Digital Carier Modulation, Exams of Marketing

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Lecture 16: Digital Carier Modulation

John M Pauly

November 15, 2021

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)

I Example of a high-speed 8b/10b serial link

Based on lecture notes from John Gill

Eye Diagram

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

AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEtMeCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUem4NgUK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJa37GZZIalGy5KEwFMTGZ/02GXCEzYmoJZYrbWwkbU0WZsemUbAje6svrpH1V9W6q3sN1pV7L4yjCGZzDJXhwC3W4hwa0gMEInuEV3hzhvDjvzseyteDkM6fwB87nDx4Sjak=

Tb

AAAB6HicbVBNS8NAEN3Ur1q/qh69LBbBU0lEtMeCF48t2A9oQ9lsJ+3azSbsToQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSNnGqObR4LGPdDZgBKRS0UKCEbqKBRYGETjC5m/udJ9BGxOoBpwn4ERspEQrO0EpNHJQrbtVdgK4TLycVkqMxKH/1hzFPI1DIJTOm57kJ+hnTKLiEWamfGkgYn7AR9CxVLALjZ4tDZ/TCKkMaxtqWQrpQf09kLDJmGgW2M2I4NqveXPzP66UY1vxMqCRFUHy5KEwlxZjOv6ZDoYGjnFrCuBb2VsrHTDOONpuSDcFbfXmdtK+q3k3Va15X6rU8jiI5I+fkknjkltTJPWmQFuEEyDN5JW/Oo/PivDsfy9aCk8+ckj9wPn8A3x+M9A==

t

Timing Tolerance

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Tb

AAAB6HicbVBNS8NAEN3Ur1q/qh69LBbBU0lEtMeCF48t2A9oQ9lsJ+3azSbsToQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSNnGqObR4LGPdDZgBKRS0UKCEbqKBRYGETjC5m/udJ9BGxOoBpwn4ERspEQrO0EpNHJQrbtVdgK4TLycVkqMxKH/1hzFPI1DIJTOm57kJ+hnTKLiEWamfGkgYn7AR9CxVLALjZ4tDZ/TCKkMaxtqWQrpQf09kLDJmGgW2M2I4NqveXPzP66UY1vxMqCRFUHy5KEwlxZjOv6ZDoYGjnFrCuBb2VsrHTDOONpuSDcFbfXmdtK+q3k3Va15X6rU8jiI5I+fkknjkltTJPWmQFuEEyDN5JW/Oo/PivDsfy9aCk8+ckj9wPn8A3x+M9A==

t

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.

Polar Signaling with Raised Cosine Transform (r = 0. 5 )

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

Eye Diagram Measurements

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

Eye Diagrams and PAM: M -ary Baseband Signaling

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.

PAM Eye Diagram

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.

ISDN Power Spectrum

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.

On-Off Keying (OOK)

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

OOK Example

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

Example: BPSK

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

Frequency Shift (FSK)

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.

FSK Example: f 0 = 8, f 1 = 12

−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

Differential PSK (DPSK)

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.