1 efficiency: low ber at low snr channel: multipath & fading conditions minimize bandwidth...
TRANSCRIPT
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• efficiency: low BER at low SNR• channel: multipath & fading conditions• minimize bandwidth required• cost-effective & easy implementation
Performance Measures for Modulation Schemes
(i) p = power efficiency
(ii)B = bandwidth efficiency
Factors in Digital Modulation
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Goals in designing a DCS Goals:
Maximizing the transmission bit rate Minimizing probability of bit error Minimizing the required power Minimizing required system
bandwidth Maximizing system utilization Minimize system complexity
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Limitations in designing a DCS
The Nyquist theoretical minimum bandwidth requirement
The Shannon-Hartley capacity theorem (and the Shannon limit)
Government regulations Technological limitations Other system requirements (e.g satellite
orbits)
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Nyquist minimum bandwidth requirement
The theoretical minimum bandwidth needed for baseband transmission of Rs symbols per second is
Rs/2 hertz ?
t
)/sinc()( Ttth 1
0 T T2TT2
T2
1
T2
1
T
)( fH
f0
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Shannon limit Channel capacity: The maximum data rate
at which the error-free communication over the channel is performed.
Channel capacity on AWGV channel (Shannon-Hartley capacity theorem):
][bits/s1log2
N
SWC
power noise Average :[Watt]
power signal received Average :]Watt[
Bandwidth :]Hz[
0WNN
CES
W
b
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Shannon limit … Shannon theorem puts a limit on
transmission data rate, not on error probability:
Theoretically possible to transmit information at any rate Rb , where Rb C with an arbitrary small error probability by using a sufficiently complicated coding scheme.
For an information rate Rb > C , it is not possible to find a code that can achieve an arbitrary small error probability.
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Shannon limit …C
/W [
bits
/s/H
z]
SNR [dB]
Practical region
Unattainableregion
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Shannon limit …
There exists a limiting value of below which there can be no error-free communication at any information rate.
By increasing the bandwidth alone, the capacity cannot be increased to any desired value.
W
C
N
E
W
C b
02 1log
WNN
CES
N
SWC
b
0
2 1log
[dB] 6.1693.0log
1
:get we,0or As
20
eN
EW
CW
b
0/ NEb
Shannon limit
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Shannon limit …
[dB] / 0NEb
W/C [Hz/bits/s] Practical region
Unattainableregion
-1.6 [dB]
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Bandwidth efficiency plane
R<C
Practical region
R>CUnattainable region
R/W
[bi
ts/s
/Hz]
Bandwidth limited
Power limited
R=C
Shannon limit510BP
MPSKMQAMMFSK
M=2
M=4
M=8
M=16
M=64
M=256
M=2M=4
M=8
M=16
[dB] / 0NEb
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Error probability plane(example for coherent MPSK and MFSK)
[dB] / 0NEb [dB] / 0NEb
Bit
erro
r pr
obab
ility
M-PSK M-FSK
k=1,2
k=3
k=4
k=5
k=5
k=4
k=2
k=1
bandwidth-efficient power-efficient
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Power and bandwidth limited systems
Two major communication resources: Transmit power and channel bandwidth
In many communication systems, one of these resources is more precious than the other. Hence, systems can be classified as:
Power-limited systems: save power at the expense of bandwidth (for example by using coding schemes)
Bandwidth-limited systems: save bandwidth at the expense of power (for example by using spectrally efficient modulation
schemes)
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M-ary signaling Bandwidth efficiency:
Assuming Nyquist (ideal rectangular) filtering at baseband, the required passband bandwidth is:
M-PSK and M-QAM (bandwidth-limited systems) Bandwidth efficiency increases as M increases.
MFSK (power-limited systems) Bandwidth efficiency decreases as M increases.
][bits/s/Hz 1log2
bs
b
WTWT
M
W
R
[Hz] /1 ss RTW
][bits/s/Hz log/ 2 MWRb
][bits/s/Hz /log/ 2 MMWRb