Digital communications - week 1 1

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Malcolm Wilkins
5 years ago
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1 Digital communications - week 1 1

2 A new signal alternative is sent every Ts. Ts = the signaling (or symbol) time. t new signal sent new signal sent new signal sent 0 Ts 2Ts 3Ts The signaling (or symbol) rate = Rs = 1/Ts [symbols/s]. A signal alternative carries k information bits, and Note: T=pulse duration, Tb=bit time, Ts=symbol time=k*tb Digital communications - week 1 2

3 Average signal energy and signal power Digital communications - week 1 3

4 M=2: Antipodal signals are better then orthogonal signals Digital communications - week 1 4

5 Digital communications - week 1 5

6 4-ary PSK Digital communications - week 1 6

7 4-ary FSK (orthogonal) Digital communications - week 1 7

8 Digital communications - week 1 8

9 16-ary QAM with Gray-coding Digital communications - week 1 9

10 Orthogonal Frequency-Division Multiplex (OFDM) OFDM = the sum of N orthogonal QAM signals. Example: N= ary QAM in each QAM signal Then an QFDM signal carries bits! How can this be built? An OFDM signal alternative? Digital communications - week 1 10

11 The bandwidth W of a signal is the width of the frequency interval where most of the signal energy (or power) is located. f [Hz] W Digital communications - week 2 11

12 How large is the bandwidth W [Hz] for a given information bit rate Rb [bps]? Digital communications - week 2 12

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14 G(f+fc) is left shift. G(f-fc) is right shift. Digital communications - week 2 14

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16 Consequently, to find the bandwidth we need to find R(f) for the given set of M signal alternatives. Digital communications - week 2 16

17 Useful for: M=2 and equally likely antipodal signals! Remember Appendix D! Digital communications - week 2 17

18 Digital communications - week 2 18

19 Bandpass case. Digital communications - week 2 19

20 VERY USEFUL! Digital communications - week 2 20

21 Consequently, Table 2.1 can be used also in this M-ary PAM case! Digital communications - week 2 21

22 Consequently, Table 2.1 can also be used for: M-ary QAM M-ary PSK M-ary bandpass PAM Digital communications - week 2 22

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24 Consequently, the bandwidth efficiency is bad for large M! Digital communications - week 2 24

25 General bandpass: A practical implementation is therefore: Digital communications - week 3 25

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27 Common challenge in both Wireless and Wireline applications! Remember the training bits in the GSM-example! Digital communications - week 3 27

28 This will cause overlapping signals unless Tb is increased to 3 s! Digital communications - week 3 28

29 The noise power is equally distributed over all frequencies. Digital communications - week 3 29

30 What is the probability that the output noise is above a critical level A ( bit-error )? Gaussian probability distribution: Digital communications - week 3 30

31 Very useful tables! Digital communications - week 3 31

32 Sent message (k bits): Decided message: Digital communications - week 3 32

33 Digital communications - week 3 33

34 ML receiver when M=2. Digital communications - week 4 34

35 FUNDAMENTAL RESULT! Digital communications - week 4 35

36 How much received energy per bit is required for a given Pb? d2 measures energy efficiency: the larger the better. Digital communications - week 4 36

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39 A typical problem formulation. Consequences: Note! The received signal power Pz decreases with communication distance. Digital communications - week 4 39

40 The union bound is an upper bound and it is especially good at high signal-to-noise ratios. In that case it is also easy to calculate! Assume 4-PAM: Then 3 different distances exist. So, the minimium Euclidean distance is very important! Digital communications - week 4 40

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54 How large is ISI? Is it too large? Can we make ISI=0? Digital communications - week 5 54

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59 Digital communications - week 6 59

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61 How can we get better Pb than binary antipodal signals? PAM, PSK, QAM, PWM, PPM, FSK? Uncoded: memoryless, i.e. no dependency between sent signal alternatives. Coding: In a clever way introduce memory (dependency, redundancy) between the sent signal alternatives! The memory can be used by the receiver to significantly reduce Pb! Digital communications - week 6 61

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63 Adaptive coding and modulation! Digital communications - week 6 63

EITG05 Digital Communications

Fourier transform EITG05 Digital Communications Lecture 4 Bandwidth of Transmitted Signals Michael Lentmaier Thursday, September 3, 08 X(f )F{x(t)} x(t) e jπ ft dt X Re (f )+jx Im (f ) X(f ) e jϕ(f ) x(t)f