Different Evaluation Metrices Used in Engineering New

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

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Different Evaluation Metrics used

in Engineering

Presented by

Ahmad Shah

Hafeez ur Rehman


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Introduction

Different metrics provide means for evaluating and comparing

system performances in various contexts.

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 study area has got its own metrics. Efficiency and Mechanical advantage (Machines)

Directivity, Beam-width and gain etc (Antennas)

Bandwidth, gain, gain bandwidth product (Amplifiers)and roll-off factor

BER, bandwidth , bps, SNR,CNR (Communication systems)

MIPS(Million of instructions per second), LoCs (Computers)


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Transmission Constraints Signals travelling through a medium whether guided or

unguided, suffers from impairments.

Impairments arise due to imperfections in the medium/channel

or the transmitting or receiving devices.

The received signal is a erroneous/distorted w. r. t the

transmitted signal.


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Causes of impairment


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Attenuation

Loss of energy results in weaker signal

When a signal travels through a medium it loses energy in

overcoming the resistance of the medium.

Amplifiers/Repeaters are used to compensate for this loss of

energy by amplifying the signal.


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Amplifying the attenuated signal


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Measurement of Attenuation

To show the loss or gain of energy the unit

decibel is used.

dB = 10 log10 (Po/Pi)


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Distortion

Means that the signal changes its form or shape.

Each frequency component has its own propagation speedtraveling through a medium.

The different components therefore arrive with different delaysat the receiver.

Signals have different phases at the receiver than they did atthe source.


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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 wire creates anextra signal.

Induced: from motors and appliances, devices act astransmitter antenna and medium as receiving antenna.

Crosstalk: same as above but between two wires.

Impulse : Spikes that result from power lines, lightning 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]


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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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SNR

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 an increase in thenumber of signal levels we use to 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 the probability of an erroroccurring in the presence of transmission impairments.


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Nyquist Theorem

Nyquist gives the upper bound for the bit rate of atransmission system by calculating the bit rate directly fromthe number of bits in a symbol (or signal levels) and thebandwidth of the system (assuming 2 symbols/per cycle and

first harmonic).

Nyquist theorem states that for a noiseless channel:

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

The ratio of the received modulated carrier signal powerC

to the received noise powerN


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Difference between SNR and CNR

Carrier-to-noise ratio, often written CNR orC/N, is the

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

CNR is a measurement for modulated signals while SNR is

usually used for baseband signals.


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Carrier-to-Interference ratio (CIR)

The ratio of received modulated carrier powerC to theaverage received co-channel interference powerI.

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

CIR allows analysis and rating of channels robustness in the

presence 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: carrier power, and R is the actual information bit rate.

Using the Eb rather than overall carrier power (PC) 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

Eb/No is the measure of signal to noise ratio for a digital

communication system

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 dividedby the total number of transferred bits during a studied

time interval.

Sent Bits 1101101101

Received Bits 1100101101

BER =No. of Bits in error

No. of Total Bits

=1

10

= 0.1

error


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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 the system tooperate.

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 and

Better BER

Decim a l Sc ie 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 intermittent problems such

as loose connectors.

Spaced Errors 1101101011010011100

Burst Errors 1111101011101101101

This Example Shows the Same Error Rate But the Burst

Errors are More Difficult to Correct


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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.


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Throughput

The throughput is a measure of how fast we can actually send

data through a network.

A link may have a bandwidth of B bps, but we can only send T

bps through this link with T always less than B.

The bandwidth is a potential measurement of a link; the

throughput is an actual measurement of how fast we can send

data.

Different Evaluation Metrices Used in Engineering New

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