Subiecte Rezolvate 2010

8/14/2019 Subiecte Rezolvate 2010

1/31

1. Basic parameters of a communication system (power, bandwidth, noises), capacity

theorems (with examples)

Basic parameters of a communication systemTransmitted power: the transmission power of the message signal [Watts] Frequency bandwidth: the physical spectrum available for a certaintransmission [Hz, bps]Noises: undesired signals distorting the useful signal (channel noise, receivernoise, interferences)Shannon used these terms in its famous capacity theorem

ExamplesBandwidth:

300 3400 Hz for PSTN networks (adapted to the human hears spectrum):

restricted byregulations; 1.1 MHz for twisted pairs cables (such as in PSTN): restricted by physicalfeatures;

10 Mbps: total bandwidth available for an Ethernet transmission (100 Mbps forFast Ethernet ): restricted by regulations and physicalfeatures;

Power and noisesSNR (signal-to-noise ratio):

Examples: 0dB means unitary SNR, 10 dB means that the signal is ten timesstronger, 20 dB means 100 times more signal power than noise power etc.

2. Channels: noises

Noises Definition: unwanted signals that are inserted somewhere betweentransmission and receptionFour categories:

Thermal noise Intermodulation noise Crosstalk Impulse noise


2/31

Thermal noiseThermal noise

Due to thermal agitation of electrons Uniformly distributed in frequency Generally modeled as white noiseThe amount of thermal noise in 1Hz

N 0 = kT k = 1.3803 10 23 [J/ oK ]

N0 is the power spectral density [Watts/Hz]The amount of thermal noise in W HzN = kTWOther types of noisesIntermodulation

Produces components having frequencies f1+f2 and f1-f2

Caused by non-linearity of the transfer functionCrosstalk

A signal from one line is picked up by another Electrical coupling between nearby twisted pairsImpulse

Irregular pulses or spikes e.g. External electromagnetic interference Short duration and high amplitude Important source of errors for the digital signalsCrosstalk noiseFar end and near end crosstalkNear end crosstalk predominatesNear end crosstalk falls off with frequency

Other noisesThree categories: fluctuation, oscillation and pulse noiseFluctuation noise: caused by the power supply networks, radio stations etcUniformly distributed in the useful bandwidthOscillation noise: parasite harmonics of 50HzPulse noise: issued from crosstalk (pulses transmitted in the neighbor lines) orbecause of the switches from the telephone exchange


3/31

3. Channels: attenuation, delay distortions, crosstalk, other impairments

AttenuationSignal strength decreases with distanceDepends on the transmission mediumReceived signal strength:

must be enough to be detected must be sufficiently higher than noise to be received without error (Solution:repeaters, amplifiers)

higher the transmission frequency, higher the attenuation is (mainly concernsthe analog signals)

Delay distortionSpecific to guided media (wires)Signal propagation speed depends on the frequency Frequency selectivity arises: various frequency components of the signal willarrive at receiver with different delaysA kind of Inter Symbol Interference (ISI) occurs

Other distortions Frequency deviation of the oscillator from the receiver, compared to thetransmitterEchoes: at the transitions between 2 wires and 4 wires

Counteracted by echo suppressors (echo attenuations >19dB)Short duration cuts of the signal, caused by power supply back off activation,redundancy mechanisms in case of failure They are defined as a decrease of at least 6dB of the signal level, for aduration ranging from 3 to 300 ms

4. Channels capacity (Nyquist and Shannon theorems with computation examples)

Channel capacity Definition: the rate at which data can be transmitted over a givencommunication path, under given conditions

Four important concepts in defining capacityData rate

In bits per second Rate at which data can be communicatedBandwidth

In Hertz Constrained by transmitter (regulations) and medium NoiseNoiseBit Error Rate (BER)


4/31

Nyquist formulationFor noise-free channels:

W is the bandwidth, M is the number of signaling levelsQuestion: What is the capacity of a telephone line modem that uses 8 signalinglevels?Answer:

Shannon theoremFormulationThis is the original Shannon formulation

Interpretation: What Shannon says?

Reminder:Capacity [bps], W[Hz] Shannons formula expresses the theoretical maximum rate that can beachievedShannon decoded: Give me enough bandwidth (power) and I will shake theworld

5. Digital encoding: key terms (definition, uni/bi-polar encoding, differential vs absoluteencoding, baseband transmission, data rate )

Digital encodingWhat is digital encoding anyway?Information is an abstract concept, the bit concept tooWhen transmitting, we must face the physical realitySignals are used to figure and to transmit the bitsDigital encoding = a set of rules used in order to map a sequence of bits to asignal Depending on the transmission environment, the signal can be an electricalsignal, a radio wave (modulation) or a sequence of light pulses


5/31

Mostly, digital encoding refers to transmission through guided media (cables)

Key termsUnipolar: all signal elements have same polarity (+ or -) Polar (bipolar): one logic state represented by positive voltage the other bynegative voltageMark stands for 1 and Space stands for 0 (from telegraphy)Differential encoding: the signal element(s) which encode a bit are a function ofthe previous bit representationE.g.: a bit of 1 determines a transition from the previous signal stateAbsolute encoding: the signal element(s) encoding a bit are only a function ofthe current bit to be encoded Baseband transmission: the signal occupies a spectrum which is locatednearby the 0 frequency (and NOT centered to a high frequency carrier)

Data rate

The modulation rate is different of the data rate (can be lower or higher) Defined as: Rate at which the signal level changes (the reversed of theduration for which the signal level stays constant)Measured in baud = signal elements per second

6. The objectives of the digital encoding

Objectives of digital encoding [1]Spectral efficiency

Lack of high frequencies reduces required bandwidth Concentrate power in the middle of the bandwidthNo DC component: allows AC coupling via transformer, providing isolationSynchronization

The receiver must have exactly the same time reference as the transmitter(beginning of the bit interval, bit duration etc)

Sampling must be very precise, especially at high data rates External clock versus sync mechanism based on the received signal

Objectives of digital encoding [2]Error detection

Usually the task of the upper layers, but some mechanisms can beincorporated in the digital encoding strategy too (phy layer)Signal interference and noise immunity

Some codes are better than others (in terms of BER versus SNR)Cost and complexity

Higher signaling rate lead to higher costs Some codes require modulation rate greater than data rate The relation between the modulation and the data rate is critical


6/31

7. Digital encoding techniques (NRZ, Binary AMI, bi-phase): principles, versions,advantages and drawbacks

NRZ codesRule: bits are represented with constant levels, for the whole bit durationNo voltage for 0, constant positive voltage for 1 (unipolar)In practice, negative voltage is assigned to 1More often, bipolar version used (+ and pulses, zero voltage avoided)Used in slow speed communication interfaces (e.g. RS232) and storage media(e.g. magnetic tapes) NRZI is the differential version of NRZ (1 encoded by transition from thevoltage level which represents the previous bit)

NRZ pros and consPros

Easy to engineer Makes good use of bandwidth: can achieve 2 bps per Hz of spectral efficiencyCons

DC component (for the unipolar version) Lack of synchronization capability: long runs of identical bits mean no transitionin the signal

Multi-level binary codesAlternate Mark Inversion (AMI) and pseudoternary

Three signal levels (0, +V and -V) AMI rule: 0 means no signal, 1 is represented by voltage pulses withalternating signPseudo-ternary is the opposite of AMIUsed in first generation PCM equipmentsImproved versions of AMI are currently in use

Pros and cons of multi-level binary codesPros

No loss of sync if a long string of ones (in AMI) Zero DC component by the nature of these codes

Bandwidth efficiency (main amount of power concentrated in less bandwidththan in NRZ case)

Simple mechanism for error detection (two consecutive pulses of the same signcan only be caused by an error)Cons:

synchronization issues for long runs of 0 (AMI) or of 1 (pseudo-ternary) They introduce some kind of redundancy: three levels to encode two bits 3dB SNR loss versus the BER performance of NRZ

Biphase codes


7/31

Manchester and differential ManchesterPrinciple: supplementary transitions introduced compared to NRZ, AMIManchester rule: there is always a transition in the middle of the bit period, andsometimes at the beginning

E.g.: 1 is represented by a low-high transition at the middle of the bit interval,0 is the reversed

Inherently, a transition will be performed at the beginning of the bit, if thecurrent bit its identical with the previous oneDifferential Manchester: always transition at the middle of the bit (clocking only,it doesnt meter the sense of the transition)

Information is carried by the transition at the beginning of the bit: 0 meanstransition, 1 means no transitionManchester is used in IEEE 802.3 Ethernet

Biphase codes pros and consPros

Predictable transition at the middle of each bit, which can be used forsynchronization (selfclocking codes)

Error detection possible due to the same feature No DC componentCons

Bandwidth efficiency issues (half the bandwidth efficiency of NRZ) Modulation rate can be two times the data rate

8. Improved versions of AMI (HDB-3, B8ZS): motivation, principles, advantages and

drawbacks, examples.

B8ZSBipolar With 8 Zeros SubstitutionCan be considered as an improvement of the bipolar-AMI Rule: 8 consecutive zeros are NOT encoded with no signal for eight bit

periods, a signal which has 4 transitions being used insteadWhen an all-zero octet occur:

encode as 000+-0-+ if last non-zero voltage pulse was positive encode as 000-+0+- if the last non zero pulse was a -AMI code rules are broken twice by polarity violation: once inside of the eight-zeros group, once between the first non-zero pulse preceding the group and itscorrespondent within the groupUnlikely to occur as a result of noiseReceiver detects and interprets as octet of all zeros


8/31

HDB3High-density Bipolar, order 3Another improvement of the bipolar-AMI Rule: 4 consecutive zeros are NOT encoded with no signal for eight bitperiods, but with a signal which has at least one transitionWhen a group of 4 zeros occurs:

encode as 000V if the number of bits of 1 after the last polarity violation is odd B00V if the number of bits of 1 after the last polarity violation is even V means the same polarity as the previous one, B respects AMI patternThis rule aims to remove the DC component (polarity violation always changesits sign)

Scrambling pros and consPros:

Classical drawbacks of AMI are eliminated No redundancy, therefore the same rate is maintained Error detection capabilities Good spectral efficiencyCons:

Extra-processing needed at transmitter and, especially at receiver sideB8ZS employed in 1.544 Mbps-T1, HDB-3 in 2.048 Mbps-E1


9/31

9. Baseband transmission chain (with explanations about the role of each block)

Model for baseband data transmission

Legend:an: sequence of bits to be transmittedPAM: pulse amplitude modulator

GE(

), GR(

): emission/reception filters (their transfer function)s(t): signal which carries data, transmitted in the channelC(): channels (physical environment) transfer functionn(t): additive white noiser(t): received signal (based on it, a decision is made)Threshold comparison: e.g. positive value leads to 1, negative to 0ean: estimation of the received bits (ideally, identical to an)

10. Nyquist theorem for ISI-less data transmission in the baseband (deduction)

Nyquist theorem


10/31

In a channel which is equivalent with an ideal low-pass filter having the cutofffrequency F, it is possible to transmit symbols with a modulation rate equal orless to 2F symbols/sec, without ISIThe characteristics of such a channel are shown below

Graphical view of the Nyquist theorem


11/31

11. Nyquist filters (infer the mathematical criterion for the raised-cosine Nyquist filters)

The raised-cosine familyThe previously formulated criteria is met if:

The impulse response will be:

12. Transmission with controlled ISI (motivation, the cosine filter: frequency and impulse

response, precoding, decision)

Transmission with controlled ISIMotivation:

In practice, the raised cosine filters will not reach the Nyquist rate Closer they are to this objective, higher is the transmission sensitivity tosynchronization errorsSolution:

Some degree of ISI can be tolerated, if the ISI is controlled Higher rates can be obtained The cosine filter allows to reach the Nyquist rate

Principle: every waveform g(t) will carry two-bits of informationThis is the reason for calling this transmission duobinary


12/31

The cosine filter

Pre-codingDisadvantage of transmission with controlled ISI: every decision depends ontwo successive bits (error propagation)Solution: pre-coding performedInstead of ak, another sequence bk is transmitted, encoded as:

This leads to a one-sample based decision, as follows:

13. Modulation: key terms (carrier, message) with one graphical example for binary AM,

FM, and PM.

Modulations key termsModulator signal: the signal to be transmitted

The signal can be analog or digital Especially in the digital signal context, the modulator signal can be referred toas messageCarrier signal: used to transport the message signal

Carrier signal is a sine wave (continuous wave modulation) or a periodicrectangular wave


13/31

Amplitude modulationAM is referred to as linear modulationThe amplitude of the carrier is changed by the signal to be transmittedWhen the message signal is digital, we obtain Amplitude Shift Keying (ASK)The simplest form of ASK is called On/Off Keying (OOK)

Frequency ModulationDefinition: FM is a method used to transmit analog or digital signals, in whichthe information is carried by the instantaneous frequency of a high-frequencycarrierExamples: FM radio (modulator=audio signal), FM modems (modulator=digitaldata) When the modulator is digital, the frequency modulation is referred to asfrequency shift keying


14/31

Phase ModulationDefinition: PM is a method used to transmit analog or digital signals, in whichthe information is carried by the initial phase of a high-frequency carrierPM is not so popular as FM, especially for analog signal modulators (becauseof its complexity)When the modulator is digital, the frequency modulation is referred to as phaseshift keying (PSK)

14. AM types (mathematical model of the AM, AM with supressed carrier, SSB-AM,

VSB-AM).

AM Frequency domain view [2]The spectrum of the modulated signal is:

Suppressingand un-suppressing the carrierIf the carrier has a DC component:

The modulated signal is:


15/31

In this case, in the spectrum of the AM signal, we will retrieve the Dirac pulsescorresponding to the sine carrier

SSB-AMSSB signal can be expressed as:

is the Hilbert transform of g, which can be obtain by passing g(t)through the filter:

SSB-AM is spectrally efficient Difficult to implement in practice: the filters which separate the side-bandsmust be very selective

AM with Vestigial Side-Band (VSB)Only part of the side-bands is suppressed Lower frequencies transmitted with both Side-Bands, upper frequencies withone side-band

This allows easier filtering to separate the bands (frequencies near the carriermust not be filtered)25% more bandwidth required than in SSB, but easier to implementExample: NTSC TV system: all upper sideband of bandwidth W2 = 4 MHz, butonly W1 = 1.25 MHz of the lower sideband are transmitted

15. Coherent demodulation for AM signals (mathematical model, principles, the

importance of the phase synchronization)

Coherent demodulation [1]

Principle: locally generated carrier must be used in receiver This carrier must be synchronized (frequency, phase) with the one used fortransmissionThe modulated signal can be expressed as:


16/31

The LPF cuts-off the 2

0 component, and r(t) is obtained

16. The Costas loop for receivers carrier synchronization

Comments on the previous schemeCostas loop: used by the coherent AM demodulators to regenerate the carrierIt uses the received data signalIf we assume that there is an initial phase shift , this shift is used to tune theVCO, via an error signal (e)The error signal is obtained from u(t) (eq. 10) and it is a kind of average valueof x2(t), weighted by This average value is computed by the LPF (only the frequency componentsaround 0 are maintained after the filter)


17/31

17. Frequency modulation: definition, principles, mathematical approach (formulas forfrequency modulated signals, instantaneous frequency definition, continuous and

discontinuous frequency modulation), advantages and drawbacks

IntroductionDefinition: FM is a method used to transmit analog or digital signals, in whichthe information is carried by the instantaneous frequency of a high-frequencycarrierExamples: FM radio (modulator=audio signal), FM modems (modulator=digitaldata) When the modulator is digital, the frequency modulation is referred to asfrequency shift keying

Mathematical approachConsidering a rectangular form of the modulator signal:

g(t): rectangular pulse-shaperan: data sequence to be transmittedThe FM modulated signal is:

Instantaneous frequencyThe instantaneous frequency represents the derivate of the phase:

FM: pros and consPros

Higher resilience to additive noise and interference, compared to AM Possibility to use non-linear amplifiers to amplify the FM signals Non-coherent detection is an available optionCons:

Much larger bandwidth than AM (e.g. 240 KHz vs 30 KHz for a 15 KHz audiochannel)


18/31

18. Frequency demodulation using a narrowband limiter

DemodulationTwo types of demodulation: coherent and noncoherentA non-coherent demodulator is presented below:

BPF: eliminates out-of-band signals (noises, interference)Narrowband limiter: limits the peaks of the signal and than applies a band-passfiltering around the carrier

19. Frequency demodulation using a wideband limiter

A different approach

The limiter is wide-bandIt transforms the modulated sine into rectangles (trapezoidal) waveformsThe differentiator highlights the transitions in these waveformsThe signal is rectified to obtain only positive impulsesThey command a constant-duration pulse generator, which generates pulses

having the same duration, but different periods given by the bit valueLPF averages the signal over one bit duration, thus transforming the frequencyinformation into an amplitude one

20. Differential frequency demodulation

Differential demodulator

The delayed version of the signal u(t) is:


19/31

After, the multiplier, we get:

21. Phase modulation: principles, mathematical approach, graphical examples,

advantages and drawbacks.

IntroductionDefinition: PM is a method used to transmit analog or digital signals, in which

the information is carried by the initial phase of a high-frequency carrierPM is not so popular as FM, especially for analog signal modulators (becauseof its complexity)When the modulator is digital, the frequency modulation is referred to as phaseshift keying (PSK)

Mathematical approachConsidering a rectangular form of the modulator signal, x(t):

g(t): rectangular pulse-shaper (pulse with amplitude 1 and duration T)an: data sequence to be transmitted (bits)If we associate a phase, n with each symbol an, we get :

xremains constant during the symbol interval (T)n is a phase value, associated with the symbol to be transmittedIn the digital PM (PSK) we have a finite number of possible symbols, M M=2, corresponds to BPSK (e.g.: 90o phase shift corresponds to 1, -90o

phase shift corresponds to 0)

PM: pros and consProsNarrow bandwidth compared to FMNon-coherent detection, with small performance degradationConsHigh complexity (especially for analog PM)


20/31

22. QPSK modulator (QPSK principles, modulators scheme, constellation, phase table,

mathematical expression for the generated signals)

QPSK Modulator For the BPSK case, the modulation is implemented by simply inversing thesign (0o/180o phase shift)In QPSK (Quadrature PSK), the modulation symbol is a group of two bits

Comments on the previous schemeEvery symbol is a group of two bits (AB)On the upper branch, the signal corresponding to bit A (e.g.:+V voltage for1, -V voltage for 0) modulates a cosineOn the lower branch, the signal representing the bit B, modulates a cosine of

the same frequency, but shifted by 90oThats the reason behind the Q in QPSKThe signal from the two branches is summed an transmitted in the channel

23. 8-PSK modulator ((QPSK principles, modulators scheme, constellation, phase table,mathematical expression for the generated signals)

8-PSK modulator

A group of three bits composes a symbola and b will be 4-levels AM signalsThe second modulator is a phase modulator


21/31

A B C a b Phase(sign) (sign) (level)

0 0 0 Negative,

small

amplitude

Negative,

high

amplitude

-112.5o

0 0 1 Negative,

High

amplitude

Negative,

Small

amplitude

-157.5o

0 1 0 Negative,Small

amplitude

Positive,high

amplitude

+112.5o

0 1 1 Negative,

High

amplitude

Positive,

Small

amplitude

+157.5o

1 0 0 Positive,

Small

amplitude

Negative,

High

amplitude

-67.5o

1 0 1 Positive,High

amplitude

Negative,small

amplitude

-22.5o

1 1 0 Positive, Positive, +67.5oSmall

amplitude

high

amplitude

1 1 1 Positive, Positive, +22.5oHigh

amplitude

Small

amplitude

24. Coherent demodulation of QPSK signals.

QPSK demodulation


22/31

PhaseSA SB sd

+45o + + 11

-45o + - 10

+135o- +

01

-135o - - 00

Local reference oscillatorAfter the LPF, the 20 component is removedAfter sampling, a positive value indicates a 1, a negative sample indicates a 0(on both branches)Equivalently, a single phase detector and a multi-level comparator can be used

25. DBPSK: principles, demodulation.

DBPSK PrinciplesDBPSK=Differential Binary Phase Shift KeyingAt modulator, a pre-coder provides a differential phase shift Instead of transmitting an (the initial bit sequence), the data sequencetransmitted in the channel is precoded:

Example:

DBPSK Demodulator


23/31

For the n-th bit, the received signal (after) BPF is:

After the LPF (which eliminates the second harmonic), we get:

Remarks on the DBPSK demodulator The signal delay, T, introduced in the demodulator, must equal the symbolperiodThe delayed signal will then correspond to the previously transmitted bitThe signal entering the LPF will be:

By transforming this product into a sum we will obtain an oscillating component(20 and a DC component, indicated by eq. 8)

26. Classification of the data transmission systems for the synchronicity point of view.

Synchronous systems: every bit has the same duration, T The same time interval is preserved between any two consecutive bits (multipleof T)

Bit-level synchronized systems Referred to as start/stop asynchronous systems Synchronization realized at bit level No synchronization between two successive characters (words)Step-by-step synchronized systems

Fully asynchronous systems No synchronization neither at bit, nor at character level


24/31

27. One-step digital synchronization

Digital approach: one-step Synchronizer

Input: data signalOutput: clock signal synchronized with dataOne-step synchronizer: comments on the schemeTransition time instant compared to the clock transitionIf there is a time shift between them, the receivers time basis is tunedThe scheme uses a higher resolution clock (clock frequency: 64/T)Frequency divisors are used to tune the clock frequency

28. Two steps digital synchronization (fine and coarse tuning)

Two-step synchronization

Input: data signal

Output: clock signal synchronized with data

Two-step synchronization Principle: the high and the low synchronization errors in the receivers clocktreated differentlyIf the synchronization error is high, a coarse tuning takes place

An impulse is added/cleared, having a weight of 1/24 (4%) The weight is given by the multipliers (4x6=24)If the synchronization error is small, a fine tuning takes place

Impulse added/cleared, having the weight 1/192 The weight results from 4x2x6x4=192


25/31

29. USB (definition, channels, transmission speed, signal encoding at PHY layer,power supply).

USB InterfaceUSB = Universal Serial BusDefinition: serial bus standard to interface devices to a host computer Used for plug-and-play peripherals connection: mouse, keyboard, PDA,printer, scanner, digital camera Provides power for low-consumption devices (no need for external powersupply)

USB Channels4 data channels for the communication between the device and the USB host

controller Control data transfer- uses pipe 0: commands towards the device or statusreporting Isochronous transfer- for the transmission at a guaranteed speed of real timedata (e.g. voice, video) Interruption data transfer- from some peripherals to the host (e.g. keyboard,mouse, joystick), requires small delay guaranteesBulk transfers: they may use the whole bandwidth, but they are not time-critical(e.g transfers to/from a storage device)

Transmission speeds

Low speed (


26/31

PHY layer details [2]Signal encoding: NRZI with bit-stuffingOnly 0 introduces a change in the transmitted signalAfter six bits of 1, a 0 is introduces and it is ignored by the receiverSynchronization byte at the beginning of the frame (01111110)Power supply of 5V (between 5.25 V and 4.75 V allowed between the line +Dand -D)

30. V.24 (RS232) serial interface: number of pins, data pins, electrical and functionalspecification (circuit types)

V.24 interfaceITU-T v.24Only specifies functional and procedural

References other standards for electrical and mechanicalEIA-232-F (USA)

RS-232 (more popular name)

Mechanical ISO 2110 Electrical V.28 Functional V.24 Procedural V.24


27/31

Mechanical specification

25 wires for serial communication Far fewer ports used in practice (oftentimes)

Electrical specificationDigital signals transmittedValues interpreted as data or control, depending on circuitless than -3V is binary 1, more than +3V is binary 0 (NRZ-L)

Signal rate < 20kbpsDistance


28/31

31. Session establishment and communication DTE-DCE using the RS232 interface

Example 1: Asynchronous private line modemWhen turned on and ready, modem (DCE) applies negative voltage to DCEready (pin 6)When DTE ready to send data, it asserts Request to Send (pin 4)

Also inhibits receive mode in half duplexModem responds when ready by activating Clear to send (pin 5)DTE sends dataWhen data arrives, local modem asserts Receive Line Signal Detector anddelivers data

Example 2: Telephone line-modem

Supplementary circuits required for the operation over telephone line (DTEready, Ring indicator)

32. Present briefly, the OFDM principles.

The need for OFDMMost of the transmission channels are frequencyselective

frequency components from the input signal affecteddifferently by the channel

meaning that the channels transfer function H(f) is not flatover the bandwidth

this introduces Inter-Symbol interference (ISI)

ISI can be seen as a time-domain manifestation of thefrequency selectivityOFDM is exceptionally robust to IISWell suited to all the dispersive channels, andespecially to the wireless channel

33. The cyclic prefix in OFDM.

Cyclic prefix: why?If the channel is not ideal (is time-dispersive), thesuccessive OFDM blocks will interfere

This happens because each symbol is dispersed in timeby the channel (see silde 6)


29/31

Inter-Block Interference (IBI) arises

Sometimes referred to as Inter-(OFDM)Symbol Interference

OFDMs cyclic prefixSometimes referred to as guard timeCancels IBISimplifies equalizationEases synchronization (a signal is always transmitted)Cyclic Prefix is removed by the demodulator

Comments on the cyclic prefixIBI cancellation

Occurs only if the CP is longer than the multipath delay Longer CP duration means higher protection against ISI, but

smaller efficiencySynchronization is simpler if a signal is always transmitted E.g. a peak in the autocorrelation of the OFDM symbol couldindicate the OFDM symbol startEqualization is simpler, because the linear convolution(x[n]*h[n]) is transformed into a periodic one

This allows to use a very simple, one-tap, frequency domainequalizer

Every received sample R[k], must be divided by H[k], the channelsresponse at the k-th frequency line


30/31

34. Explain the OFDM's carriers orthogonality in time and frequency domain (graphicalillustration too).

Orthogonal carriersThe OFDM carriers are orthogonal, theirfrequencies being f0, 2f0, 3f0 etc.

Complex exponentials of limited durationused in practice

Their duration equals OFDMs symbol time (T)The orthogonality is met if: f0=1/T

OFDM: the carriers and their spectra

Comments on the previous slideIn the time domain, every carrier covers an integer number of

cycles (periods) during the symbol time (T) This is a condition for orthogonalityThe carriers are time-bounded by a rectangular window, givingthe symbol durationThe sinc shape of the spectrum corresponds to a sine carriermultiplied by a rectangular time windowAt the central frequency of each carrier, all the other carrierscross zero

This is the orthogonality frequency view Carriers must be separated by 1/T on the frequency axis


31/31

35. OFDM block diagram (transmitter, receiver).

Subiecte Rezolvate 2010

Documents

Transcript of Subiecte Rezolvate 2010