Presentation on theme: "Network/Link Design Factors"— Presentation transcript:
1 A primer on Information Theory & Fundamentals of Digital Communications
2 Network/Link Design Factors Transmission mediaSignals are transmitted over transmission mediaExamples: telephone cables, fiber optics, twisted pairs, coaxial cablesChannel capacity and Bandwidth (εύρος ζώνης)Higher channel capacity (measured in Hz), gives higher bandwidth (range of frequencies), gives higher data rateTransmission impairmentsAttenuation (εξασθένηση)Interference (παρεμβολή)Number of receiversIn guided mediaMore receivers (multi-point) introduce more attenuation
3 Channel Capacity and data rate BandwidthIn cycles per second, or Hertz (e.g. 10 Mhz bandwidth)Available bandwidth for signal transmission is constrained by transmitter and transmission medium makeup and capacityData rateRelated to the bandwidth capabilities of the mediumin bits per second (the higher the bandwidth the higher the rate)Rate at which data can be communicatedBaud rate (symbols/sec) ≠ bit rate (bits/sec)Number of symbol changes made to the transmission medium per secondOne symbol can carry one or more bits of information
4 Data Rate and Bandwidth Any transmission system has a limited band of frequenciesThis limits the data rate that can be carriedE.g., telephone cables due to construction can carry signals within frequencies 300Hz – 3400HzThis has severe effect on what signals and what capacity in effect the channel has.To understand this lets consider any complex signal and see if we can analyse its frequency content, and what effect the channel may have on the signal (distortion?) and in effect limit the rate of the transmitted signal (measured in bits/sec)
5 Frequency content of signals any repeating, non-sinusoidal waveform can be equated to a combination of DC voltage, sine waves, and/or cosine waves (sine waves with a 90 degree phase shift) at various amplitudes and frequencies.This is true no matter how strange or convoluted the waveform in question may be. So long as it repeats itself regularly over time, it is reducible to this series of sinusoidal waves.
6 Fourier seriesMathematically, any repeating signal can be represented by a series of sinusoids in appropriate weights, i.e. a Fourier Series.
7 The Mathematic Formulation A periodic function is any function that satisfieswhere T is a constant and is called the period of the function.Note: for a sinusoidal waveform the frequency is the reciprocal of the period (f=1/T)
8 T is a period of all the above signals SynthesisT is a period of all the above signalsEven PartOdd PartDC PartLet 0=2/T.
9 Example (Square Wave)2345--2-3-4-5-6f(t)1
10 Fourier series example Thus, square waves (and indeed and waves) are mathematically equivalent to the sum of a sine wave at that same frequency, plus an infinite series of odd-multiple frequency sine waves at diminishing amplitude
11 Another exampleWith 4 sinusoids we represent quite well a triangular waveform
12 The ability to represent a waveform as a series of sinusoids can be seen in the opposite way as well:What happens to a waveform if sent through a bandlimited (practical) channelE.g. some of the higher frequencies are removed, so signal is distorted…E.g what happens if a square waveform of period T is sent through a channel with bandwidth (2/T)?
13 The Electromagnetic Spectrum Useful spectrum is limited, therefore its allocation/usage is managedThe electromagnetic spectrum and its uses for communication.Note: frequency is related to wavelength (f=1/l)
14 Electromagnetic Spectrum Note: frequency is related to wavelength (f=1/l) which is related to antenna length for radio, capacity, power and distance trade-offs exist, etc…
15 Generally speaking there is a push into higher frequencies due to: efficiency in propagation,immunity to some forms of noise and impairments as well as the size of the antenna required.The antenna size is typically related to the wavelength of the signal and in practice is usually ¼ wavelength.
16 Data and Signal: Analog or Digital Digital data – discrete value of data for storage or communication in computer networksAnalog data – continuous value of data such as sound or imageSignalDigital signal – discrete-time signals containing digital informationAnalog signal – continuous-time signals containing analog information
17 Periodic and Aperiodic Signals (1/4) Spectra of periodic analog signals: discretef1=100 kHz400kFrequencyAmplitudeTime100kf2=400 kHzperiodic analog signal
18 Periodic and Aperiodic Signals (2/4) Spectra of aperiodic analog signals: continousaperiodic analog signalf1Amplitudef2TimeFrequency
19 Periodic and Aperiodic Signals (3/4) Spectra of periodic digital signals: discrete (frequency pulse train, infinite)frequency = f kHzAmplitudeperiodic digital signalfrequency pulse trainTimeFrequencyf2f3f4f5f...
20 Periodic and Aperiodic Signals (4/4) Spectra of aperiodic digital signals: continuous (infinite)aperiodic digital signalAmplitudeTimeFrequency...
21 Sine Wave Peak Amplitude (A) Frequency (f) Phase () maximum strength of signalvoltsFrequency (f)Rate of change of signalHertz (Hz) or cycles per secondPeriod = time for one repetition (T)T = 1/fPhase ()Relative position in time
25 Modulation (Διαμόρφωση) Η διαμόρφωση σήματος είναι μία διαδικασία κατά την οποία, ένα σήμα χαμηλών συχνοτήτων (baseband signal), μεταφέρεται από ένα σήμα με υψηλότερες συχνότητες που λέγεται φέρον σήμα (carrier signal)Μετατροπή του σήματος σε άλλη συχνότηταΧρησιμοποιείται για να επιτρέψει τη μεταφορά ενός σήματος σε συγκεκριμένη ζώνη συχνοτήτων π.χ. χρησιμοποιείται στο ΑΜ και FM ραδιόφωνο
26 Πλεονεκτήματα Διαμόρφωσης Δυνατότητα εύκολης μετάδοσης του σήματοςΔυνατότητα χρήσης πολυπλεξίας (ταυτόχρονη μετάδοση πολλαπλών σημάτων)Δυνατότητα υπέρβασης των περιορισμών των μέσων μετάδοσηςΔυνατότητα εκπομπής σε πολλές συχνότητες ταυτόχροναΔυνατότητα περιορισμού θορύβου και παρεμβολών
32 Encoding (Κωδικοποίηση) Signals propagate over a physical mediummodulate electromagnetic wavese.g., vary voltageEncode binary data onto signalsbinary data must be encoded before modulatione.g., 0 as low signal and 1 as high signalknown as Non-Return to zero (NRZ)
33 Encodings (cont)If the encoded data contains long 'runs' of logic 1's or 0's, this does not result in any bit transitions. The lack of transitions makes impossible the detection of the boundaries of the received bits at the receiver.This is the reason why Manchester coding is used in Ethernet.
34 Other Encoding Schemes Unipolar NRZPolar NRZPolar RZPolar Manchester and Differential ManchesterBipolar AMI and PseudoternaryMultilevel CodingMultilevel Transmission 3 LevelsRLL
35 The Waveforms of Line Coding Schemes 1ClockData streamPolar RZPolar NRZ-LManchesterPolar NRZ-IDifferentialAMIMLT-3Unipolar NRZ-L
36 The Waveforms of Line Coding Schemes 1ClockData streamPolar RZPolar NRZ-LManchesterPolar NRZ-IDifferentialAMIMLT-3Unipolar NRZ-L
37 Bandwidths of Line Coding (2/3) The bandwidth of Manchester.The bandwidth of AMI.
38 Bandwidths of Line Coding (3/3) The bandwidth of 2B1Q
39 Digital Data, Analog Signal After encoding of digital data, the resulting digital signal must be modulated before transmittedUse modem (modulator-demodulator)Amplitude shift keying (ASK)Frequency shift keying (FSK)Phase shift keying (PSK)
41 Constellation Diagram (1/2) A constellation diagram: constellation points with two bits: b0b1+1-1IAmplitueAmplitue of I componentAmplitue of Q componentPhaseIn-phase CarrierQQuadrature Carrier11011000Chapter 2: Physical Layer
42 Amplitude Shift Keying (ASK) and Phase Shift Keying (PSK) The constellation diagrams of ASK and PSK.QI110011101000111100001010QI+1QI1+1-1QI1+1-1QI11011000(a) ASK (OOK): b0(b) 2-PSK (BPSK): b0(c) 4-PSK (QPSK): b0b1(d) 8-PSK: b0b1b2(e) 16-PSK: b0b1b2Chapter 2: Physical Layer
43 The Circular Constellation Diagrams The constellation diagrams of ASK and PSK.+1-1QI11011000+1-1QIQI(a) Circular 4-QAM: b0b1(b) Circular 8-QAM: b0b1b2(c) Circular 16-QAM: b0b1b2b3Chapter 2: Physical Layer
45 Quadrature PSKMore efficient use if each signal element (symbol) represents more than one bite.g. shifts of /2 (90o) 4 different phase anglesEach element (symbol) represents two bitsWith 2 bits we can represent the 4 different phase anglesE.g. Baud rate = 4000 symbols/sec and each symbol has 8 states (phase angles). Bit rate=??If a symbol has M states each symbol can carry log2M bitsCan use more phase angles and have more than one amplitudeE.g., 9600bps modem use 12 angles, four of which have two amplitudes
54 Nyquist BandwidthIf rate of signal transmission is 2B then signal with frequencies no greater than B is sufficient to carry signal rateGiven bandwidth B, highest signal (baud) rate is 2BGiven binary signal, data rate supported by B Hz is 2B bps (if each symbol carries one bit)Can be increased by using M signal levelsC= 2B log2M
55 Transmission Impairments Signal received may differ from signal transmittedAnalog degradation of signal qualityChannel impairementsDigital bit errorsCaused byAttenuation and attenuation distortionDelay distortionNoise
56 Attenuation Signal strength falls off with distance Depends on medium Received signal strength:must be enough to be detectedmust be sufficiently higher than noise to be received without errorAttenuation is an increasing function of frequency
57 Noise (1)Additional signals, exisiting or inserted, between transmitter and receiverThermalDue to thermal agitation of electronsUniformly distributedWhite noiseIntermodulationSignals that are the sum and difference of original frequencies sharing a medium
58 Noise (2) Crosstalk Impulse A signal from one line is picked up by anotherImpulseIrregular pulses or spikese.g. External electromagnetic interferenceShort durationHigh amplitude
59 signal + noise signal noise High SNR noise signal signal + noise Low tttsignalnoisesignal + noiseLowSNRtttAverage Signal PowerSNR =Average Noise PowerSNR (dB) = 10 log10 SNR
60 Shannon’s TheoremReal communication have some measure of noise. This theorem tells us the limits to a channel’s capacity (in bits per second) in the presence of noise. Shannon’s theorem uses the notion of signal-to-noise ratio (S/N), which is usually expressed in decibels (dB):