Comp 346/488: Intro to Telecommunications

Tuesdays 4:15-6:45, Lewis Towers 412

Class 5, Feb 14

Reading (7th -- 9th editions)
10.1, 10.2, 10.3

Read:
Chapter 5:
    §5.1: digital data / digital signal: b8zs, 4b/5b
    §5.2: digital data/analog signal: ASK, FSK, MFSK
    §5.3: analog data / digital signal: digitized voice, PCM, µ-law
    §5.4: analog data / analog signal: AM/FM modulation

4.2: Antennas

mostly we will skip this.

Satellite note: I used to have satellite internet.
My transmitter was 2 watts. This reached 23,000 miles.

Problem with satellite phone (and internet) links: delay

Frequencies: < 1.0 gHz: noisy
> 10  gHz: atmospheric attenuation
Wi-fi uses the so-called "ISM" band, at around 2.4 gHz

4.3: propagation
High-frequency is line-of-sight, but low frequency (<= ~ 1 mHz) bends
In between is "sky-wave" or ionospheric skip (2-30mHz)

Once upon a time, AT&T had chains of microwave towers, ~50 miles apart. They would relay phone calls. They're obsolete now, replaced by fiber. The old tower in the picture below is the original phone microwave-relay tower; the newer steel tower arrived much later. The single-story base building is huge; it was built to house vacuum-tube electronics and early transistor technology. Nowadays the electronics fit within the base of each antenna.

old ATT microwave-relay tower

Suppose you could have 100 mHz of band width (eg 2.5-2.6 gHz). At 4 kHz per call, that works out to 25,000 calls. That many calls, at 64kbps each, requires a 1.6-gbit fiber line. In the SONET hierarchy, that just below OC-36/STS-36/STM-12. Single fiber lines of up to STM-1024 (160 Gbps; almost 100 times the bandwidth) are standard, and are usually installed in multiples.

Is it cheaper to bury 50 miles of cable, or build one tower?

4.4: line-of-sight:

Attenuation, inverse-square v exponential

water vapor: peak attenuation at 22gHz (a 2.4gHz microwave is not "tuned" to water)
rain: scattering
oxygen: peak absorption at 60 gHz

cell phones: 824-849mhz
pcs: 1.9ghz

It's not clearly spelled out in one place in chapter 4, but be aware that wire attenuation is exponential, while wireless attenuation is proportional to the square of the distance, meaning that in the long run wire attenuation becomes much more significant than wireless. See the beginning of 4.4 for the wireless-attenuation issue ("free space loss").

chapter 5: encoding techniques

5.1  digital data/digital signal

data rate v modulation rate
(ethernet: data rate 10Mbps, modulation rate 20Mbaud)
phone modems: data rate 56kbps, modulation rate 7kbaud

RZ, NRZ

    issues:
        clocking
        analog band width: avoid needing waveforms that are *too* square
        DC component (long distances don't like this)
        noise
       
             
NRZ flavors
inversion (NRZ-I) v levels (NRZ-L)
differential coding (inversion) may be easier to detect than comparison to reference level
Also, NRZ-I guarantees that long runs of 1's are self-clocked
Problems:
DC component: non-issue with short (LAN) lines, huge issue with long lines
losing count / clocking (note that NRZ-I avoids this for 1's)

Requirements:
bipolar (bipolar-AMI): 1's are alternating +/-; 0's are 0
    Fixes DC problem! Still 0-clocking problem
   
Note that bipolar involves three levels: 0, -1, and +1.

biphase: (bi = signal + clock)
Example: Manchester (10mbps ethernet)
    10mbps bit rate
    20mbps baud rate (modulation rate)

bipolar-8-zeros (B8ZS)

This is what is used on most North American T1 lines (I'm not sure about T3, but probably there too)

1-bits are still alternating +/-; 0-bits are 0 mostly.
If a bytes is 0, that is, all the bits are 0s (0000 0000), we replace it with 000A B0BA, where A = sign of previous pulse and B=-A.
This sequence has two code violations. The receiver detects these code violations & replaces the byte with 0x00.
Note the lack of a DC component

Example: decoding a signal

Bipolar-HDB3: 4-bit version of B8ZS


4b/5b

4-bit data
 5-bit code
0000  
11110
0001  
01001
0010  
10100
0011  
10101
...
1100  
11010
1101  
11011
1110  
11100
1111  
11101
IDLE  
11111
DEAD  
00000
HALT  
00100
        
        
4b/5b involves binary levels, unlike bipolar. It does entail a 20% reduction in the data rate.

It is used in 100-mbit Ethernet (and maybe gigabit Ethernet?)



Fig 5.3 (8th, 9th edition): spectral density of encodings

Lowest to highest:
  1. biphase (Manchester, etc)
  2. AMI,
  3. B8ZS
Latter is narrower because it guarantees more transitions
=> more consistent frequency

Fig 5.4: theoretical bit error rate
biphase is 3 dB better than AMI: not sure why. This means that, for the same bit error rate, biphase can use half the power per bit.



5.2:  digital data/analog signal: deferred to below

5.3:  analog data/digital signal

sampling theorem: need to sample at twice the max frequency, but not more
basic idea of PCM
sampling v quantization
nonlinear encoding versus "companding" (compression/expansion)
   
µ-law (mu-law) encoding (used in the US)
   
    µ = 255

If x is the signal level, on a 0≤x≤1 scale, then F(x) is what we actually transmit. More precisely, we transmit 128*F(x), rounded off to the nearest 8-bit integer.
   
    F(x) = sgn(x)*log(1+µ*|x|) / log(1+µ), -1<=x<=1
    -1<=F(x)<=1
   
    F(1)=1, F(-1)=-1, F(0)=0
    F(0.5)= .876,      × 128 = 112
    F(0.1)= .591       × 128 = 76
    F(0.01)= .228     × 128 = 29
    F(0.001)= .041   × 128 =  5

These last values mean that faint signals (eg, x = 0.001) still get transmitted with reasonable amplitude. Otherwise, a signal level of 0.01 (relative to the maximum) would encode as 1 (0.01 × 128 = 1.28 ≃ 1), and anything fainter would round off to 0.

Demo of what happens if you play a µ-law-encoded file without the necessary expansion: faint signals (including hiss and static) get greatly amplified.

A-law encoding: slightly different formula, used in Europe.

delta modulation: I have no idea if this is actually used. It has a bias against higher frequencies, which is ok for voice but not data
advantage: one bit!

Performance:
voice starts out as a 4kHz band width.
7-bit sampling at 8kHz gets 56kbps, needs 28kHz analog band width (by Nyquist)
(Well, that assumes binary encoding....)
BUT: we get
voice: often analog=>digital, then encoded as analog signal!

5.4:  analog data/analog signal

Why modulate at all?
        FDM (Frequency-Division Multiplexing)
        higher transmission frequency
simplest is AM.
band width is worth noting
new frequencies at carrier +/- signal are generated because of nonlinear interaction (the modulation process itself).

SSB: slightly more complex to generate and receive, but:
Sound files: beats.wav v modulate.wav
Latter has nonlinearities

(1+sin(sx)) sin(fx)  = sin(fx) + sin(sx)sin(fx)
        = sin(fx) + 0.5 cos((f-s))x) - 0.5 cos((f+s)x)

reconsider "intermodulation noise". This is nonlinear interactions between signals, which is exactly what modulation here is all about.