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 • 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

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

8. 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. Shannon limit

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

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

11. Error probability plane(example for coherent MPSK and MFSK) M-FSK bandwidth-efficient power-efficient M-PSK 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.