Analog/Digital Modulation

1. Analog/Digital Modulation • Analog Modulation • The input is continuous signal • Used in first generation mobile radio systems such as AMPS in USA. • Digital Modulation • The input is time sequence of symbols or pulses. • Are used in current and future mobile radio systems

2. Performance Metrics • In analog communications we want, • Digital communication systems: • Data rate (R bps)  Limited by Channel Capacity • Probability of error • Without noise, there are no bit errors • Bit Error Rate (BER): Number of bit errors that occur for a given number of bits transmitted. • What’s BER if Pe=10-6 and 107 bits are transmitted?

3. Frequency versus Amplitude Modulation • Frequency Modulation (FM) • Most popular analog modulation technique • Amplitude of the carrier signal is kept constant (constant envelope signal), the frequency of carrier is changed according to the amplitude of the modulating message signal; hence info is carried in the phase or frequency of the carrier. • Has better noise immunity: • atmospheric or impulse noise cause rapid fluctuations in the amplitude of the received signal • Performs better in multipath environment • Small-scale fading cause amplitude fluctuations as we have seen earlier. • Can trade bandwidth occupancy for improved noise performance. • Increasing the bandwith occupied increases the SNR ratio. • The relationship between received power and quality is non-linear. • Rapid increase in quality for an increase in received power. • Resistant to co-channel interference (capture effect).

4. Digital Modulation • modulating signal (message) represented as pulses; • n bits represented by m finite states ; n = log2m • Cost effective because of advances in digital technology • (VHDL, DSP, FPGA…) • Advantages/disadvantages vs analog • - Better noise immunity • - Robustness to channel impairments • - Ability to multiplex information • - Error control: detect & correct corrupt bits • - Able to encrypt data • - Flexible software modulation & demodulation • - Requires complex signal conditioning

5. Factors that Influence Choice of Digital Modulation Techniques • A desired modulation scheme • Should provide low bit-error rates at low SNR • Power efficiency • Should occupy minimum RF channel bandwidth • Bandwidth efficiency • Should perform well in multi-path and fading conditions • Should be easy and cost-effective to implement • Depending on the demands of a particular system or application, tradeoffs are made when selecting a digital modulation scheme.

6. Tradeoff between BW Efficiency and Power Efficiency • Adding error control codes • Improves the power efficiency • Reduces the required received power for a particular bit error rate • Decreases the bandwidth efficiency • Increases the bandwidth occupancy • M-ary keying modulation • Increases the bandwidth efficiency • Decreases the power efficiency • More power is required at the receiver

7. Power Efficiency of Modulation • Power efficiency is the ability of the modulation technique to preserve fidelity of the message at low power levels. • Usually in order to obtain good fidelity, the signal power needs to be increased. • Tradeoff between fidelity and signal power • Power efficiency describes how efficiently this tradeoff is made Eb: signal energy per bit N0: noise power spectral density PER: probability of error

8. Bandwidth Efficiency of Modulation • Ability of a modulation scheme to accommodate data within a limited bandwidth. • Bandwidth efficiency reflect how efficiently the allocated bandwidth is utilized R: the data rate (bps) B: bandwidth occupied by the modulated RF signal

9. Noiseless Channels and Nyquist Theorem • For a noiseless channel, Nyquist theorem gives the relationship • between the channel bandwidth and maximum data rate that can be transmitted over this channel. Nyquist Theorem C: channel capacity (bps) B: RF bandwidth m: number of finite states in a symbol of transmitted signal Example: A noiseless channel with 3kHz bandwidth can only transmit a maximum of 6Kbps if the symbols are binary symbols.

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

11. Shannon’s Bound for noisy channels There is a fundamental upper bound on achievable bandwidth efficiency. Shannon’s theorem gives the relationship between the channel bandwidth and the maximum data rate that can be transmitted over a noisy channel . Shannon’s Theorem C: channel capacity (maximum data-rate) (bps) B or W : RF bandwidthS/N: signal-to-noise ratio (no unit)

12. 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.

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

14. 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

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

16. 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

17. 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

18. 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.

19. 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)

20. 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

21. 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)