Different Evaluation Metrices Used in Engineering Old

7/29/2019 Different Evaluation Metrices Used in Engineering Old

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Different Evaluation Metrices

used in Engineering

Presented by

Ahmad Shah

Hafeez ur Rehman


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Different metrics provide means for evaluating

and comparing system performances in variouscontexts. A variety of metrics are available as

analytic tools but must be carefully and properly

applied in order to obtain accurate and useful

results. Each area has got its own metrices.


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For example

Efficiency and Mechanical advantage (Machines)

Directivity, beamwidth and gain etc (Antennas)

Bandwidth, gain ,gain bandwidth product (Amplifers)

and rolloff factor BER,bandwidth ,bps,SNR,CNR (Communication systems)

MIPS(million of instructions per second) (computers)

Execution time and memory (Softwares)


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TRANSMISSION IMPAIRMENT

Signals travelling through a medium(guided or

unguided) suffers from impairments.This

arises due to imperfections in themedium/channel.

The received signal is a bit different from what issent.


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Causes of impairment


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Attenuation

loss of energy -> weaker signal

When a signal travels through a medium it

loses energy overcoming the resistance of the

medium

Amplifiers are used to compensate for this loss

of energy by amplifying the signal.


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Measurement of Attenuation

To show the loss or gain of energy the unit

decibel is used.

dB = 10log10 (P2/P1)

P1 - input signal power

P2 - output signal power


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Amplifying the attenuated signal


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Distortion

Means that the signal changes its form or

shape

Each frequency component has its ownpropagation speed traveling through a medium.

The different components therefore arrive withdifferent delays at the receiver.

That means that the signals have differentphases at the receiver than they did at thesource


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Distortion


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Noise

Any unwanted signal that corrupts the signal of interest


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Noise

There are different types of noise

Thermal - random noise of electrons in the wirecreates an extra signal

Induced - from motors and appliances, devices actas transmitter antenna and medium as receivingantenna.

Crosstalk- same as above but between two wires.

Impulse - Spikes that result from power lines,lighning, etc.


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Noise spectral density (No)

Noise spectral density (No) is defined as the amount of (white)noise energy per bandwidth unit (Hz).

No = N / B

No is often expressed as

No = k T

where K is the Boltzmann's constant in Joules per Kelvin [J/K]

T is the receiver system noise temperature in Kelvin [K]

Ambient thermal noise is typically calculated at 290K, or 16.85C


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Signal to Noise Ratio (SNR)


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SNR

Obviously, we want as high an SNR as possible


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The received SNR may be different at different points in the

receiver, as various components, such as amplifiers, mixers,

filters, etc., all add small amounts of noise to the total noise

power.

The sum of the noise contributions of the various components

in the receive chain is often called the Noise Figure (NF) of

the receiver.

Digital processing can add noise in the form of quantization

errors and other effects, and while these noise sourcescontribute to the total noise that may be seen at a detector, they

are not the same as the thermal noise.


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Capacity of a System

The bit rate of a system increases with anincrease in the number of signal levels we useto denote a symbol.

A symbol can consist of a single bit or n bits. The number of signal levels = 2n.

As the number of levels goes up, the spacing

between level decreases which increasing theprobability of an error occurring in thepresence of transmission impairments.


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Nyquist Theorem

Nyquist gives the upper bound for the bit rate ofa transmission system by calculating the bit ratedirectly from the number of bits in a symbol (orsignal levels) and the bandwidth of the system

(assuming 2 symbols/per cycle and firstharmonic).

Nyquist theorem states that for a noiselesschannel:

C = 2 B log22nC= capacity in bps

B = bandwidth in Hz


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Shannons Theorem

Shannons theorem gives the capacity of a

system in the presence of noise.

C = B log2(1 + SNR)


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CNR

Carrier power

Noise powerCNR =

The ratio of the received modulated carrier signalpower C to the received noise power N


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Difference between SNR and CNR

carrier-to-noise ratio, often written CNR or C/N, is the

signal-to-noise ratio (SNR) of a modulated signal.

CNR and SNR represent quite different measurement

parameters, one in the RF domain (Figure 1) and the other inthe baseband domain


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Carrier-to-interference ratio (CIR)

The ratio of received modulated carrier power S or C to theaverage received co-channel interference powerI.

C / I = C / (I1+ I2 + In)

Allows analysis and rating of

channel robustness in thepresence of co-channel

interference.


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Carrier-to-Noise Density (C/N0)

The ratio of carrier power divided to the noise

power spectral density


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Energy per Bit (Eb)

Energy per information bit (i.e. the energy per bit net of FECoverhead bits)

Eb= C / R

where

C is the carrier power, and R is the actual information bit rate.Using the Eb rather than overall carrier power (C) allows comparing different

modulation schemes easily.


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Energy per Bit to Noise Spectrum

Density (Eb/No)

Eb/No is the ratio of the Energy per Bit divided by the noise

power density.


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Eb/No

Allows comparing bit error rate (BER) performance (effective-

ness) of different digital modulation schemes. Both factors are

normalized, so actual bandwidth is no longer of concern.

Modulation schemes are compared through BER plots against

Eb/No.


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BER

bit error ratio (BER) is the number of bit errors

divided by the total number of transferred bits

during a studied time interval.

Sent Bits 1101101101

Received Bits 1100101101

BER = # of Wrong Bits

# of Total Bits

= 1

10

= 0.1

error


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BER, Coding Scheme and Eb/No


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Coding gain

For a given bit-error probability, the reduction in the Eb/N0 that

can be realized through the use of code.

(dB)/ 0NEb

BP

A

F

B

D

C

EUncoded

Coded


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BER

BER is normally displayed in Scientific Notation. The more negative the exponent, the better the BER.

Better than 1.0E-6 is needed after the FEC for thesystem to operate.

D e ci m a l S c i e n ti fi c N o ta t io n

1 1. 0 E + 0 0

0. 1 1 . 0 E -0 1

0. 0 1 1 . 0 E -0 2

0 . 00 1 1 . 0 E -0 3

0 . 00 0 1 1 . 0 E -0 4

0 . 0 00 0 1 1 . 0 E -0 5

0 . 0 00 0 0 1 1 . 0 E -0 6

0 . 0 0 00 0 0 1 1 . 0 E -0 7

0 . 0 0 00 0 0 01 1 . 0 E -0 8

0. 0 0 0 00 0 0 01 1 . 0 E -0 9

Lower andBetter BER

De cim a l Scie nt ific Nota tion

0 . 0 0 00 1 1 . 0E -05

0. 0 0 0 00 9 9 . 0E -06

0. 0 0 0 00 8 8 . 0E -06

0. 0 0 0 00 7 7 . 0E -06

0. 0 0 0 00 6 6 . 0E -06

0. 0 0 0 00 5 5 . 0E -06

0. 0 0 0 00 4 4 . 0E -06

0. 0 0 0 00 3 3 . 0E -06

0. 0 0 0 00 2 2 . 0E -06

0. 0 0 0 00 1 1 . 0E -06


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Noise and Intermittents

Errors caused by noise or intermittent causes can

have the same BER, but very different effects.

Errors that are spread out are due to noise problems

Errors that are grouped are due to intermittentproblems such as ingress or loose connectors.

Spaced Errors 1101101011010011100

Burst Errors 1111101011101101101

This Example Shows the Same Error Rate But theBurst Errors are More Difficult to Correct


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Pre and Post FEC BER

The Forward Error Correction (FEC) can correct errors upto a point, after which errors are passed on to the decodingcircuitry.

Its important to know the Pre and Post FEC BER to know

how hard the FEC is working to correct errors. The harderits working, the closer the system is to failure.

Pre FEC BER(Before Correction)

Post FEC BER(After Correction)


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BER

BER is a very importantmeasurement for determiningthe health of digital systems.

Determining the PRE andPOST FEC BER can tell youhow hard the FEC is workinggiving an indication of systemmargin.

Error seconds or severely

errored seconds canindicate intermittenterrors.

CM1000 CableModem SystemAnalyzer

AT2000SpectrumAnalyzer


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packet error rate (PER)

The packet error rate (PER) is the number of

incorrectly received data packets divided by

the total number of received packets
http://en.wikipedia.org/wiki/Network_packethttp://en.wikipedia.org/wiki/Network_packet


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Throughput

A network with bandwidth of 10 Mbps can pass only anaverage of 12,000 frames per minute with each framecarrying an average of 10,000 bits. What is the throughputof this network?

SolutionWe can calculate the throughput as

The throughput is almost one-fifth of the bandwidth in thiscase.


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Thanks

Different Evaluation Metrices Used in Engineering Old

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