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OCR for page 348
Once digitized, a signal can be communicated 100 meters or internationally, typically web no
additional degradation as long as Me signal on each intermediate link is maintained above
threshold. For example, We current predominantly aB digital public telephone network permits
local, national, and international cans usually of equal quality while the old analog network often
degraded badly on national and international calls. Similarly, Me evolving commercial digital
television win provide exceptional quality TV to most of Me public; however, viewers on the
fringe of the signal coverage area may no longer get a chewable picture (without cable or over
source) because the weaker RF signal win create a badly detenoratM (unusable) video signal
when below Ashore. Fringe area viewers of cunTent analog TV simply get a noisy, snowy
picture. ITS will undoubtedly evolve to digital TV to permit sharing of high quality full motion
video images among jurisdictions regardless of location.
Our focus win be on digital communication networks as this is He modern trend Cat industry is
increasingly evolving toward. Digital networks are support by He most cost-effective
components, equipment, systems, and services. Additionally, designers for digital
communication are more readily available.
A.2.2 Theoretical and "In Practice" Capacity of Digital Communication
Mediums
In 194S, C. E. Shannon published a seminal paper on "A Mathematical Theory of
Communication" In He Bell System Technical journal. It established the ~eoredcal bit rate of a
digital communication channel. It also established a relationship between:
BR = BW*Iog2 ~ ~ + STIR );
where (eq. A.2.2-~)
I. BR is He ~eoredcal maximum digital bit rate possible on a communication channel.
2. BW is He available communication channel band in Hertz.
c:`NCHR~\ NCHRP3-51 · Pnase2F'nalReport
A2 -
OCR for page 349
3. SNR is Me signal-to-noise ratio of We desired source digital signal to corrupting "white" noise
("white noise" for statistical analysis is uncorrelated gaussian samples).
4. Note: SNR = lO^(SNRDJ1O) as most SNR are specified in dB.
[Also note Me inverse: SNRDB = JO*IOgIO (SNR)~[Note: X^Y = XY]
The proof of this relationship is based on very sophisticated mathematics and is beyond Me
scope of this work. It should be noted Mat Shannon, in his derivation of this limit, used very
clever statistical and mathematical techniques Hat did not require him to develop the actual
techniques to achieve He predicted limidng performance. Thus, communication practitioners
continually strive in R&D for the theoretical performance limim for various mediums. They have
yet to achieve Hem in practice; however, it is He measure by which communications engineers
judge He efficiency of utilization of Heir con~mun~cadon channels.
As an example, a 25 kHz Bandwidth (BOO) RF channel at 10 and 15 dB SNR, can support bit
rates of:
BR = 25 kHz * logic ~ ~ + 10~5~°~/ log~0~2) = 125.7 kbps
Typical RF Channels
BR = 25 kHz * logic ~ ~ + 10~°~°~/ log~0~2) = 25.0 kbps
In practice, bit rates of 4.8 to 19.2 kbps are being obtained over 25 kHz radio channels. RF bit
rates in practice are usually substantially less Han Be theoretical limits due primarily to
extensive portable transceivers dial cannot employ specially efficient modulation techniques due
to battery drain requirements, small equipment size and weight requirements, and cost
constraints. Fixed RF transceivers without these constraints can be more speck y efficient and
therefore more closely approach these theoretical limits. In fact, microwave radio does employ
specmally efficient modulation techniques.
Similarly, an SMFO fiber typically has a bandy ink over 10 GHz and a SNR of over 40 DB and
can support a BR over:
BR= 10 GHz * logic ~ ~ + 104°~°~/log~0~2) = 132.9 Gbps
L:wa~P ~NCHRP3-51 · Phase2FmalReport
A2-5
OCR for page 350
In practice, He current long distance fiber network is 2.488 Gbps (OC48) and is evolving to 10
GHz (OC-192). The limiting factors in SMFO are the electronics and optical components with
speed to support the potential of the optical channel. In realibr, the available bandwidth and bit
rate of fiber is adequate without near tenn concern for efficiency.
The modem industry appears to have most closely approached He attainable limits predicted by
Shannon's theory, thus it is instructive to review modem performances achieved in practice and
to note that the recent ITU V.34, 28.8 kbps starboard, over a 3500 Hz public circuit, is operating
close to the limit. Figure A.2~2-1 plots bandwidth required versus required signal-to-noise
(SNR) for popular modem bit rates. Also, depicted on He graph is He actual range of operation
in practice for He following modems:
1. Bell 202 (Model 400), 1200 bps modem (1970 origins)
2. ITU V.32' 9600 bps modem (1984 origins)
3. ITU V.34, 28,800 bps modem (1994 ongins)
The range of operation must be above and to the right of the appropriate bit rate curve. As can be
observed, the modem industry, through extensive R&D activities, has improved (or moved) the
range of operation closer to the theoretical bit rate limit for bandwidth and SNR. The V.34 will,
in fact, only work over higher quality dial-up circuits and must fall back to lower speeds on lower
quality circuits (e.g., bandwidth constraints or inadequate SNR). Shannon's theory predicts this
requirement.
Table A.2.~! presents a matrix of popular ITS comn~un~cation mediums and He ~eoredcal
maximum bit rate. It should be noted Hat fiber does not achieve comparable spectral efficiency
In terms of bits/Hertz Hat is achieved with wireline modems. With the exception of microwave,
wireless is also usually less specify efficient
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A2-6
OCR for page 351
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Representative terms from entire chapter:
bit rates
