Course 4 Transmission impairments Channel capacity Nyquist formulation Shannon theorem

Transmission impairments The received signal may differ from the

transmitted one Analog - degradation of signal quality Digital - bit errors may occur Most important impairments:

Attenuation and attenuation distortion Delay distortion Noise Free space loss Atmospheric absortion Multipath Refraction

Attenuation Signal strength decreases with distance Depends on the transmission medium

Guided unguided

Received signal strength: must be sufficient that the receiver can detect and

interpret it must be sufficiently higher than noise, thatthe signal to be received accurately Solution: repeaters, amplifiers The problem becomes

more complicated in case of more receivers placed at different distances

higher the transmission frequency, higher the attenuation is -mainly concerns the analog signals-much less of a problem with digital signals

Solution: equalizers

Attenuation distortion is much less of a problem with digital signals, because, the strength of a digital signal falls off rapidly with frequency. Most of the content is concentrated near the fundamental frequency, or bit rate, of the signal

The frequency domain function for a single square pulse that has the value 1 between -XI2 and Xl2, and is 0 elsewhere.

Frequency dependency

Attenuation curve for a voice channel 1. without equalization 2. with equalization

Attenuation of typical guided media

Delay distortion Specific to guided media (wires) Signal propagation speed depends on the

frequency Frequency selectivity arises: various

frequency components of the signal will arrive at receiver with different delays

A kind of Inter Symbol Interference (ISI) occurs

Particularly annoying for digital data

Relationship between phase and frequency. In a distortionless channel, all frequencies all frequencies

pass through it at the same speedpass through it at the same speed, resulting in frequency and phase having a constant linear relationship with respect to time.

When distortion occurs, the relationship becomes nonlinear with respect to time, causing some frequencies of a signal to reach the distant end of a channel before other frequencies

Delay distortion. The late arriving energy of one pulse can be misinterpreted as a new pulse, resulting in the occurrence of a digital error

Delay distortion versus frequency for a voice channel1 without equalization 2. with equalization

Noises Definition: “unwanted signals that are

inserted somewhere between transmission

and reception” Four categories:

– Thermal noise two common types of noise – Impulse noise that can affect the quality of circuit

– Intermodulation noise– Crosstalk

Thermal noise

generated by the thermal agitation of electrons

Uniformly distributed in frequency generally modeled as white noise

Cannot be eliminated Present in all electronic devices and transmission media Function of temperature Particularly significant for satellite communications

The amount of thermal noise in the band of 1Hz

N0=kT

N0 is the power spectral density [Watts/Hz] K- Bolzmann constant=1,38 .10-23 J/°K T -temperature in Kelvins degrees (absolute) The amount of thermal noise in a bandwidth of B Hz is:

In dBW:

kTB=N

B10+T10+6228

=B10+T10+k10=N

loglog,_

logloglog

Thermal (white) noise.

Thermal noise is characterized by a near uniform distribution of energy over the frequency spectrum

Impulse noiseImpulse noise

– Irregular pulses or spikes formed from the effect of lightning and electromagnetic machinery disturbances

–– of relatively high amplitude and short duration– Important source of errors for the digital signalsExample, a sharp spike of energy of 0.01-second durationwould not destroy any voice data, but would wash out

about 50 bits of data being transmitted at 4800 bps.

Other types of noises IntermodulationIntermodulation– Produces components having frequencies f1+f2

and f1-f2

– Caused by non-linearity of the channel’s transfer function

CrosstalkCrosstalk– A signal from one line is picked up by another

line– Electrical coupling between nearby twisted

pairs, or rarely between coaxial cble lines carying multiple signals

Crosstalk can also occur when unwanted signals are picked up by microwave antennas; although highly directional, microwave energy does spread during propagation.

Typically, crosstalk is of the same order of magnitude (or less) as thermal noise.

Far end and near end crosstalk A special type of crosstalk, referred to as near

end crosstalk and abbreviated as NEXT, represents the biggest source of noise in twisted-pair cables

Near end crosstalk falls off with frequency

Jitter Definition: a random distortion of signal durations

caused by the rapid fluctuation of the frequency of the transmitted signal

May have different meanings, depending on the application

Examples: the difference (in periods) between two

successive clock cycles, the difference (in phase) between the initial

phase of the carrier for two transmitted symbols Causes:

imperfections of the transmission media the noise of the electronic devices used

Other noises

Fluctuation noise: caused by the power supply networks, radio stations etc

Oscillation noise: parasite harmonics of 50Hz

Pulse noise: issued from crosstalk (pulses transmitted in the neighbour lines) or because of the switches from the telephone exchange

Other distortions Frequency deviation of the oscillator from the

receiver, compared to the transmitter Echoes: at the transitions between 2 wires and 4

wires Traditionally counteracted by echo suppressors

(echoattenuations >19dB)

Echo eliminators 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 a duration ranging from 3 to 300 ms

Effect of noise on a digital signal

Multipath Appears in terrestrial, fixed microwave

and in mobile communications Due to the existent obstacles the signal

can be reflected, so that multiple copies of the same signal, with varying delays might be received.

In extreme cases, the receiver may capture only the reflected signal an not the direct one

Reinforcement and/or cancellation of the multipath signals

Multipath propagation

Three important propagation mechanisms R Reflection D Difraction S Scattering

Multipath effects Multiple copies of a signal may arrive at different

phases If phases add destructively, the signal level

relative to noise declines, making detection more difficult

Intersymbol interference (ISI) One or more delayed copies of a pulse may arrive

at the same time as the primary pulse for a subsequent bit

Tropospheric radio wave propagation factors that influence satellite links include :

gaseous absorption, cloud attenuation, Melting layer attenuation, rain attenuation, rain and ice depolarization tropospheric scintillation. EMW interactions with atmosphere particles depend

on frequency and are significant above 10GHzGaseous absorption and cloud attenuation

determine the clear-sky performance of the system. Clouds are present for a large fraction of an average year, and gaseous absorption varies with the temperature and relative humidity

At specific frequencies appear resonance phenomena and attenuations became important

- Resonance absorption with water vapors at about 22.235GHz;

- With oxygen molecules between 56.5GHz şi 65.2GHz;

- Other resonance absorptions above 100GHz.

Rain attenuation — and to some extent melting layer attenuation — determine the availability of the system. Typical rain time is on the order of 5 to 10 percent of an average year.

At frequencies above 10 GHz, rain has been recognized as the most fundamental obstacle in the earth-space path.

Rain causes: attenuation phase difference depolarization of radio waves.

Rain attenuation and atmospheric propagation effects are not significant at L-, S- and C-bands.

At high elevation angles the communications between satellites and terminals at L- and S-bands is very reliable.

The troposphere can produce significant signal impairments at the Ku-, Ka- and V-band frequencies, especially at lower elevation angles, thus limiting system availability and performance.

Fading effectsFading effects

Fast fading Slow fading Flat Selective Fading channel model:

Additive Gaussian noise Rayleigh Rician

Error Compensation Mechanisms

Forward error correction Adaptive equalization Diversity techniques

Forward Error Correction

Transmitter adds error-correcting code to data block Code is a function of the data bits

Receiver calculates error-correcting code from incoming data bits If calculated code matches incoming code, no error

occurred If error-correcting codes don’t match, receiver attempts

to determine bits in error and correct

Adaptive Equalization

Can be applied to transmissions that carry analog or digital information Analog voice or video Digital data, digitized voice or video

Used to combat intersymbol interference Involves gathering dispersed symbol energy back

into its original time interval Techniques

Lumped analog circuits Sophisticated digital signal processing algorithms

Diversity Techniques

Diversity is based on the fact that individual channels experience independent fading events

Space diversity – techniques involving physical transmission path

Frequency diversity – techniques where the signal is spread out over a larger frequency bandwidth or carried on multiple frequency carriers

Time diversity – techniques aimed at spreading the data out over time

Example The satellite (space) diversity where the best satellites, i.e., satellites with LOS conditions, are always selected and combined (for only one satellite with LOS, it is simply selection combining) even in a time-varying propagation environment due to mobile terminals

Channel capacity

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

Four important concepts in defining capacity Data rateData rate

– In bits per second – Rate at which data can be transmitted

Bandwidth Bandwidth – In Hertz – Constrained by transmitter (regulations) and medium

Noise NoiseNoise Bit Error Rate (BER)Bit Error Rate (BER)

Nyquist formulation

For noise-free channels (1924)For noise-free channels (1924): Channel Capacity

C = 2 B log 2 M

B is the bandwidth M is the number of signalling levels

Example 1: What is the capacity of a telephone line modem that uses 8 signalling levels?

Shannon theorem

*Shannon,C.E., “Communication in the presence of noise”, Proceedings of the IRE,Volume 37, Issue 1, Jan. 1949 Page(s):10 - 21

Shannon theorem

The widely used form is:

SNR is absolute value, not expressed in dB!

For high values of SNR expressed in [dB]

N

S1logBC 2

N

S

3

BC

Shannon’s formula expressesShannon’s formula expresses the theoretical maximum rate that can be achieved referred to as the error free capacity.error free capacity.

In practice much lower rates are achieved. One reason is that only white noise is considered (not impulse noise, nor attenuation)

Shannon proved that if the actual information rate on a channel is less than the error-free capacity, then it is theoretically possible to use a suitable signal code to achieve error-free transmission through the channel.

Shannon “decoded”: Give me enough bandwidth, or enough power and we can shake the world !

Example 2 Consider a voice channel being used, viamodem, to transmit digital data. Assume a bandwidth of 3100 Hz. A typical value of S/N for a voice-grade line is 30 dB, or a ratio of 1000:l. Which is the information capacity of the channel?

Example 3 which relates the Nyquist formula to the Shannon formulaLet’s consider a signal with a spectrum between 3 MHz and 4 MHz and a SNR=24 dB. Which is the channel capacity?Supposing that this is achieved how many signals levels are needed?

The ratio of C/B is efficiency of a efficiency of a digital transmissiondigital transmission, which is the bps per hertz that is achieved

The ratio of signal energy per bit to noise-power density per hertz

Eb/N0 is more convenient for determining digital data rates and error rates.

Consider a signal, digital or analog, that contains binary digital data transmitted at a certain bit rate R. Recalling that 1 watt = 1 joules/1 s, the energy per bit in a signal is given by Eb = STb, where

-S is the signal power -Tb is the time required to send one bit.

The data rate R is just R = l/Tb. Thus

The ratio EbINo is important because the bit error rate for digital data is a (decreasing) function of this ratio.

Given EbINo needed to achieve a desired error-the parameters in the preceding formula may be selected.

Note that as the bit rate R increases, the transmitted signal power, relative to noise, must increase to maintain the required EbINo.

The advantage of Eb/N0 comparative to S/N is that the latter depends on the bandwidth

Tlog10Rlog10dBW6,228)dBW(S)dB(N

E

0

b

Example 4

Suppose a signal encoding technique requires a ratio Eb/No = 8.4 dB for a bit error rate of 10 -4 (probability of one bit error out of 10000).

If the effective noise temperature is 290°K (room temperature) and the data rate is 2400 bps, what received signal level is required to overcome the signal noise?

Relation between spectral efficiency C/B and Eb/N0

Noise N0 is the power density in Watts/Hertz. Noise in a B bandwidth is

So N0=N/B The Shannon relation can be rewritten Considering R=C it is obtained a useful formula

Example 5 Calculate the minimum Eb/N0 to achieve a spectral efficiency of 6 bps/Hz

RN

S=

N

E

00

b

BN=N 0

12=N

S BC _/

)_( / 12C

B=

N

E BC

0

b