1. EE 6331, Spring, 2009 Advanced Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 11 Feb. 24 th, 2009

2. ECE6331 Spring 2009 Outline Speed and tradeoff Review –Simulation on Rayleigh channel –Modulation u Basics u Analog modulation Digital Modulation –Basic –Sampling theorem

3. ECE6331 Spring 2009 Fading Parameters

4. ECE6331 Spring 2009 What is modulation Modulation is the process of encoding information from a message source in a manner suitable for transmission It involves translating a baseband message signal to a bandpass signal at frequencies that are very high compared to the baseband frequency. Baseband signal is called modulating signal Bandpass signal is called modulated signal

5. ECE6331 Spring 2009 Modulation Techniques Modulation can be done by varying the –Amplitude –Phase, or –Frequency of a high frequency carrier in accordance with the amplitude of the message signal. Demodulation is the inverse operation: extracting the baseband message from the carrier so that it may be processed at the receiver.

6. EE 542/452 Spring 2008 Modulation Process of varying a carrier signal in order to use that signal to convey information –Carrier signal can transmit far away, but information cannot –Modem: amplitude, phase, and frequency –Analog: AM, amplitude, FM, frequency, Vestigial sideband modulation, TV –Digital: mapping digital information to different constellation: Frequency- shift key (FSK)

7. ECE6331 Spring 2009 Analog/Digital Modulation Analog Modulation –The input is continues 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

8. ECE6331 Spring 2009 Goal of Modulation Techniques Modulation is difficult task given the hostile mobile radio channels u Small-scale fading and multipath conditions. The goal of a modulation scheme is: –Transport the message signal through the radio channel with best possible quality –Occupy least amount of radio (RF) spectrum.

9. ECE6331 Spring 2009 Amplitude Modulation The amplitude of high-carrier signal is varied according to the instantaneous amplitude of the modulating message signal m(t). AM Modulator m(t) s AM (t)

10. ECE6331 Spring 2009 AM Modulation/Demodulation Modulator Demodulator Baseband Signal with frequency f m (Modulating Signal) Bandpass Signal with frequency f c (Modulated Signal) Wireless Channel Original Signal with frequency f m Source Sink f c >> f m

11. ECE6331 Spring 2009 AM Spectrum

12. ECE6331 Spring 2009 AM Decoder Rectifier Detector: synchronous Envelope Detector: asynchronous AM signalR C + v c (t) -

13. ECE6331 Spring 2009 Angle Modulation Angle of the carrier is varied according to the amplitude of the modulating baseband signal. Two classes of angle modulation techniques: –Frequency Modulation l Instantaneous frequency of the carrier signal is varied linearly with message signal m(t) –Phase Modulation The phase  (t) of the carrier signal is varied linearly with the message signal m(t).

14. ECE6331 Spring 2009 Angle Modulation k f is the frequency deviation constant (kHz/V) If modulation signal is a sinusoid of amplitude A m, frequency f m : k  is the phase deviation constant PHASE MODULATION FREQUENCY MODULATION

15. ECE6331 Spring 2009 FM Example -+-- Message signal FM Signal Carrier Signal 0 -4 4 1 0.5 1.5 + 2

16. ECE6331 Spring 2009 FM Index W: the maximum bandwidth of the modulating signal  f: peak frequency deviation of the transmitter. A m : peak value of the modulating signal Example: Given m(t) = 4cos(2  x10 3 t) as the message signal and a frequency deviation constant gain (k f ) of 10kHz/V; Compute the peak frequency deviation and modulation index! f m =4kHz  f = 10kHz/V * 4V = 40kHz.  f = 40kHz / 4kHz = 10 Answer:

17. ECE6331 Spring 2009 Spectra and Bandwidth of FM Signals An FM Signal has 98% of the total transmitted power in a RF bandwidth B T Lower bound Upper bound Example: Analog AMPS FM system uses modulation index of B f = 3 and f m = 4kHz. Using Carson’s Rule: AMPS has 32kHz upper bound and 24kHz lower bound on required channnel bandwidth. Carson’s Rule

18. ECE6331 Spring 2009 FM/PM Example (Frequency)

19. ECE6331 Spring 2009 Slope Detector LimiterDifferentiator Envelope Detector V in (t) V 1 (t) V 2 (t) V out (t) Proportional to the priginal Message Signal

20. ECE6331 Spring 2009 Digital Modulation The input is discrete signal –Time sequences of pulses or symbols Offers many advantages –Robustness to channel impairments –Easier multiplexing of various sources of information: voice, data, video. –Can accommodate digital error-control codes –Enables encryption of the transferred signals u More secure link

21. ECE6331 Spring 2009 Digital Modulation Example The modulating signal is represented as a time-sequence of symbols or pulses. Each symbol has m finite states: That means each symbol carries n bits of information where n = log 2 m bits/symbol.... 0 1 2 3 T One symbol (has m states – voltage levels) (represents n = log 2 m bits of information) Modulator

22. ECE6331 Spring 2009 Claude Elwood Shannon, Harry Nyquist

23. ECE6331 Spring 2009 Pulse Modulation Introduction

24. ECE6331 Spring 2009 2 Sampling Theorem

25. ECE6331 Spring 2009 3 Sampling Theorem

26. ECE6331 Spring 2009 4 Reconstruction Theorem

27. ECE6331 Spring 2009 Interpolation If the sampling is at exactly the Nyquist rate, then

28. ECE6331 Spring 2009 5 Sampling Theorem

29. ECE6331 Spring 2009 Figure 3.3 (a) Spectrum of a signal. (b) Spectrum of an undersampled version of the signal exhibiting the aliasing phenomenon. 6 Aliasing

30. ECE6331 Spring 2009 Aliasing 2D example

31. ECE6331 Spring 2009 Figure 3.4 (a) Anti-alias filtered spectrum of an information-bearing signal. (b) Spectrum of instantaneously sampled version of the signal, assuming the use of a sampling rate greater than the Nyquist rate. (c) Magnitude response of reconstruction filter. 7 Anti-Alias Filter

32. ECE6331 Spring 2009 Example: Aliasing of Sinusoidal Signals Frequency of signals = 500 Hz, Sampling frequency = 2000Hz

33. ECE6331 Spring 2009 Example: Aliasing of Sinusoidal Signals Frequency of signals = 1100 Hz, Sampling frequency = 2000Hz

34. ECE6331 Spring 2009 Example: Aliasing of Sinusoidal Signals Frequency of signals = 1500 Hz, Sampling frequency = 2000Hz

35. ECE6331 Spring 2009 Example: Aliasing of Sinusoidal Signals Frequency of signals = 1800 Hz, Sampling frequency = 2000Hz

36. ECE6331 Spring 2009 Example: Aliasing of Sinusoidal Signals Frequency of signals = 2200 Hz, Sampling frequency = 2000Hz