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Digital communications - week 1 1
Digital communications - week 1 2
Note: T=pulse duration, Tb=bit time, Ts=symbol time=k*Tb
___________________________________ t | new signal sent | new signal sent | new signal sent | 0 Ts 2Ts 3Ts
A new signal alternative is sent every Ts. Ts = the signaling (or symbol) time.
A signal alternative carries k information bits, and
The signaling (or symbol) rate = Rs = 1/Ts [symbols/s].
Digital communications - week 1 3
Average signal energy and signal power
Digital communications - week 1 4
M=2: “Antipodal signals are better then orthogonal signals”
Digital communications - week 1 5
Digital communications - week 1 6
4-ary PSK
Digital communications - week 1 7
4-ary FSK (orthogonal)
Digital communications - week 1 8
Digital communications - week 1 9
16-ary QAM with Gray-coding
Digital communications - week 1 10
Orthogonal Frequency-Division Multiplex (OFDM)
OFDM = the sum of N orthogonal QAM signals. Example: N=6000 64-ary QAM in each QAM signal Then an QFDM signal carries 36000 bits! How can this be built? An OFDM signal alternative?
Digital communications - week 2 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 12
How large is the bandwidth W [Hz] for a given information bit rate Rb [bps]?
Digital communications - week 2 13
Digital communications - week 2 14
G(f+fc) is left shift. G(f-fc) is right shift.
Digital communications - week 2 15
Digital communications - week 2 16
Consequently, to find the bandwidth we need to find R(f) for the given set of M signal alternatives.
Digital communications - week 2 17
Remember Appendix D!
Useful for: M=2 and equally likely antipodal signals!
Digital communications - week 2 18
Digital communications - week 2 19
Bandpass case.
Digital communications - week 2 20
VERY USEFUL!
Digital communications - week 2 21
Consequently, Table 2.1 can be used also in this M-ary PAM case!
Digital communications - week 2 22
Consequently, Table 2.1 can also be used for: M-ary QAM M-ary PSK M-ary bandpass PAM
Digital communications - week 2 23
Digital communications - week 2 24
Consequently, the bandwidth efficiency is bad for large M!
Digital communications - week 3 25
A practical implementation is therefore:
General bandpass:
Digital communications - week 3 26
Digital communications - week 3 27
Common challenge in both Wireless and Wireline applications!
Remember the training bits in the GSM-example!
Digital communications - week 3 28
This will cause overlapping signals unless Tb is increased to 3 s!
Digital communications - week 3 29
The noise power is equally distributed over all frequencies.
Digital communications - week 3 30
Gaussian probability distribution:
What is the probability that the output noise is above a critical level A (“bit-error”)?
Digital communications - week 3 31
Very useful tables!
Digital communications - week 3 32
Sent message (k bits): Decided message:
Digital communications - week 3 33
Digital communications - week 4 34
ML receiver when M=2.
Digital communications - week 4 35
FUNDAMENTAL RESULT!
Digital communications - week 4 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 37
Digital communications - week 4 38
Digital communications - week 4 39
A “typical” problem formulation.
Consequences:
Note! The received signal power Pz decreases with communication distance.
Digital communications - week 4 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 41
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Digital communications - week 4 50
Digital communications - week 5 51
Digital communications - week 5 52
Digital communications - week 5 53
Digital communications - week 5 54
How large is ISI? Is it too large? Can we make ISI=0?
Digital communications - week 5 55
Digital communications - week 5 56
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Digital communications - week 5 58
Digital communications - week 6 59
Digital communications - week 6 60
Digital communications - week 6 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 62
Digital communications - week 6 63
Adaptive coding and modulation!