1. 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

2. Goals in designing a DCS
Maximizing the transmission bit rate
Minimizing probability of bit error
Minimizing the required power
Minimizing required system bandwidth
Maximizing system utilization
Minimize system complexity

3. 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)

4. Nyquist minimum bandwidth requirement
The theoretical minimum bandwidth needed for baseband transmission of Rs symbols per second is Rs/2 hertz ?

5. 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):

6. 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.

7. Shannon limit … Unattainable region C/W [bits/s/Hz] Practical region
SNR [dB]
Practical region
Unattainable
region

8. Shannon limit …
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.

9. Shannon limit … Practical region W/C [Hz/bits/s] -1.6 [dB]
Unattainable
region
-1.6 [dB]

10. Bandwidth efficiency plane
R>C
Unattainable region
M=256
M=64
R=C
M=16
M=8
M=4
Bandwidth limited
R/W [bits/s/Hz]
M=2
M=4
M=2
R<C
Practical region
M=8
M=16
Shannon limit
MPSK
MQAM
MFSK
Power limited

11. Error probability plane (example for coherent MPSK and MFSK)
bandwidth-efficient
power-efficient
k=5
k=4
k=1
k=2
Bit error probability
k=4
k=3
k=5
k=1,2

12. 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)

13. 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.