3. Carrier-Amplitude modulation In baseband digital PAM: (2d - the Euclidean distance between two adjacent points)

4. the transmitted signal waveforms: special case: rectangular pulse

5. the Amplitude modulated Carrier signal is usually called amplitude shift keying (ASK)

6. 0 r WW- Figure 7.1: Energy density spectrum of the transmitted signal g T (t).

7. Figure 7.2: amplitude modulation of a sinusoidal carrier by the baseband PAM signal

8. 0 r WW- 1 (a) f 0 (b) - f c + W- f c - W- f c f c + Wfcfc f c - W Figure 7.3: Spectra of (a) baseband and (b) amplitude- modulated signal.

9. 0-5dd-d-d-3d3d3d5d5d Figure 7.4: Signal points that take M values on the real line The baseband PAM signal waveforms in general:

10. Demodulation of PAM Signal

11. when we cross correlate the signal r(t) with the signal waveform we get: the variance can expressed as:

12. Figure 7.5: Demodulation of bandpass digital PAM signal. X X

13. Answer ip_07_01 Example 7.1: In an amplitude-modulated digital PAM system, the transmitter filter with impulse response g T (t) has a square-root raised-cosine spectral characteristic as described in Illustrative problem 6.7, with a roll-off factor a=0.5. The carrier frequency is f c =40/T. evaluate and graph the spectrum of baseband signal and the spectrum of the amplitude-modulated signal

14. Carrier-Phase Modulation This type of digital phase modulation is called Phase-Shift-Key where gT(t) is the transmitting filter pulse shape.

15. when gT(t) is a rectangular pulse we expressed the transmitted signal waveform (at 0 < t <T) as:

16. Example 7.2: Generate the constant-envelope PSK signal waveforms given by (1.3.4) for M=8. For convenience, the signal amplitude is normalized to unity. Answer ip_07_02

17. 110 M=2 EE 01 10 00 11 E s M=4 E s 100 101111 010 011001 000 M=8 Figure 7.8:PSK signal constellations

18. Phase Demodulation and Detection the two quadrature components of the additive noise

19. The correlation metrics the received signal vector r is projected onto each of the M possible transmitted signal vector {S m }and select the vector corresponding to the largest projection. we select the {S m } signal whosh phase is the closet

20. Example 7.3: We shall perform a Monte Carlo simulation of M=4 PSK communication system that models the detector as the one that computes the correlation metrics given in (7.3.15). The model for the system to be simulated is shown in Figure 7.11. Answer ip_07_03 Uniform random number generator compare 4-PSK MAPPER Detector Bit-error counter Symbol-error counter 2-bit symbol Figure 7.11:Block diagram of an M=4 PSK system for Monte Carlo simulation + + Gaussian RNG

21. Differential Phase Modulation and Demodulation

23. X X Block diagram of DPSK demodulator

24. Example 7.4: implement a differential encoder for the case of m=8 DPSK. Answer ip_07_04

25. Example 7.5: Perform a Monte Carlo simulation of an M=4 DPSK communication Answer ip_07_05

26. Figure 7.15: Block diagram of m=4 DPSK system for the Monte Carlo simulation Uniform random number generator compare 4-DPSK MAPPER Delay Symbol-error counter 2-bit output + + Gaussian RNG M=4DPSK Detector

27. Quadrature Amplitude Modulation the transmitted signal waveform the combined digital amplitude and digital-phase modulation form

28. Transmitting filter g T (t) Binary data Serial-to- parallel converter Transmitting filter g T (t) Oscillator Balanced modulator 90 Phase shift Transmitted QAM signal + Functional block diagram of modulator for QAM

31. Quadrature Amplitude demodulation X X X X Demodulation and detection of QAM signals

32. Probability of Error for QAM in an AWGN Channel

33. Example 7.6: perform a Monte Carlo simulation of am M=16-QAM communication system using a rectangular signal constellation. The model of the system to be simulated is shown in figure 7.22. Answer ip_07_06 Figure:Block diagram of an M=16-QAM system for the Monte Carlo simulation Uniform random number generator compare M=16-QAM signal selector Detector Bit-error counter Symbol-error counter 4-bit symbol + + Gaussian RNG

34. Carrier-Frequency Modulation

35. Frequency-Shift Keying

36. Demodulation and detection of FSK signals the filter received signal at the input The additive bandpass noise phase shift

38. Sample at t=T PLL1 Sample at t=T Received signal Output decision Figure 7.26: Phase-coherent demodulation of M-ary FSK signals. PLL1

39. Figure 7.26: Demodulation of M-ary signals for noncoherent detection. Sample at t=T Received signal Sample at t=T Detector Sample at t=T Output decision r1cr1c r1cr1c r1cr1c r1cr1c r1cr1c r1cr1c

40. Example 7.7:Consider a binary communication system that employs the two FSK signal waveforms given as Answer ip_07_07 Where f 1 =1000/T b and f 2 = f 1 +1/T b. The channel imparts a phase shift of =45 on each of the transmitted signals, so that the received signal in the absence of noise is Numerically implement the correlation-type demodulator for FSK signals.

41. Probability of Error for Noncoherent Detection of FSK

42. Answer ip_07_08 Example 7.8: perform a Monte Carlo simulation of a binary FSK communication system in which the signal waveforms are given by(7.5.1) where f 2 = f 2 +1/ T b and the detector is a square- law detector. The block diagram of the the binary FSK system to be simulated is shown in Figure 7.30. Uniform RNG FSK signal selector ( ) Detector ( ) 2 Gaussian RNG compare Bit-error counter Figure7.30: Block diagram of a binary FSK system for the Monte Carlo simulation Output bit Gaussian RNG 2 2 2 Uniform RNG Uniform RNG

43. Synchronization in Communication Systems Carrier Synchronization: A local oscillator whose phase is controlled to be synch with the carrier signal. Phase-Locked Loop: A nonlinear feedback control sys for controlling the phase of the local oscillator. the input to the PLL

44. the input of the loop filter ( e(t) has a high and a low frequency component. ) The role of the loop filter is to remove the high frequency component.

45. Figure 7.32: The

46. Input signal r(t) + - Figure 7.33: The phase-locked loop after removal of high-frequency components

47. Figure 7.34: The linearized model for a phase-locked loop. - +

48. Answer ip_07_09 Example 7.9: [First-order PLL] Assuming that And K=1, determine and plot the response of thePLL to an abrupt change of height 1 to the input phase.

49. Clock Synchronization early-late gate : A simple implementation of clock synch based on the fact that in a PAM communication sys the output of the matched filter is the autocorrlation function of the basic pulse signal used in the PAM sys. The autocorrlation function is MAX and symmetric

50. when we are not sampling at the optimal sampling time:

51. in this case the correct sampling time is before the assumed sampling time, and the sampling should be done earlier / be delayed. The early-late gate synch sys therefore takes three samples at T 1, T -, T + and then compares |y(T - ) | and |y(T + ) | and, depending on their relative values,generates a signal to correct the sampling time.

52. Late sample Early sample T- T T+ Matched filter output Optimum sample T- T T+ Figure 7.36: The matched filter output and early and late samples

53. Example 7.10:[clock synchronization] A binary PAM communication systems uses a raised- cosine waveform with a roll-off factor of 0.4. The system transmission rate is 4800 bits/s. write a MATLAB file that simulates the operation of an early-late gate for this system Answer ip_07_10