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Digital Carrier Modulation Lecture topics I Eye diagrams I Pulse amplitude modulation (PAM) I Binary digital modulation I Amplitude shift keying (ASK) I Frequency shift keying (FSK) I Phase shift keying (PSK)
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John M Pauly
November 15, 2021
Based on lecture notes from John Gill
I (^) When we decide if a particular bit is ± 1 , we choose a threshold level and a time.
I (^) If the eye diagram is open, we can make that decision without error.
I (^) The dimensions of the ”eye” tell you the tolerance to timing and noise
Timing Tolerance
Amplitude Tolerance
I (^) Timing jitter will make the eye narrower, and noise will make the height
of the eye smaller
I (^) The shape of the eye depends on the pulse shape (last time), channel
distortion, and timing errors.
Last time we talked about Nyquist pulses. These were designed to be zero at the adjacent samples, but (1 + r) times wider in bandwidth than a sinc.
The timing sensitivity is less than Tb, and the noise sensitivity increases roughly linearly with timing error.
P (f ) =
1 |f | < 14 Rb 1 2
( 1 − sin π
( f − 12 Rb Rb
)) ||f | − 12 Rb| < 12 Rb
0 |f | > 3 Rb
I (^) Maximum opening affects noise margin
I (^) Slope of signal determines sensitivity to timing jitter
I (^) Level crossing timing jitter affects clock extraction
I (^) Area of opening is also related to noise margin
I (^) So far we’ve just been considering the case were we are ending one bit at a time. We can also vary the pulses to convey information, and send multiple bits of information with each pulse, or symbol.
I (^) We’ll talk much more about this next time. For now, we just consider
the simple case where there is just one pulse p(t), and we vary the amplitude. y(t) =
k
akp(t − kTb)
where ak is chosen from a set of more than two values (i.e., not just ± 1 ).
I (^) Eye diagrams are useful for understanding this case also.
I (^) The eye diagram for 4-level PAM using Nyquist r = 0. 5 pulses looks like this
I (^) Timing is even more critical
I (^) The noise sensitivity is increased by a factor of 4, since each eye is 1/
the height.
I (^) Power of 4 -ary signaling:
R 0 = 14 ((−3)^2 + (−1)^2 + 1^2 + 3^2 ) = 14 · 20 = 5.
If digital values are independent, Rn = 0 for n 6 = 0.
I (^) Thus PSD is
Sy(f ) =
Ts
|Px(f )|^2 ,
I (^) The PSD is the same as binary signaling.
I (^) More bits use more power.
I (^) We’ll return to M-ary signaling next class.
I (^) A simple version of ASK
I (^) Modulated signal is m(t) cos 2πfct.
Carrier
t Message
Transmited Signal^ t
t
I (^) Easy to generate, gate an oscillator on and off
I (^) Easy to receive, a simple envelope detector suffices
Baseband signal may use shaped pulses, so cosine amplitude varies. Digital input: 1 0 0 1 1 0 1 0 0. Square wave and shaped pulses.
0 1 2 3 4 5 6 7 8 9
−
−0.
0
1
−1.5 0 1 2 3 4 5 6 7 8 9
−
−0.
0
1
I (^) One PSK methods that is easy to decode is BPSK31, widely used in amateur radio.
I (^) A ”1” is a constant phase interval , and a ”0” is sent with a phase inversion.
I (^) The shaped pulses minimize the bandwidth
I (^) After demodulating to baseband, lowpass filter follow by an envelope
detector will decode the bits.
Figure from Wikipedia
I (^) Binary FSK uses two frequencies for 1 and zero. M-ary will be next time.
Carrier
t
Transmited Signal
t
Message
t
I (^) Usually integer numbers of cycles of each offset frequency, so that they
are orthogonal
I (^) Easy to receive, can be done with filters and an envelope detector (see this week’s lab!). Does not need to be synchronous.
−1 0 1 2 3 4 5 6 7 8 9
−0.
0
1
−40 0 1 2 3 4 5 6 7 8 9
−
0
20
40
−40 0 1 2 3 4 5 6 7 8 9
−
0
20
40
I (^) Differential PSK encodes the bits as the phase difference between two PSK pulses.
I (^) ”1” is a change of phase, and ”0” is the same phase.
I (^) This doesn’t need a synchronous receiver! The signal is its own
reference.