Dasar Sistem Komunikasi Digital13 Pebruari 2014

A Brief Review

A Transmission SystemTransmitterConverts information into signal suitable for transmissionInjects energy into communications medium or channelTelephone converts voice into electric currentModem converts bits into tonesReceiverReceives energy from mediumConverts received signal into form suitable for delivery to userTelephone converts current into voiceModem converts tones into bits

Transmission ImpairmentsCommunication ChannelPair of copper wiresCoaxial cableRadio Light in optical fiberLight in airInfrared

Transmission ImpairmentsSignal attenuationSignal distortionSpurious noiseInterference from other signals

Analog Long-Distance CommunicationsEach repeater attempts to restore analog signal to its original formRestoration is imperfectDistortion is not completely eliminatedNoise & interference is only partially removedSignal quality decreases with # of repeatersCommunications is distance-limitedStill used in analog cable TV systemsAnalogy: Copy a song using a cassette recorder

Analog vs. Digital TransmissionAnalog transmission: all details must be reproduced accuratelySentReceivedReceivedDistortionAttenuationDigital transmission: only discrete levels need to be reproducedDistortionAttenuationSimple Receiver: Was original pulse positive or negative?

Digital Long-Distance CommunicationsRegenerator recovers original data sequence and retransmits on next segmentCan design so error probability is very smallThen each regeneration is like the first time!Analogy: copy an MP3 fileCommunications is possible over very long distancesDigital systems vs. analog systemsLess power, longer distances, lower system costMonitoring, multiplexing, coding, encryption, protocols

System Overview

System OverviewInformation Source: Analog (voice) or digital (e-mail, SMS, fax)Source Encoding: Removing redundancy (to reduce bit rate)Encrypt: introduce security (optional)Channel Encoding: Adding redundancy to overcome channel impairments such as noise & distortion Multiplex: Share the channel with other sources

System OverviewPulse Modulation: Generate waveform suitable for transmissionBandpass (Passband) Modulation: Translate the baseband waveform to passband using a carrier

The ChannelTelephone wire (twisted pair), TV Cable (coaxial), air (wireless), optical fiberAdds noise: and distortionAdditive White Gaussian Noise (AWGN)Multipath fading (wireless)Could be stationary (wires) or time varying (wireless)Usually band-limited (lowpass), sometimes bandpass (air why?) Optical fiber offers huge bandwidth

Why Digital?A digital receiver need to exactly reproduce the waveformIt need to make only binary (or M-ary) decision

Why Digital?More tolerant to channel noise & distortion Need to detect only one of the few finite states

Why Digital? Complete clean-up and regeneration is possibleAdvanced processing is possible, such as:Channel coding (Ex: parity)Source coding (compression)Encryption & watermarkingMultiplexing different users (TDMA, CDMA)Multiplexing data from different sources (voice, video, data, medical)Lossless storing and retrievalMuch more

An Example

Digitization of Analog SignalsSampling: obtain samples of x(t) at uniformly spaced time intervalsQuantization: map each sample into an approximation value of finite precisionPulse Code Modulation: telephone speechCD audioCompression: to lower bit rate further, apply additional compression methodDifferential coding: cellular telephone speechSubband coding: MP3 audio

Sampling Rate and BandwidthA signal that varies faster needs to be sampled more frequentlyBandwidth measures how fast a signal varies

What is the bandwidth of a signal?How is bandwidth related to sampling rate?

Periodic SignalsA periodic signal with period T can be represented as sum of sinusoids using Fourier Series:DC long-term averagefundamental frequency f0=1/T first harmonickth harmonicx(t) = a0 + a1cos(2pf0t + f1) + a2cos(2p2f0t + f2) + + akcos(2pkf0t + fk) + |ak| determines amount of power in kth harmonicAmplitude specturm |a0|, |a1|, |a2|,

Example Fourier Series

Spectra & BandwidthSpectrum of a signal: magnitude of amplitudes as a function of frequencyx1(t) varies faster in time & has more high frequency content than x2(t) Bandwidth Ws is defined as range of frequencies where a signal has non-negligible power, e.g. range of band that contains 99% of total signal powerSpectrum of x1(t)Spectrum of x2(t)

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Bandwidth of General SignalsNot all signals are periodicE.g. voice signals varies according to soundVowels are periodic, s is noiselikeSpectrum of long-term signalAverages over many sounds, many speakersInvolves Fourier transformTelephone speech: 4 kHzCD Audio: 22 kHzs (noisy ) | p (air stopped) | ee (periodic) | t (stopped) | sh (noisy)speech

Interpolationfilter(a)(b)Nyquist: Perfect reconstruction if sampling rate 1/T > 2WsSampling Theorem

Quantization error:noise = x(nT) y(nT)Quantizer maps inputinto closest of 2mrepresentation valuesQuantization of Analog Samples

M = 2m levels, Dynamic range( -V, V) = 2V/MAverage Noise Power = Mean Square Error:If the number of levels M is large, then the error isapproximately uniformly distributed between (-/2, 2)Quantizer Performance

Figure of Merit: Signal-to-Noise Ratio = Avg signal power / Avg noise powerLet x2 be the signal power, thenx2/12=12x24V2/M2=x3 (V)2 M2=3 (V)2 22mxSNR =The ratio V/x 4The SNR is usually stated in decibels:SNR db = 10 log10 x2/e2 = 6 + 10 log10 3x2/V2SNR db = 6m - 7.27 dB for V/x = 4.Quantizer Performance

Communications ChannelsA physical medium is an inherent part of a communications systemCopper wires, radio medium, or optical fiberCommunications system includes electronic or optical devices that are part of the path followed by a signalEqualizers, amplifiers, signal conditionersBy communication channel we refer to the combined end-to-end physical medium and attached devicesSometimes we use the term filter to refer to a channel especially in the context of a specific mathematical model for the channel

How good is a channel?Performance: What is the maximum reliable transmission speed? Speed: Bit rate, R bpsReliability: Bit error rate, BER=10-kCost: What is the cost of alternatives at a given level of performance?Wired vs. wireless?Electronic vs. optical?Standard A vs. standard B?

Communications ChannelSignal BandwidthIn order to transfer data faster, a signal has to vary more quickly.Channel BandwidthA channel or medium has an inherent limit on how fast the signals it passes can varyLimits how tightly input pulses can be packedTransmission ImpairmentsSignal attenuationSignal distortionSpurious noiseInterference from other signalsLimits accuracy of measurements on received signalTransmitted SignalReceived SignalReceiverCommunication channelTransmitter

Channelttx(t)= Aincos 2fty(t)=Aoutcos (2ft + (f))Frequency Domain Channel CharacterizationApply sinusoidal input at frequency fOutput is sinusoid at same frequency, but attenuated & phase-shiftedMeasure amplitude of output sinusoid (of same frequency f)Calculate amplitude response A(f) = ratio of output amplitude to input amplitudeIf A(f) 1, then input signal passes readilyIf A(f) 0, then input signal is blockedBandwidth Wc is range of frequencies passed by channel

Ideal Low-Pass FilterIdeal filter: all sinusoids with frequency f

Example: Low-Pass FilterSimplest non-ideal circuit that provides low-pass filteringInputs at different frequencies are attenuated by different amountsInputs at different frequencies are delayed by different amounts

Example: Bandpass ChannelSome channels pass signals within a band that excludes low frequenciesTelephone modems, radio systems, Channel bandwidth is the width of the frequency band that passes non-negligible signal power

Channel DistortionChannel has two effects:If amplitude response is not flat, then different frequency components of x(t) will be transferred by different amountsIf phase response is not flat, then different frequency components of x(t) will be delayed by different amountsIn either case, the shape of x(t) is alteredLet x(t) corresponds to a digital signal bearing data information How well does y(t) follow x(t)?y(t) = A(fk) ak cos (2fkt + k + (fk ))

Example: Amplitude DistortionLet x(t) input to ideal lowpass filter that has zero delay and Wc = 1.5 kHz, 2.5 kHz, or 4.5 kHzx(t)Wc = 1.5 kHz passes only the first two termsWc = 2.5 kHz passes the first three termsWc = 4.5 kHz passes the first five terms

Amplitude DistortionAs the channel bandwidth increases, the output of the channel resembles the input more closely

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Channelt0Time-domain CharacterizationTime-domain characterization of a channel requires finding the impulse response h(t)Apply a very narrow pulse to a channel and observe the channel outputh(t) typically a delayed pulse with ringingInterested in system designs with h(t) that can be packed closely without interfering with each other

Nyquist Pulse with Zero Intersymbol InterferenceFor channel with ideal lowpass amplitude response of bandwidth Wc, the impulse response is a Nyquist pulse h(t)=s(t t), where T = 1/2 Wc, ands(t) has zero crossings at t = kT, k = +1, +2, Pulses can be packed every T seconds with zero interference

Example of composite waveformThree Nyquist pulses shown separately+ s(t)+ s(t-T)- s(t-2T)Composite waveformr(t) = s(t)+s(t-T)-s(t-2T)Samples at kTr(0)=s(0)+s(-T)-s(-2T)=+1r(T)=s(T)+s(0)-s(-T)=+1r(2T)=s(2T)+s(T)-s(0)=-1Zero ISI at sampling times kTr(t)+s(t)+s(t-T)-s(t-2T)

0fA(f)Nyquist pulse shapesIf channel is ideal low pass with Wc, then pulses maximum rate pulses can be transmitted without ISI is T = 1/2Wc sec. s(t) is one example of class of Nyquist pulses with zero ISIProblem: sidelobes in s(t) decay as 1/t which add up quickly when there are slight errors in timingRaised cosine pulse below has zero ISIRequires slightly more bandwidth than WcSidelobes decay as 1/t3, so more robust to timing errors1(1 )Wc Wc (1 + )Wc

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