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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_packet7/29/2019 Different Evaluation Metrices Used in Engineering Old
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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
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