Factors in Digital Modulation
• 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
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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
2
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
h(t )  sinc( t / T )
H( f )
1
T
1
2T
?
0
1
2T
f
 2T  T
0
T 2T
t
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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 (ShannonHartley capacity theorem):
S

C  W log 2 1  
 N
[bits/s ]
W [Hz ] : Bandwidth
S  EbC [ Watt ] : Average received signal power
N  N 0W
[Watt] : Average noise power
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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/Hz]
Unattainable
region
Practical region
SNR [dB]
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Shannon limit …
S

C  W log 2 1  
 N
S  EbC

 N  N 0W
 Eb C 
C

 log 2 1 
W
 N0 W 
C
As W   or
 0, we get :
W
Eb
1

 0.693  1.6 [dB]
N0
log 2 e


Shannon limit
There exists a limiting value of Eb / N 0 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.
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Shannon limit …
Practical region
W/C [Hz/bits/s]
Unattainable
region
-1.6 [dB]
Eb / N 0 [dB]
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Bandwidth efficiency plane
R>C
Unattainable region
M=256
M=64
R=C
R/W [bits/s/Hz]
M=16
M=8
M=4
Bandwidth limited
M=2
M=4
M=2
R<C
Practical region
M=8
M=16
Shannon limit
Power limited
Eb / N 0 [dB]
MPSK
MQAM
MFSK
PB  105
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Error probability plane
(example for coherent MPSK and MFSK)
M-PSK
bandwidth-efficient
M-FSK
power-efficient
k=5
Bit error probability
k=4
k=1
k=2
k=4
k=3
k=5
k=1,2
Eb / N 0 [dB]
Eb / N 0 [dB]
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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:
Rb log 2 M
1


W
WTs
WTb
[bits/s/Hz ]
W  1 / Ts  Rs [Hz]

Assuming Nyquist (ideal rectangular) filtering at baseband,
the required passband bandwidth is:
Rb / W  log 2 M [bits/s/Hz ]

M-PSK and M-QAM (bandwidth-limited systems)
 Bandwidth efficiency increases as M increases.
Rb / W  log 2 M / M [bits/s/Hz ]

MFSK (power-limited systems)
 Bandwidth efficiency decreases as M increases.
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