Today

1
Todays Schedule

• Reading Lathi Chapter 1 7.1, beginning of
  7.2-7.7
• Mini-Lecture 1
• Line Codes and their characteristics
• Activity Analyze this?!
• Mini-Lecture 2
• Power Spectral Densities and Bandwidth
• Activity Analyze this?! Part 2
• Mini-Lecture 3 Repeaters and M-ary comm

2
Line Codes

• Take the bit stream from the data formatter
  and/or coding blocks and prepare it for
  transmission over the channel
• Assign waveforms to the digital data
• Handout shows the binary case (2 symbols)

3
Examples

• On/Off (unipolar)
• 1 send p(t), 0 nothing
• Return to zero (RZ)
• Non-Return to Zero (NRZ)
• Polar (bipolar)
• 1 send p(t), 0 send -p(t)

1 1 1 0 0 1 1
1 1 1 0 0 1 1
1 1 1 0 0 1 1
1 1 1 0 0 1 1
4
More Line Codes

• Alternate Mark Inversion
• 0 has no pulse
• 1 changes the sign of the waveform p(t)

1 1 1 0 0 1 1
5
Bi-phase Codes

• More complex waveforms can split the phase of
  the two signals

1 1 1 0 0 1 1
1 1 1 0 0 1 1
6
Properties of Line Codes

• Transmission Bandwidth
• Power Efficiency
• Error Detection and Correction
• Favorable power spectral density (PSD)
• DC Value equals zero due to repeaters
• Timing content (synchronization)
• Transparency

7
Activity

• Choose a different partner from lecture 1
• Look at the Manchester Bi-f-M, an AMI code where
  1 is a mark
• Code changes in level with each bit and has a
  transition half-way if a one.
• With your partner, analyze this code using the
  categories given on the previous page

8
Bandwidth

• Recall In Fourier Analysis, signals cannot be
  both time and frequency(band) limited
• For real-world (time-limited) signals this means
  BW can be difficult to define
• Look at handout for some examples of bandwidth
  which are based on the Power Spectral Density
  (PSD)

9
Baseband and Bandpass

• Baseband
• Bandpass

X(f)
fm
Xc(f)
fc
2fm Double sided bandwidth
10
Transmission Bandwidth(6.2.3)

• Binary systems
• L ( of levels) 2n or nlog2L
• Signal m(t), bandlimited to B hertz requires AT
  LEAST 2B samples/sec (Nyquist)
• For reconstruction, we need 2Bn bits/sec or 2nB
  pieces of information

11
Information/Hertz

• 1 Hertz can transmit a maximum of 2 pieces of
  information per second
• Noiseless channel of B Hz can transmit a signal
  of B Hz error-free
• Can reconstruct this signal with 2B samples
• Thus, channel of B Hz can transmit 2B pieces of
  information or 2 pieces of information/hertz

12
Transmission BW

• Minimum theoretical channel bandwidth is
• BT n B hertz
• Now back to PSDs and what they mean

13
Pulse Shaping

• Choose p(t) so that
• Improve the shape of the PSD (e.g. Manchester
  (Split-phase) Waveform (f))
• Minimize interference between adjacent pulses at
  RCV (trade off bandwidth and PSD shape)
• Make PSD zero at w0 if

14
Good PSDs

• Low peak power
• Small bandwidth, most power at small number of
  frequencies
• PSD 0 at DC and low frequencies

15
Activity

• Look at Figure 7.8 (page 308) in your textbook
• Use the PSDs to rank the codes wrt
• Bandwidth
• Power Efficiency
• DC coupling

16
Repeaters

• Regenerate digital signals and send on with
  minimal errors
• Reshape pulse to account for channel and XMT
• Extract timing
• Decide what waveform was sent

Sampler/Detector
Preamp and Equalizer
Regenerator
Channel and Noise
Timing Extraction
17
M-ary Communications

• Send multiple, M, waveforms
• Choose between one of M instead of 1 or 0.
• Waveforms differ by phase, amplitude, and/or
  frequency
• Advantage Send more information
• Disadvantage Harder to tell the signals apart or
  more bandwidth

18
Next Time

• Reading Lathi Chapter 7.7-7.9
• Mini-Lecture 1
• Digital Carriers and M-ary Communications
• Activity Detection
• Mini-Lecture 2
• Intersymbol Interference
• Activity Bad Decisions
• Mini-Lecture 3 Scramblers