DCStradeoff docx

:
Modulation and Coding Tradeoff and
Digital Communications Design
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
Error probability plane
(example for coherent MPSK and MFSK)
[dB] /
0
NE
b
[dB] /
0
NE
b
Bit error probability
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
Design on the Error probability plane
Bit error probability
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
Selection of parameters
- M in MP vs. MF
- Eb/No for Pb requirement
Limitations in designing a DCS

Limitations:


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)
Nyquist minimum bandwidth requirement

The theoretical minimum bandwidth
needed for baseband transmission of R
s

symbols per second is R
s
/2 hertz.
T2
1
T2
1−
T
)( fH
f
t

)/sinc()( Ttth =
1
0
T
T2
T−
T2
−
0
Shannon limit

Channel capacity: The maximum data rate at
which error-free communication over the channel is
performed.

Channel capacity of AWGV channel (Shannon-
Hartley capacity theorem):
][bits/s1log
2






+=
N
S
WC
power noise Average :[Watt]

power signal received Average :]Watt[
Bandwidth :]Hz[
0
WNN
CES
W
b
=
=
Shannon limit …

The Shannon theorem puts a limit on
the transmission data rate, not on the
error probability:

Theoretically possible to transmit
information at any rate , with an
arbitrary small error probability by using a
sufficiently complicated coding scheme

For an information rate , it is not
possible to find a code that can achieve an
arbitrary small error probability.
CR
b
≤
b
R
CR
b

>
Shannon limit …
C/W [bits/s/Hz]
SNR [bits/s/Hz]
Practical region
Unattainable
region
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 can not be
increased to any desired value.








+=
W
C
N
E
W
C
b

0
2
1log



=
=






+=
WNN
CES
N
S
WC
b
0
2
1log
[dB] 6.1693.0
log
1
:get we,0or As
20
−≈=→

→∞→
eN
E
W
C
W
b
0
/ NE
b
Shannon limit
Shannon limit …
[dB] /
0
NE
b
W/C [Hz/bits/s]
Practical region
Unattainable
region
-1.6 [dB]
Bandwidth efficiency plane
R<C
Practical region
R>C
Unattainable region
R/W [bits/s/Hz]
Bandwidth limited
Power limited
R=C

Shannon limit
MPSK
MQAM
MFSK
5
10
−
=
B
P
M=2
M=4
M=8
M=16
M=64
M=256
M=2M=4
M=8
M=16
[dB] /
0
NE
b
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)
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
1log
2
bs

b
WTWT
M
W
R
==
[Hz] /1
ss
RTW ==
][bits/s/Hz log/
2
MWR
b
=
][bits/s/Hz /log/
2
MMWR
b
=
Design example of uncoded systems

Design goals:
1. The bit error probability at the modulator output must meet the
system error requirement.
2. The transmission bandwidth must not exceed the available
channel bandwidth.
M-ary
modulator
M-ary
demodulator

][symbols/s
log
2
M
R
R
s
=
[bits/s] R
s
sb
r
R
N
E
R
N
E
N
P
000
==
[ ]
)( ,)(
0
MPgP
N
E
fMP
EB

s
E
=








=
Input
Output