ECEN 5032 Data Networks Communication Theory: PAM Examples Peter - - PowerPoint PPT Presentation

ECEN 5032 Data Networks

Communication Theory: PAM Examples

Peter Mathys

mathys@colorado.edu

University of Colorado, Boulder

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.1/8

Polar PAM, Rect.

• ✁✄✂

, Width

5 10 15 20 25 30 35 40 −1.5 −1 −0.5 0.5 1 1.5 PAM, Rectangular Pulse of Width T

B, FB = 1000 Baud

t [msec] s(t) −4000 −3000 −2000 −1000 1000 2000 3000 4000 −60 −50 −40 −30 −20 −10 f [Hz] 10log10(Sx(f)) [dB] PSD, Px=1, Px(f1,f2) = 97.4285%, Fs=176400 Hz, N=88200, NN=2, ∆f=2 Hz

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.2/8

Uniploar PAM, Rect.

• ✁✄✂

, Width

5 10 15 20 25 30 35 40 −1.5 −1 −0.5 0.5 1 1.5 Unipolar PAM, Rectangular Pulse of Width T

B, FB = 1000 Baud

t [msec] s(t) −4000 −3000 −2000 −1000 1000 2000 3000 4000 −60 −50 −40 −30 −20 −10 f [Hz] 10log10(Sx(f)) [dB] PSD, Px=0.51698, Px(f1,f2) = 98.7566%, Fs=176400 Hz, N=88200, NN=2, ∆f=2 Hz

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.3/8

Uniploar PAM, Rect.

• ✁✄✂

, Width

5 10 15 20 25 30 35 40 −1.5 −1 −0.5 0.5 1 1.5 Unipolar PAM, Rectangular Pulse of Width T

B/2, FB = 1000 Baud

t [msec] s(t) −4000 −3000 −2000 −1000 1000 2000 3000 4000 −60 −50 −40 −30 −20 −10 f [Hz] 10log10(Sx(f)) [dB] PSD, Px=0.25342, Px(f1,f2) = 95.0163%, Fs=176400 Hz, N=88200, NN=2, ∆f=2 Hz

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.4/8

Polar PAM, Tri.

• ✁✄✂

, Width

5 10 15 20 25 30 35 40 −1.5 −1 −0.5 0.5 1 1.5 PAM, Triangular Pulse of Width 2T

B, FB = 1000 Baud

t [msec] s(t) −4000 −3000 −2000 −1000 1000 2000 3000 4000 −60 −50 −40 −30 −20 −10 f [Hz] 10log10(Sx(f)) [dB] PSD, Px=0.67555, Px(f1,f2) = 99.9859%, Fs=176400 Hz, N=88200, NN=2, ∆f=2 Hz

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.5/8

Polar PAM, Rcf.

• ✁✄✂

, Width

,

• ✁

5 10 15 20 25 30 35 40 −1.5 −1 −0.5 0.5 1 1.5 PAM, Raised Cosine in Frequency Pulse of Width T

B, α =0.2, FB = 1000 Baud

t [msec] s(t) −4000 −3000 −2000 −1000 1000 2000 3000 4000 −60 −50 −40 −30 −20 −10 f [Hz] 10log10(Sx(f)) [dB] PSD, Px=0.95616, Px(f1,f2) = 99.9992%, Fs=176400 Hz, N=88200, NN=2, ∆f=2 Hz

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.6/8

Prob Symbol Error: PSK, QAM

2 4 6 8 10 12 14 16 18 20 10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 Probability of Symbol Error Ps(E) for M−ary (Equally Likely) Digital PAM Ps(E) Eb/N0 [dB] M=2, polar M=2 unipolar M=4 QPSK M=8 PSK M=16 QAM−16 M=64 QAM−64

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.7/8

Prob of Symbol Error: FSK

2 4 6 8 10 12 14 16 10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 Probability of Symbol Error Ps(E) for M−ary (Equally Likely) Digital PAM Ps(E) Eb/N0 [dB] M=2, polar M=4 QPSK M=2 FSK coh M=2 FSK noncoh M=4 FSK coh M=8 FSK coh

Data Networks, PAM Examples, c

• 1996–2005, P

. Mathys – p.8/8