Digital Multiplexing, Channel Banks and Fiber Optics

1
Digital Multiplexing, Channel Banks and Fiber
Optics

• Southern Methodist University
• EETS7320
• Spring 2010
• Slides only. (No notes.)

2
Multiplexing

• Two multiplexing technologies have been used in
  traditional telephone transmission systems
• 1. Frequency Division Multiplexing (FDM). -
  Historical analog system in early 20th century.
  Used in combination with operator-to-operator
  conversations for long distance call setup.
• Analog FDM is very similar to radio broadcasting
  (although via wires and not via an antenna)
• Each voice signal is instantaneously amplutude
  modulated onto a distinct frequency sine wave for
  analog FDM. Typically 12 voice channels (Type N
  analog carrier-multiplexer.)
• Each voice signal has a pre-designated receive
  frequency

3
Multiplexing

• Subscriber dialed long distance calling (DDD) was
  introduced in North America in 1950s. DDD used
  in-band audio frequency tones for signaling and
  supervisionl
• FDM was the only telephone multiplexing
  technology used until 1961
• Only radio exception to FDMA is pulse position
  modulation (PPM) also called ultra wide band,,
  a recent proposal for radio purposes having some
  supporters and some opposition.
• FDM is used in almost all wireless systems,
  combined with TDMA, CDMA, etc. on the radio trunk
  channels linking handsets to a base station.
• 2. Digital waveform coding with Time Division
  Multiplexing (TDM).
• TDM (T-1) combines 24 voice conversations onto
  four wires. Now the dominant method for
  terrestrial trunks

4
FDM Analog Telephone Carrier

• Feasible with hardware available in 1920s.
• Derived from radio communication techniques
• FDM reached a high state of technical refinement
• Single Side Band (SSB) analog amplitude
  modulation (AM) (invented and analyzed by J.R.
  Carson) is the most spectrum-efficient method of
  modulation, using only about 4 kHz bandwidth per
  telephone voice channel
• SSB still used extensively in military and
  amateur radio
• Second and third order FDM systems hierarchy were
  then used to multiplex the lower order multiplex
  groups for more channels per link. Microwave and
  co-ax cable used FDM extensively in this way.
• FDM installations declined after 1960s, replaced
  by digital multiplexing
• Digital technology, although understood
  theoretically in 1930s, was not economically
  feasible until transistors and integrated
  circuits were developed as well

5
FDM Disadvantages

• Basic limitations of analog amplifier noise and
  distortion were still present
• Longer transmission distance requires more
  amplifiers. More amplifiers produces more audio
  noise and distortion
• Negative Feedback design, based on the invention
  of H.S.Black, produces a low distortion, low
  noise, (high fidelity) amplifier. The noise and
  distortion is lower but not eliminated!
• Although highly refined in design, analog
  hardware was still relatively costly to make,
  install, adjust
• With todays integrated circuit technology, it
  could be improved further, (examine a cellular
  radio unit, for example, which uses similar
  analog RF technology), but would not be quite as
  compact and low cost as equivalent functionality
  using digital multiplexing

6
Digital Multiplexing

• T-1, developed in 1961, quickly displaced FDM
• An almost ideal new product
• Better speech quality than analog FDM
• 24 channels double the capacity of predecessor
  12 channel analog N-carrier
• Direct replacement for 2 N-carrier links
• Installed cost about equal to N-carrier (thus
  half the cost per channel)
• Cost has since reduced even further due to use of
  integrated circuits, etc.
• Little or no field adjustment, calibration, etc.
  (low maintenance costs)
• Most new products are not simultaneously better
  in price and quality, or may have backward
  compatibility problems

7
Advantages of Digital Systems and Digital TDM

• The error due to digital coding and transmission
  in a properly functioning system can be
  controlled (and made very small) by the designer
• The quantizing or coding error arising from
  encoding round off should be the only practical
  error in a properly functioning system
• In a properly designed system, the difference in
  signal value (voltage, phase, etc..) for two
  distinct digital symbols is chosen to be much
  larger than any expected but undesired noise
  and interference
• Practical bit error rate (BER) in a good
  telephone system is 10-14
• At 50 Mb/s, one bit error occurs per 555.5 hours
  (23.15 days) on average
• Certain processing is more feasible when the
  signal is represented in digital form
• Digital Signal Processing (DSP), including
  logical processes
• Encryption (where required) is simpler
• Transmission of digital data and digitally coded
  speech should, in principle, permit less costly
  shared facilities (I.e., no modems needed)
• This is one of the motivations for ISDN, although
  the promised cost savings over modem use is not
  fully realized with present-day ISDN

8
Digital Telephone Systems

• Speech quality is equally good regardless of
  geographical distance
• Delay, and thus possibly echo, is the only
  negative consequence of distance, and echo can be
  very effectively reduced to a negligible level
  via echo-canceling equipment
• Equipment is superior to analog transmission for
  several reasons
• Lower initial capital and recurring (maintenance)
  costs
• Very compact, high capacity per wire or fiber
• Cross-Fertilization benefits from other digital
  technologies
• Digital switching
• Computers
• Data communications
• all use similar technology, sometimes the exact
  same parts (e.g. memory, logic gates, etc.),
  leading to economy of scale. Design and
  development cost is amortized over a large
  quantity production.

9
Mild Disadvantages of Digital Systems

• More complexity, more components than some cases
  of corresponding analog systems
• Not economically feasible historically with
  vacuum tube hardware
• Integrated circuits make this a much less
  significant disadvantage
• A digitally coded representation of a waveform
  may require more bandwidth for transmission than
  the original analog waveform
• Transmission signal bandwidth is less important
  for wire/cable/fiber transmission than for radio
  transmission
• Use of a sophisticated encoding process can
  reduce this problem in some cases...
• For example, several low bit rate speech coders
  (8 kb/s or less) use less radio bandwidth for
  cellular and PCS radio than the corresponding
  analog FM radio signal, and produce similar
  perceived speech quality

10
T-1 and E-1 Use Digital Waveform Coding

• Waveform coding is the first step in all types of
  speech coding
• Waveform coding allows digital transmission of
  signals that must preserve the desired waveform,
  such as MODEM signals
• Waveform coding typically produces the largest
  number of bits/second
• More complex and sophisticated coding methods
  reduce the bit rate
• Some waveform coding methods such as Delta
  modulation exploit waveform continuity
• Some methods produce good encoding of the audio
  frequency power spectrum, but dont preserve the
  waveform. OK for voice purposes.

11
Digital Coding of a Waveform

• Two Major Issues
• Required number of time samples/second
• Required number and distribution of amplitude
  (voltage) samples
• We will consider these issues in that order
• How many samples per second are required to avoid
  missing a short-time-duration wiggle in the
  waveform?
• How closely spaced must the amplitude quantizing
  levels be to achieve a particular accuracy goal?
• One goal hold the ratio of signal to quantizing
  noise below a specific level.

12
Telephone Voice Bandwidth Previously Standardized

• Result of FDM design studies in 1920s and 1930s
• 3.5 kHz upper frequency, approximately 300 Hz
  lower frequency. (using 3 dB half power points
  to define bandwidth)
• Lowest frequency is nominally 300 Hz.
• Not high fidelity, (examples CD disk or FM
  broadcasting on 100 MHz band) which requires 15
  kHz to 20 kHz audio bandwidth, and low frequency
  response down to 20 or 30 Hz.
• 3.5 kHz is inadequate to recognize some isolated
  phoneme sounds without benefit of known language
  context
• Examples f, s, sh, th (so-called fricatives) are
  sometimes confused
• Spelling (names of alphabetic characters) b, d,
  t, even v etc. are sometimes confused
• Requires phonetic alphabet for spoken spelling,
  like ICAO Alpha, Bravo, Charlie, Delta, Echo,
  Foxtrot,
• ICAOInternational Civil Aviation Organization

13
Empirical Telephone Bandwidth

• The nominal 3.5 kHz bandwidth for telephone voice
  connections was established by simple empirical
  testing in 1920s
• Human subjects listened to recordings of
  connected speech statements in their own language
• Various samples were low-pass filtered with upper
  cutoff frequency adjusted
• Percentage of incorrectly perceived samples was
  examined vs. cutoff frequency
• Bandwidth which permitted 99.9 accurate
  perception was used
• Incidentally, narrower 2 kHz bandwidths giving
  only 75 accuracy were used temporarily during
  World War 2 to increase link capacities.
• Different low frequency cutoffs (300, 500, 800
  Hz) affect naturalness (presence) of speech,
  but have little effect on accuracy of
  understanding.
• Existing telephone hardware causes 300 Hz lower
  frequency cutoff, primarily from coupling
  transformers in subscriber loop and
  microphone/earphone limitations.

14
Why use the Narrowest Bandwidth?

• Narrower signal bandwidth permits packing more
  individual channels into a fixed total bandwidth
• This is particularly important in analog FDM
• In digitally coded systems, less bit rate is
  needed to properly code a narrow band signal
  (more later on this point)
• Engineers are usually required to build the most
  economical system which meets quality
  requirements (Barely Adequate system)
• Systems with higher quality requirements use
  greater audio bandwidth
• AM Broadcasting 5 kHz (4.5 kHz in some
  countries)
• FM Broadcasting at least 15 kHz audio bandwidth
• Hi-Fi audio 20 Hz lows and 20 kHz highs (Compact
  Disks)

No standard on low audio frequency. Most AM
broadcasts roll off at about 100 Hz.
15
The Nyquist Sampling Theorem

• A band-limited waveform can be accurately
  reconstructed if sampled at a rate greater than
  twice its bandwidth.
• Example a 4 kHz bandwidth signal must be sampled
  slightly more than 8000 samples per second
• Exactly 8000 samples/sec would sample each 4000
  Hz sine wave component exactly twice per cycle.
• Theoretical truly band-limited signal has
  absolutely no audio power above some upper
  frequency
• could be produced most practically by a test
  signal generator via adding several sine waves
• Real band-limited voice signal is produced by
  low-pass filtering a real speech source waveform.
  Power above 4 kHz is 30 dB below (1/1000 of) the
  in-band typical power
• Nyquist theorem does not consider amplitude
  quantization errors
• Published by Harry Nyquist of Bell Laboratories
  in 1930s. Nyquist did not consider effects of
  digital quantization, but investigated a
  continuous accurate representation of each sample
  with perfect error-free addition of samples.

16
Recall waveforms can be analyzed into sine waves
Example shows one cycle (T1 second) of a square
wave and lowest three harmonics, sine wave
components.
17
Fourier Analysis

• How big should each sine wave component be? What
  is the appropriate multiplier bk for the k-th
  sine wave
• J.B.Fourier found in 18th century that the
  multiplier can be found from the product integral
• This formula computes the cross correlation
  coefficient between the sine wave and the square
  wave f(t). This is the area on graph paper of
  the product waveform from multiplying an
  appropriate frequency sine wave together with the
  waveform to be analyzed.
• Because the sine wave and this particular example
  square wave have the same so-called odd
  symmetry we do not expect to find a cosine wave
  as well. In general, for non-symmetric waveforms
  f(t), each harmonic term comprises both a cosine
  and sine term.

18
Fourier Coefficients

• From the previous formula and this particular
  square wave we find the first 5 coefficients
• Note that even harmonics (k2, 4,) are all zero.
  This is a special result for a square wave. A
  triangular wave has non-zero even harmonics, for
  example.
• Incidentally, when a non-linear distortion causes
  peak flattening of a waveform, thus making it
  appear more like a square wave, we quantitatively
  measure this by measuring the amount of odd
  harmonics power produced due to the flattening
  of the peaks. This measurement is used
  extensively in high fidelity equipment
  descriptions.

19
Approx. Square Wave Using First Three Odd (1,3,5)
Harmonics
Proper amplitude of each harmonic sine wave was
found from a product integral formula (same as
statistical cross correlation).
20
Example- I

• Consider a waveform like the approximate square
  wave made of only 3 odd-multiple frequency
  harmonics
• The highest frequency sine wave in that example
  was at 5 times the basic periodic frequency
• This synthetic waveform can be generated with
  absolutely no power above a specified upper
  frequency limit
• A filtered real waveform has very little (but
  not zero) power above a specified upper frequency
  limit
• If we can sample that highest sine wave
  frequently enough to capture its amplitude and
  phase precisely, we can reproduce it from the
  sample information
• Sampling exactly 2 times in a cycle is not quite
  enough, but slightly more than 2 samples per
  cycle is OK
• ?t lt t/2, where t (1/fmax) is the period of the
  highest frequency sine wave component.
• No problem to accurately represent lower
  frequency sine wave components using this
  sampling rate

21
Example- II
tT/5 one cycle of 5th harmonic
t/5one cycle
Two sine waves same frequency different
amplitude, phase
?tt/2

• Exactly 2 samples/cycle is ambiguous which sine
  wave is it? This problem
• is called aliasing since more than one sine
  wave (different amplitude and
• phase) fit the same sample points.

22
Example- III

• More than 2 samples/cycle is unambiguous.

?tltt/2




23
Time-Domain Nyquist Rule

• In the time domain, the equivalent rule is that a
  waveform consisting of sine waves can be measured
  at time intervals of ?t and then accurately
  reconstructed if the waveform has no significant
  wiggles (half-period sine wave components)
  which are shorter than the ?t time interval.
• This requires examining the entire time history
  of the waveform, in principle.
• But Fourier analysis of a waveform implies that
  we have examined the entire time history to
  compute the integral products used to evaluate
  the coefficients of the various sine wave terms.
  When we know the amplitude and phase of all the
  frequency components, we can predict the value
  of the sum of all frequency components for any
  time.
• Therefore, the frequency domain statement of
  Nyquists rule implies a complete (time history)
  examination of the waveforms properties.
• Furthermore, telephone engineers were already
  used to measuring the bandwidth of audio
  signals.

24
Band-limited Signals

• Real filtered signals cannot have zero power over
  a non-zero range of frequencies
• OK to have zero power at discrete individual
  frequencies. (for example the case of no even
  harmonic power for square waves)
• ITU-T and other telephone systems standards call
  for the filter to reduce the audio power (above 4
  kHz) to approximately 30 dB below (that is 1/1000
  of) the mid-band power level
• for example, see Bellamy (3rd Ed.) Digital
  Telephony, page 97, Fig. 3.6. Precise limit is 28
  dB below midband audio level
• This implies that noise power from imperfect
  filtration will be of a similar low magnitude
• Observe that the ITU curve is 3dB below the 0dB
  reference level at 3500 Hz frequency
• This 3 dB or half-power point is one of several
  ways to describe the bandwidth of a filter. It is
  easy to measure but not fully descriptive.

25
Digital Multiplexer Processes

• Measure the voice waveform voltage to obtain 8000
  samples per second
• Digitally encode this voltage into a binary code
  value of 8 bits
• Original T-1 multiplexer used a time-shared
  analog-digital converter
• Telephone systems use a non-uniform mapping from
  the signal voltage to the binary code value
• Serially transmit 8 bits consecutively for each
  such coded sample
• Insert extra bit(s) in the transmitted bit
  stream for synchronizing purposes
• De-multiplexer operations are substantially the
  reverse of those listed here

26
Amplitude Quantization

• The most obvious initial approach to amplitude
  quantization is to use uniform (linear)
  voltage steps, with enough steps to quantize the
  largest expected amplitude into many small
  intervals
• This is done for musical compact disk (CD)
  digital recording using 16 binary bits,
  corresponding to 65536 distinct fixed voltage
  levels. CD sampling rate is 42 ksamples/sec
• Uniform quantizing is the best encoding for
  signals which will be processed via Digital
  Signal Processing (DSP)
• Arithmetic adding, subtracting, etc. are
  straightforward
• Signals not already represented by uniform
  quantization must be converted before DSP
  processing.
• Yet another special jargon meaning of the word
  linear

27
How many bits?

• 16 bits resolution is much better than is needed
  for telephone purposes.
• Remember, the voice waveform has already been
  band-limited to 3.5kHz bandwidth
• Filter imperfections add about -30 dB noise
  (so-called fold-over noise)
• Carbon microphone is not high-fidelity
• Why bother with extra bits?? They cost more in
  hardware and precision of design and manufacture,
  and in transmission cost.
• Empirical listener testing indicates about 12-13
  bits of uniform resolution is adequate
• No perception of degradation in telephone voice
  quality
• Logarithmically compressed (companded) steps at
  low level permit equivalent quality with even
  less bits (in fact, 8)

28
Quantizing Noise (Round off Error)

• Whenever the actual voltage falls between two
  quantized amplitude steps, there is a round off
  error (quantization error)
• The error waveform for a ramp quantized with
  uniform steps is shown in Bellamy (3rd Ed.),
  p.100, Fig.3.9.
• The importance of a mid-tread vs. a mid-riser
  quantizer design is more significant when large
  quantizing steps are used.
• Mid-tread has zero output unless analog input
  exceeds voltage step size, so background noise is
  suppressed, but produces worse quantizing error
  at low voice levels.
• Mid-riser produces worse idle channel noise by
  increasing the miniscule background room noise or
  circuit noise, but has less average quantizing
  noise at low signal levels.
• Quantizing error can be characterized as an
  equivalent additive quantizing noise

mid-tread
Quantizer output code value
Analog voltage
mid-riser
code value
Analog voltage
29
Quantizing Noise

• Unlike random additive noise (Gaussian noise),
  quantizing noise is bounded by the voltage step
  value of the least significant bit and has a
  simpler distribution of amplitude
• Quantizing noise disappears during intervals of
  absolute silence (zero analog input) for
  mid-tread quantizer
• For certain types of testing, artificial
  quantizing noise is produced by instantaneously
  multiplying true random noise by the
  instantaneous magnitude of the audio signal
• The special statistical properties of quantizing
  noise yield a better signal-to-noise ratio than
  ordinary noise
• 56 kb/s V.90 data modems work beyond the
  theoretical Shannon limit on their data rate
  because they are limited by quantizing noise, not
  random (Gaussian) noise

30
Logarithmic Companding

• The human ear exhibits a phenomenon called
  masking
• a noise signal is not perceived as objectionable
  unless it is sufficiently large in relation to a
  desired sound present simultaneously
• Small noises are objectionable in a quiet library
• The same small noise is imperceptible at a rock
  concert!
• This principle is the basis of noise reduction
  systems like the Dolby system for sound
  recording
• The recording audio level is automatically
  increased for soft passages
• The playback level is automatically reduced, to
  match, via an auxiliary control signal, so
  desired signal has the original loudness. In
  Dolby system, this is typically a low frequency
  control signal.
• Therefore, noise added by the recording medium
  (e.g., magnetic tape hiss) is not noticeable
  during soft music intervals
• Dolby systems treat different audio frequency
  bands separately (high frequency is noisiest in
  magnetic tape), and use different types of
  auxiliary signals (Dolby B, C, etc.)

31
Other Companding Stuff

• Analog FM radio of all types (broadcast, analog
  cellular, specialized mobile radio -- SMR, etc.)
  uses time-dependent amplitude companding to
  reduce perceived audio background noise.
• Low amplitude speech is automatically increased
  in power at the transmit end, reduced again at
  the receiver
• No auxiliary time-varying control signal like
  Dolbys is used, just a uniform preset adjustment
  which shrinks the amplitude scale before
  transmission and stretches the amplitude range
  after reception and detection of the audio
• Syllabic companding in analog telephone systems
  (Bellamy, 3rd Ed. p.116ff) is similar
• These systems have a specified time window to
  compute average audio power (typically 5 to 10
  milliseconds)

32
Logarithmic Instantaneous Companding

• Design objective is uniform ratio of
  instantaneous signal to instantaneous quantizing
  noise, over the range of expected amplitudes
• Achieved by using approximately logarithmically
  spaced quantizing intervals
• Quantizing error amplitude is proportional to the
  difference between adjacent levels, and it is
  then in the same proportion (call this ratio H)
  to the mid-level signal amplitude for each level
• Power is proportional to the square of voltage
  amplitude, so a fixed proportionality ratio (H2)
  holds between instantaneous mid-quantizing-level
  power and quantizing noise
• A small practical problem ideal logarithm is not
  practical for v0, since log(0) is negative
  infinity

33
Non-Uniform Amplitude Coding

• Mu (µ) Law used in North America and Japan
• In conjunction with T-1 primary rate multiplexing
• A Law used in other parts of the world
• In conjunction with E-1 primary rate multiplexing
• For international digital telephone voice or
  modem connections, a digital code converter is
  provided at the Mu-law end of the international
  link.
• Each 8-bit sample is converted based typically on
  a look-up table
• For ISDN 64 kb/s end to end international data
  connections, a special parameter used in the SS7
  call setup (IAM) message is used to ensure that
  no converter is used for that particular call to
  avoid modifying the binary data.

34
Practical Logarithmic Companding- Coding

• Two methods to shift the logarithmic function
• µ law Shift to left so it goes through v0 by
  adding a constant to the analog voltage input
• A law Shift up by adding a constant to the code
  value result, then replace a small piece with a
  straight tangent line from the origin to a
  pre-designated low voltage point

µ
A
log(1) is zero
milli
Practical peak voltage is 1.55 V (corresponds to
2mW sine wave_at_600?
35
CODEC Block Diagram
Sample time interval 1/8000 sec or 125 µs
volts
volts
volts
3.5 kHz cutoff
Digital output (serial or parallel) Pulse
Code Modulation (PCM)
ms
Analog Multiplier
Analog- Digital Converter (A or ?- law)
CODER
ms
analog input may contain some power above 3.5 kHz
filtered (smoothed) analog signal
(Pulse Amplitude Modulation- PAM) signal
Low-pass Filters
8 kHz clock pulse train
3.5 kHz cutoff
Digital input (serial or parallel)
Sample and Hold, or Pulse Stretcher (Boxcar) Circu
it
analog input
Digital- Analog Converter (A or ?- law)
DECODER
volts
01011010
volts
v
ms
ms
Example 8 serial bits in 125 µs
ms
36
Mathematical Mu (µ)-law Graphnegative voltage
graph (not shown) is odd-symmetric replica of
this, but -127 code value is modified (explained
later)
Decimal code value
Fraction of full scale
1
127
0
f(v) ln(1 ?(v/1.55))/ln(1?) where ?? 255
0.5
63
0
0
0
0.5
1
1.5
2
ln is natural (base e 2.718) logarithm, not
decimal base.
instantaneous positive voltage
37
Mathematical A-law Graphnegative voltage graph
(not shown) is odd-symmetric replica of this
Decimal code value
Fraction of full scale
1
127
f(v) (1 ln(A(v/1.55)))/(1ln(A)) where A?
87.6
0.5
63
observe the straight line segment starting here.
Green color on color display
0
0
0
0.5
1
1.5
2
instantaneous positive voltage
38
T-1 (DS-1) TDM Frame
125 ?s or 1/8000 second
F 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24
24 8-bit PCM samples per frame, plus one framing
bit per frame
one time slot
One framing pulse per frame
bit label 1 2 3 4 5 6 7 8
5.18 ?s/slot
Except when common channel signaling is used (in
slot 24 of one link for control of a group of
links), bit 8 is robbed and replaced by a
signaling status bit in all slots during one of 6
frames. Signaling synch is related to a 12 or 24
frame sequence established by the framing bit
pattern.
8000 frames/s 193 bits/frame 1.544 Mbit/s bit
rate 0.647 ?s/bit
39
E-1 (CEPT, MIC) Frame
125 ?s or 1/8000 second
0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31
32 8-bit time slots per frame, normally 30 used
for subscriber PCM, two for synch and signals
one time slot
Slot zero contains synchronizing bit pattern and
some trouble-shooting bit patterns.
Slot 16 contains common channel signaling,
either channel associated condition bits, or CCS7
bit label 1 2 3 4 5 6 7 8
3.9 ?s/slot
8000 frames/s 256 bits/frame 2.048 Mbit/s bit
rate 0.488 ?s/bit
40
Important Facts

• Both µ-law and A-law coders use 8 bits for each
  sample
• For international calls, a translation via ROM
  table look-up is done between A and µ (in the µ
  law country)
• When arithmetic operations must be done (for
  example, for echo cancellation), the 8 bit code
  sample must be converted into a 12 bit (or more)
  sample via a look-up table or other means
• 16 bits (with 12 bit accuracy) is also used
• Performing arithmetic directly on companded Mu or
  A values would not be meaningful
• Not even a precise logarithmic value is used in
  the coding. The result of adding is not the sum
  of two logarithms exactly (although it is
  numerically close for large amplitude values)

41
Other Facts

• Both µ-law and A-law use a sign and magnitude
  representation of the coded value
• Physical zero volts has two codes 0 and -0
• Virtually all computers today use
  twos-complement coding instead to represent
  negative numbers
• Conversion from 8-bit telephonic PCM codes to
  12-bit numeric codes for DSP must correct for
  this as well
• µ-law intentionally modifies the largest negative
  coded value to prevent occurrence of all-zero
  codes after bit inversion occurs for line coding
  (to be explained). A-law does not do this.
• In many transmission systems using µ-law, the 8th
  bit is modified for signaling reasons (to be
  explained) in some frames of data

42
Practical Companding

• The earliest 8-bit uniform Analog/Digital (A/D)
  converters used in D1 version of T-1 systems used
  non-linear instantaneous logarithmic companding.
• Companding was achieved using an analog
  non-linear amplifier
• Semiconductor diodes have reasonably accurate
  logarithmic relationship between current and
  voltage over part of their operating range. This
  was the technical basis of logarithmic
  companding.
• In contrast, present T-1 and E-1 designs first
  perform 13 bit uniform A/D conversion, then
  produce a companded 8-bit binary number by table
  lookup of an approximate µ-law (or A-law) table.
  (Uniform A/D conversion may use Sigma-Delta
  digitization.)
• This table represents many straight diagonal line
  segments which approximate the smooth µ-law
  formula curve

43
Sign-magnitude vs. 2s Complement

• Sign-magnitude still used in some CDC, Cray, Sun
  super-computers

This value is not used in µ-law voice encoding.
44
Channel Banks, etc..

• The first digital telephone product was the T-1
  Digital Carrier (multiplexer)
• Developed at ATT (now Lucent) Bell Labs, circa
  1961
• Time Division Multiplexing (TDM)
• Digital coding of speech waveforms (Mu-law
  companding)
• Connected to analog lines and switches as
  required
• Steadily displaced analog multiplexers
• Digital switches directly using T-1 links
  appeared in 1970s
• First ATT ESS No.4 for transit switching
• Then many digital PBX switches (Rolm, etc..)
• Digital end office switches (Nortel DMS-10,
  DMS-100, etc.)
• Today digital transmission and switching serve
  well over 99 of North American calls

45
Channel Bank

• Packaging 24 channel service units (printed
  wiring cards) abbreviated CSU (30 CSUs in E-1)
• Common module cards
• Power, line, trunk connections at back

Common (shared) equipment codecs, power supply,
bit multiplexer/demux
Approx. 19in (490mm) standard rack width
46
Typical T-1 Installation
Channel Bank
Channel Bank
Some repeaters omitted from this figure.
Repeater spacing 6000 ft. (1800 m) of wire.
4-wire (2 pairs)
.
.
Repeater
Repeater
Repeater
Maximum span 150 miles, due to timing
requirements.

• Each channel bank supports 24 voice-grade
  circuits
• Repeaters regenerate clean digital pulses with
  corrected timing, amplitude, pulse shape
• Repeaters are powered via -130 V dc from channel
  bank units, using phantom circuit feed on both
  pairs.
• When last wire section is too short, a line
  build-out (LBO) circuit pack is wired in to
  produce similar signal attenuation and related
  effects.
• LBO consists of inductors, resistors, capacitors
  comprising circuit model for missingwire
  section(s). See previous transmission line
  lectures.
• E-1 primary rate channel banks are similar, but
  have 30 traffic channels, 2000 m (6562 ft)
  repeater spacing.

47
Some CSU Types and Applications

• 4-wire (used for various trunks or data services)
• No signaling (except audio in-band tones)
• Various signaling supervision options (A-B bits,
  EM, etc..)
• Digital data 56/64 kb/s (RS-232 or RS-449
  connector)
• 2-wire (various applications)
• No signaling (except audio in-band tones)
• Supervision for one-way or both-way trunk line
• Various types of supervision
• Operates like a telephone set (connect to CO)
• dc loop current on and off
• responds/passes on ringing voltage
• Operates like a CO switch (connect to tel set)1
• Provides loop battery, ringing
• A channel with previous two CSUs at opposite ends
  will extend a subscriber telephone loop via a T-1
  link channel.

1Requires optional special ringing power supply
48
Channel Bank Applications

• 4-wire
• Trunk line between switches with signaling
• Private tie-line between switches or similar
  equipment
• Standard Mu-law 24 channel link
• 48 channel link using ADPCM or other low bit-rate
  coding
• Cellular link from MSC central switch to each
  cell
• Lately, use of low bit-rate traffic channel
  coding (13 kb/s or less) for cellular/PCS has led
  to use of specialized multiplexers rather than
  standard channel banks.
• 2-wire
• Non-concentrating remote
• Provides pair gain-- 24 channels on 4 wires
  (with T-1 repeaters, of course)
• Distinguish this from SLC-96 or similar remote
  concentrator which has more telephone sets than
  channels

49
Digital Symbols

• Separate distinct signal voltage for each binary
  bit
• BIT is a contraction of binary digit, a term
  invented by pioneer information theorist Claude
  Shannon
• Two (voltage) levels represent the two binary
  symbolic values
• Most popular text symbols are 1 and 0 (also T,F
  or H,L)
• Voltages are often 5 and 0.2 volts (TTL), or 3
  and 0.2 V in some newer portable equipment
  (convenient for 3 V batteries), or 12 and 0.2 V
  in some older equipment.
• 0.2 V is often called zero. It is the natural
  knee voltage of many electronic semiconductor
  junction devices at their practical minimum
  voltage.
• Design objective is two voltage levels more
  separated than any undesired voltages from
  interference, noise etc..
• In some (active low) designs, inverse mapping
  is used between symbols and voltages. Not used in
  this course to minimize confusion.

50
Parallel vs. Serial Binary

• Parallel Every bit appears on a separate wire,
  simultaneously
• Parallel processes require more hardware, but
  operation is faster due to simultaneous
  activity.
• Successive parallel values require simultaneous
  change in all bit signals. Difficult to hold
  parallel synchronism with many long-distance
  separate wire or fiber channels.
• All parallel signals must be reliable for good
  operation. Error in one bit makes entire set of
  parallel bits unusable.
• Parallel format used mainly within one module or
  cabinet of equipment for very short (lt 1meter)
  transmission distance
• Serial Every bit appears for a preset time
  interval, in preset serial order, on one wire
  circuit.
• Serial processes are slower, but use less
  hardware
• Favored for all long distance (even a few meters)
  connections
• Shift Register device converts between Serial and
  Parallel formats

51
Amplifier / Comparator

• A differential amplifier with sufficiently high
  amplification suddenly switches from low to
  high output when two input voltages are
  substantially equal.

vo
Graphic Symbol
4 V
v1
voltage amplification2
vo
v2
voltage amplification 5000
Power supply and other details omitted.
v1-v2
4 V
2
A linear region amplifier of this type is often
called an Operational Amplifier. The high
voltage output level may be 5 or 3 volts rather
than 4 V shown here. Several examples here use 4
V, a convenient but not representative number.
52
D/A Conversion

• Ladder network with sources for each bit
• Continuous (thick or thin film resistor)
  ladder-like network

vo4D1 D2/2 D4/4 D8/8
Symbols D
volts
Voltage Ampli- fication is 2
4
1

0
0
vo
Non-standard logic voltage levels are used for
this example
D/A convertor is also called a decoder
Parallel input Digital/Analog (D/A) convertor --
highly simplified
53
Graphic Symbols

• Analog/Digital and Digital/Analog convertor in
  one package is often called a codec (derived from
  parts of the words CODer DECoder)
• Some alphabetic labeling is used to make clear
  which type of format conversion is represented
  (A-to-D, D-to-A, etc.), to indicate serial vs.
  parallel input, output, etc.

54
A/D conversion

• Many methods in use each has different
  advantages and disadvantages
• Most methods use a very high gain (operational)
  amplifier as a comparator
• Successive Approximation A/D converter
• Ramp-clock converter
• Saw tooth or ramp waveform quickly and repeatedly
  scans from minimum to maximum voltage.
• Associated digital clock starts for each scan
• Clock value is saved in a digital memory at time
  of match. This value is proportional to measured
  match voltage.
• Sigma-delta conversion
• One bit at a time incremental voltage change,
  converted at much higher sample rate (e.g. 32
  ksamples/sec) than the 8 kHz data value sampling
  rate.
• Subsequent time integration of small 1-bit
  increments/decrements
• Discussed later with Delta Modulation and CVSD
  (not this lecture)

55
Successive Approximation A/D

• One stage of successive approximation coder or
  A/D converter

Each stage uses outputs of more significant bits
from previous stages. First stage pulls up upper
D bit and grounds 7 other D bits. Then output
average (midpoint of 2 resistors) will be at
2 volts. Comparator output will be logical 1
(high) if voltage to be digitized is gt2 V, zero
otherwise. Second stage produces D4 result.
It uses D8 value from first stage to both D/A D8
inputs. Upper D4 is pulled up. All remaining 5
inputs are grounded. Then average voltage is
either 3V (if D is hi) or 1V (if D is
low). Digital storage register (not shown)
stores the bits. Can you draw all 4 stages with
proper connections?
4V (logical 1)
voltage to be digitized
D/A
D8 D4 D2 D1
comparator
D/A
D8 D4 D2 D1
D8 bit of digital output
zero volts (ground)
56
Ramp-clock A/D Convertor
Note that sampling interval must be short to
ensure that measured voltage changes
only slightly during interval.
signal voltage
time
Match time detected by voltage comparator output
change.
comparison voltage
time
Sample time interval (125 µs for 8000 samples/sec
in telephone systems) Separate binary clock (not
shown) counts from 0 to maximum, repeatedly
during each 125 µs interval. Max count for only
positive voltage range typically 127. Counter
value at instant of voltage match is the digital
code value.
57
Synchronization, Signaling, Line Coding

• Some distinctive bit pattern is required to
  indicate the beginning/end of the multiplexer
  serial binary frame
• For various reasons, different T-1 frame
  sequences must also be identifiable
• Main reason certain signaling bits appear only
  in certain frames (one frame out of 6 consecutive
  frames)
• Secondary reason use some framing bits for use
  as low bit rate special channel (in Extended
  SuperFrame only)
• Another application is identification of frame
  groups which are internally rearranged for ZBTSI
  line coding
• Several optional combinations of framing and line
  coding are used for T-1.
• Line coding is the conversion of the digital
  pules from the internal TTL levels (typically 5
  or 0 volts) into different external voltage
  levels such as 3, 0 and -3 volts.
• Only one line coding method, HDB3, is used for
  E-1.

58
Historical Evolution Notes

• Digital multiplexing format design choices are
  shaped by the economics of the technology
  available at the time of design
• T-1 and E-1 formats assign 8 consecutive bits
  from one sample in each time slot (channel), a
  process called byte interleaving
• Primarily done to use a single A/D converter,
  shared sequentially by one channel after another,
  in the hardware design
• Bit interleaving would require multiple A/D
  converters or digital memory to store all the
  bits currently generated but not yet transmitted.
• Higher level plesiochronous multiplexers use bit
  interleaving
• The bit stream in each tributary is already
  available in digital form
• The ratio of tributary bit rate to total bit rate
  allows each tributary to be sampled and
  multiplexed without need for extra memory
• Where memory is necessary, keep in mind that
  digital memory today is much less costly than in
  1960s
• SONET/SDH does use groups of 8 consecutive bits,
  and uses memory extensively to time delay some
  tributary bits when needed
• Use of consecutive bits with pointer methods in
  SONET/SDH for handling tributary clock
  discrepancies facilitates de-multiplexing a
  particular channel or tributary for drop-insert
  applications.

59
Historical T-1 Digital Coding
vout
Code out
vout
vin
Magnified View shows stair steps
Analog compressor using diode circuits.
Uniform 8-bit digital/analog convertor. Produces
8 serial bits each of 0.647 µs. 255 steps (dual
codes for positive zero and negative zero).
Analog PAM voltage samples in and out, Pulse
duration 5.18 µs

• Analog, approximately logarithmic compression,
  followed by 8 bit uniform A/D digital coder
• Many D2 through D4 version channel banks work
  like this and are still in use

60
More Recent Digital Coding
Uniform Code in, Mu law out
Uniform Code out
vin
Magnified View shows very fine stair steps
Uniform 13-bit (or more) digital/analog
convertor. 12 bits corresponds to 4096 steps,
14 bits corresponds to 16384.
Table look-up translation from 13-bit uniform
binary code to Mu or A-law, (typically via ROM
memory), followed by parallel-serial conversion.
Example table from p.112 in Bellamy, shows only
positive values, for 13-bit positive input (8192
codes in, values above 8159 produce 01111111.
Note that multiple uniform code values map into
one compressed value.
Analog PAM voltage sample in, duration 5.18 µs
14-bit parallel digital intermediate result.

• Now 13-bit (or more) linear A/D coder, followed
  by table to convert to Mu (or A) law compression
  via straight line chord segment approximation.

61
Line Coding

• Sequence of Events in T-1
• All binary bits are inverted after the Mu-law
  speech coder output.
• See Note 1
• Recall that 11111111 binary never occurs in a
  fully processed Mu-law output stream, due to
  substitution to avoid it
• The binary bits are line coded as 3-level AMI
  (original design).
• This combination of binary inversion and AMI is
  sometimes called pseudo-ternary. See note 1.
• For clear-channel systems, B8ZS or ZBTSI is used
  instead of merely AMI
• Sequence of Events for E-1
• Binary bits at output of A-law encoder are
  treated by even bit inversion. Example
  11111111 becomes 10101010
• See Note 1.
• These binary bits are line coded using HDB3 (e.g.
  see Bellamy p. 178 or other sources)
• Note 1 Subscriber 64/56 kb/s binary data enters
  at point after this inversion or partial
  inversion.

62
Other Line Coding

• Higher rate multiplexers all use various types of
  line coding with intentional BPV substitutions
• Consequently these higher level multiplexing
  systems do not require any additional binary
  processes (bit inversions, ZBTSI, etc.) to
  protect against strings of zeros
• See Bellamy, pp. 176-189 or other sources

63
Multiple-level Line Codes

• In North America, a 4-level 2B1Q (2-Binary
  1-Quaternary) line code is used on the U
  interface of the ISDN Basic Rate Interface (BRI).
  Transmit levels are ?2.5 and ?0.83 volts. A
  sequential coding method is used to prevent
  consecutive same symbol appearance.
• Other codes are used in various European
  countries, where the operating company is
  responsible to change out the NT1 box at the
  customer location if a different line code should
  be used in the future.
• Use of multiple voltage levels makes the line
  coded signal more sensitive to noise voltage,
  but reduces the pulse (symbol or Baud) rate,
  and thus the analog bandwidth.
• One of 4 voltage levels is transmitted during an
  interval corresponding to two binary bits
• Half the symbol rate of binary and pseudo-ternary
  coding.
• For other telecom line codes used in HDSL, etc,
  see W.D.Reeve, Subscriber LoopDigital (IEEE
  Press, 1995)

volts
0.
time ms
64
Other Encoding/Modulation

• In fiber optics, only positive power levels are
  feasible (usually 2 levels off and on)
• Laboratory research on phase sensitive
  (heterodyne) optical detection would permit
  negative optical amplitude (optical sine wave 180
  deg out of phase with a reference wave), but this
  is not in commercial fiber products today.
• In many radio and wire transmission media, a
  carrier frequency (sine wave) signal is used
• The amplitude, phase and/or frequency of this
  carrier signal may be varied (a process called
  modulation) to convey intelligence. Details in
  other lecture.
• Modulation primarily method for radio, microwave,
  and cellular/PCS
• In wire transmission systems, most modems
  (modulator-demodulators) use an audio frequency
  carrier, typically with either frequency
  modulation (FM) for low bit rate modems, and QAM
  (quadrature-amplitude modulation- a combination
  of phase and amplitude) for high bit rate modems.
• Another wire application is the use of multiple
  carrier frequencies (DMT- discrete multi-tone)
  each individually QAM modulated with a portion of
  the total digital information, for ADSL
  (Asymmetrical Digital Subscriber Loop)

65
Digital Transmission Testing

• AMI or ZBTSI line coding supports simple partial
  error detection by examining bi-polar violations
  (BPVs)
• A single isolated missing pulse or a spurious
  pulse will usually produce a BPV (but not
  always!)
• Not all errors can be detected this way (consider
  two consecutive alternate voltage bad pulses, or
  two lost pulses giving zero volts on the wire)
• B8ZS and other zero-substitution codes require a
  test instrument which can distinguish the special
  intentional BPV patterns of these codes from
  errors
• Extended Super Frame (ESF) permits detection (not
  correction) of limited errors at the binary level
• Uses the 6 CRC bits contained in each 24 frames
• Does not require dedicating a payload channel for
  testing
• All error correction/detection codes have such
  limitations severe errors (many, many wrong
  bits) may escape detection

66
Special Bit Patterns

• Special bit patterns are generated by channel
  bank, switching and other multiplexing equipment
  in case of certain error conditions
• Loss of signal (no voltage pulses at all) in the
  opposite direction of that channel or link
• Loss of synchronization in opposite direction or
  from source link which produces this channel (in
  a cross-connect switch or other switch)
• These special bit patterns consist of e.g.
  checkerboard 10101010 (in comparison with
  normal idle channel 11111110) or alternating
  frames of all zeros, all 1s, etc.
• These special patterns have color names Yellow
  alarm, Red alarm, etc., based on color of panel
  alarm lights historically used.

67
Imperfections in Digital Transmission

• Malfunction of any one repeater in the chain
  causes an outage
• When high reliability is a must, parallel
  alternate links are installed, using protective
  switching to the backup link when first link
  fails.
• When connected to a channel circuit switch,
  traffic is automatically assigned only to
  properly functioning channels
• For leased or dedicated lines, protective
  switching and standby parallel links are
  installed
• Protective switch uses electro-mechanical relays,
  or other means, to transfer wires to backup links
• Optical fibers also can be installed with backup
  links
• Burst errors vs. dribbling errors
• Bit errors frequently occur in short time
  duration bursts
• Caused by short duration interference signals
  (e.g. arc welding)
• Dribbling errors are isolated, infrequent
• Carriers often guarantee less than, for example,
  2 errored seconds of operating time per day

68
Jitter, Wander, Clock Inaccuracy

• Instead of perfectly periodic pulses in step with
  a precise 1.544000 MHz clock, pulse unit
  intervals (UIs) may vary
• 1.Significant differences in consecutive (UIs)
• called jitter
• Pulses appear to jump slightly left and right on
  an oscilloscope display
• 2. Only gradually over an interval of tens to
  thousands of UIs
• Called wander, indicates short term Frequency
  errors
• Pulses appear to slowly crowd together and then
  slowly separate on an oscilloscope display
• 3. Only measurable over interval of hours or
  more
• described as inaccurate clock frequency

69
Causes of UI Time Errors

• Accuracy of clock in master end channel bank or
  switch
• Changes in wave speed of electromagnetic wave
• Primarily due to temperature-caused changes in ?,
  (and slightly for changes in ?, r, g) of cable
  and insulation
• Symbols ?, ?, r, g stand for dielectric
  permittivity (of insulation), magnetic
  permeability, specific resistivity (of wire),
  specific conductance (of insulation)
• r changes more with temp (Bellamys book only
  blames r)
• ? has greater direct effect on wave speed, but
  changes less with temperature
• Wire or cable exposed to sun or outdoor
  environment experiences diurnal (daily)
  temperature cycles
• Microwave radio links have changing reflection
  (multipath) geometry
• Ionization layer altitude or atmospheric
  dielectric changes
• Air temperature effects density, e and thus wave
  speed
• Water vapor content (relative humidity) affects
  wave speed

70
BER (Bit Error Rate)

• BER is ratio of erroneous bits to total bits
  occurring in a pre-defined time interval
• BER can be measured or estimated
• Measured when completely pre-determined bit
  stream is transmitted as a test
• Estimated from results of error detection codes,
  BPVs or other secondary manifestations
• When BER of wire telephone line exceeds 10-6 (one
  part per million, or 1ppm), line is usually
  removed from service to diagnose and repair.
• In contrast, digital cellular base-mobile links
  typically operate continuously at a BER of about
  10-2 (1 )
• BER of properly functioning typical wire or
  optical fiber is in range of 10-11 to 10-14 or
  better

71
Clock Accuracy Strata

• The telecom industry recognizes 4 levels
  (strata in Latin) of clock accuracy
• Stratum 1 10-11. Describes primary atomic clocks
  used by various network operators
• Stratum 2 1.610-8. Regional or local switches
  and transmission links
• Stratum 3 4610-6 End office switches.
• Stratum 4 3210-6 Private branch exchanges
  (PBXs) and other end-of-line devices.
• A device such as a switch or multiplexer must be
  synchronized to a source of equal or better
  accuracy than itself, unless used in a totally
  isolated private network.
• Slaving a device to a source of inferior accuracy
  will cause significant problems.

72
Higher Level Multiplexers

• In many regions, traffic between two points is
  greater than the capacity of one primary rate
  digital multiplex link (24 or 30 channels). The
  first approach is obvious install more parallel
  links!
• In late 1960s and 1970s, economic value of higher
  rate digital multiplexers (using a single bit
  stream which combines multiple primary rate
  tributary bit streams) was apparent. Several
  higher levels of multiplexing were designed
• A major technical problem at that time was the
  lack of short term and long term synchronism of