D.C.S Unit 2 Related Topic of ECE Subject

Unit 4

1. DIGITAL COMMUNICATION SYSTEMS III ECE I SEM PREPARED BY Dr T CHANDRA SEKHAR RAO, PROF

2. UNIT - 2 SYLLABUS TEXT BOOKS REFERENCES 1. Simon Haykin , “Communication Systems,” Wiley India Edition, 4th Edition, 2011. 2. B.P. Lathi & Zhi Ding, “Modern Digital & Analog Communication Systems”, Oxford University Press, International 4th edition, 2010. 1. Sam Shanmugam, “Digital and Analog Communication Systems”, John Wiley, 2005. 2. A. Bruce Carlson, & Paul B. Crilly, “Communication Systems – An Introduction to Signals & Noise in Electrical Communication”, McGraw-Hill International Edition, 5th Edition, 2010 3. Bernard Sklar , “Digital Communications”, Prentice-Hall PTR, 2nd edition, 2001. Baseband Pulse Transmission: Introduction, Matched filter, Properties of Matched filter, Matched filter for rectangular pulse, Error rate due to noise, Inter-symbol Interference(ISI), Nyquist’s criterion for distortion less baseband binary transmission, ideal Nyquist channel, Raised cosine filter & its spectrum, Correlative coding – Duo binary & Modified duo binary signaling schemes, Partial response signaling , Baseband M-array PAM transmission, Eye diagrams, Illustrative Problems.

3. INTRODUCTION The transmission of digital data over a baseband channel is discussed in this unit. Digital data have a broad spectrum with a significant low frequency content. Baseband transmission of digital data requires use of low-pass channel with a band width large enough to accommodate the essential frequency content of data. Channel is dispersive – its frequency response deviates from that of an ideal low pass filter. Data transmission over such channel results in Inter Symbol Interference which is a major source of bit errors in the reconstructed data stream at receiver output. Channel noise is another source of bit errors. This unit discusses about the pulse shaping.

4. MATCHED FILTER The device for the optimum detection of a pulse signal of known waveform that is immersed in additive white noise (Channel Noise) involves the use of a linear time invariant filter known as Matched filter. Basic task – detecting transmitted pulses at the front end of the receiver (corrupted by noise) Receiver model

5. The output signal component is required to be greater than output noise component. This is done by making the instantaneous power in output signal measured at t = T as large as possible than power of output noise. This is equivalent to maximizing the peak pulse signal to noise ratio defined as The requirement is to specify impulse response h(t) of the filter such that output SNR is maximized. We have for signal g(t) g(t) G(f) H(f) g (t) G (f)    

6. The effect on the filter output due to noise w(t) acting alone Then the peak signal to noise ratio is w(t) S W (f) = N /2 H(f) n(t) S N (f)

7. Schwarz’s inequality equality holds if and only if , we have If and then numerator of PSNR   Then,   ⟹

8. Then The maximum value of PSNR is at which H(f) is optimum denoted by H opt (f) given by Then We have Then

9. The impulse response of the optimum filter, except for scaling factor k, is a time reversed and delayed version of the input signal g(t), that is , it is matched to input signal. The linear time invariant filter defined in this way is called a Matched filter.

10. Matched Filter for rectangular pulse g(t) is rectangular pulse of amplitude A and duration T. The maximum value of output signal g o (t) is kA 2 T, which is energy of g(t) multiplied by k. The maximum value occurs at t=T For the special case of rectangular pulse, the matched filter is implemented using the Integrate and Dump circuit The output waveform of Integrate and Dump circuit for 0 ≤ t ≤ T, has the same waveform as that at the output of matched filter.

11. ERROR RATE DUE TO NOISE Consider a binary PCM system based on polar non return to zero(NRZ) signalling. Channel noise is additive white gaussian noise w(t) with zero mean and PSD N /2. In the signal interval 0 ≤ t ≤ T b , the received signal is Given the noisy channel x(t), the receiver is required to make a decision in each signal interval as to whether the transmitted symbol is 1 or 0. The structure of receiver used to perform the decision-making process is shown below    

15. Let

16. INTER SYMBOL INTERFERENCE

17. NYQUIST’S CRITERION FOR DISTORTIONLESS BASEBAND BINARY TRANSMISSION

18. For i = k , we have       -------------------------------------------------------------------------------------------------------------- For the pulse p(t)

19. IDEAL NYQUIST CHANNEL

20. Ideal Nyquist channel solves the problem of zero ISI with the minimum bandwidth possible.

21. RAISED COSINE SPECTRUM RAISED COSINE SPECTRUM The practical difficulties of ideal Nyquist channel can be overcome by extending the bandwidth from the minimum value W = R b /2 to an adjustable value W and 2W. Roll-off factor      

22. For α = 0, 0.5, 1

23. CORRELATIVE LEVEL CODING (or) By adding inter-symbol interference to the transmitted signal in a controlled manner, it is possible to achieve a signalling rate equal to the Nyquist rate of 2W symbols per second in channel of bandwidth W hertz. Such schemes are called Correlative level coding schemes or Partial response signaling schemes

24. This correlation between the adjacent pulses may be viewed as introducing inter symbol interference into the transmitted signals in an artificial manner. The ISI so introduced is under designer’s control is the basis of correlative coding. The effect of the transformation is to change the input sequence { a k } of uncorrelated two level pulses into a sequence {c k } of correlated three level pulses.

25. The technique of using a stored estimate of previous symbol is called Decision Feedback Errors tend to propagate through the output. DECODING        

26. PRECODED DUOBINARY SCHEME b k d k-1 d k 1 1 1 1 1 1

27. MODIFIED DUOBINARY SIGNALING The PSD of the transmitted pulse is non-zero at the origin, which undesirable in some applications. a k-2

28. Correlation span of two binary digits

29. Binary sequence { b k } 1 1 1 Pre-coded sequence { d k } 1 1 1 1 1 1 1 Two level sequence { a k } +1 +1 +1 +1 -1 +1 +1 -1 +1 Modified Duo-binary coder output { c k } -2 +2 -2 Binary sequence obtained by decision rule 1 1 1 Table illustrating example on Modified duo-binary coding The output of Modified duo-binary coder Pre-coder output

30. GENERALIZED FORM OF CORRELATIVE – LEVEL CODING (PARTIAL-RESPONSE SIGNALING) c k   

31. c k   

32. BASEBAND M- ary PAM TRANSMITTER

33. Design of Pulse amplitude modulator and decision-making device are more complex in M- ary PAM. ISI, Noise and imperfect synchronization cause errors to appear at the receiver output. The transmit and receive filters are designed to minimize these errors. - - - - - -

34. EYE PATTERN

35. END OF UNIT - II