal Nyquis channel: Raised cosine pulse p( = sinc(π W has zero ISI when ideal Nyquis channelresponse sampled correcly Le g( and c( be square roo of raised cosine f α = W cos(π α W 6 α W dampening, adjused by α 9 Symbol Clock Recovery Criical o sample a correc ime insances o have maximum signal power and minimum ISI Transmier and receiver normally have differen crysal oscillaors Digial receiver should ry is bes o synchronize wih ransmier clock Receiver mus exrac he clock informaion from he received signal and hen adjus is A/D iming 0 0

11 Symbol Clock Recovery The receive filer oupu x( is firs passed hrough a prefiler wih frequency response B(w. This is a bandpass filer cenered a w_s/, half he symbol frequency Symbol Clock Recovery Le he combined baseband shaping filer and prefiler frequency and impulse responses be The prefiler oupu q( = s ( g( = ak g( kt k= ( = q ( = ak am g( kt g k = m= p ( mt E{ p( } = = k= m= a g k= E{ a k ( kt a } a δ( k m g ( kt g ( mt m

12 Symbol Clock Recovery g ( is impulse response of composie channel of pulse shapier, channel, and receive lowpass filer Received signal q( q( = s ( g( = ak g( kt k = ( = q ( = ak am g( kt g k = m= p( } = E{ ak am} a δ( k m g( k= m= = a g ( kt k= p ( mt E{ kt g ( mt 3 Symbol Clock Recovery E{p(} is a periodic funcion T j k ω j k ωs E { p( } = pk e where pk = E{ p( } e k= T 0 Lowpass filer E{p(} o pass fundamenal frequency ω s and filer ou harmonics s d 4

13 Symbol Clock Recovery z( looks like a sinusoid a he clock frequency wih slowly varying ampliude and phase. Is zero crossings cluser ogeher. Exrac sine wave ha wih same frequency symbol rae Use as reference signal o digial phase locked loop or reshape i as a sampling clock 5 3