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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.