6.12 Signal-to-Noise Ratio of an Amplitude-Modulated Signal

202 CHAPTER 6. INFORMATION COMMUNICATION

Known familiarly as the speed of light, it sets an upper limit on how fast signals can propagate from one place to another. Because signals travel at a finite speed, a receiver senses a transmitted signal only after a time delay inversely related to the propagation speed:

∆t =

d c At the speed of light, a signal travels across the United States in 16 ms, a reasonably small time delay. If a lossless (zero space constant) coaxial cable connected the East and West coasts, this delay would be two to three times longer because of the slower propagation speed.

6.5 Line-of-Sight Transmission6

Long-distance transmission over either kind of channel encounters attenuation problems. Losses in wireline channels can be compensated by repeaters can extend the distance between transmitter and receiver beyond what passive losses the wireline channel imposes. In wireless channels, not only does radiation loss occur (p. 201), but also one antenna may not “see” another because of the earth’s curvature.

dLOS

earth h}

R

Figure 6.3: Two antennae are shown each having the same height. Line-of-sight transmission means the transmitting and receiving antennae can “see” each other as shown. The maximum distance at which they can see each other, dLOS, occurs when the sighting line just grazes the earth’s surface.

At the usual radio frequencies, propagating electromagnetic energy does not follow the earth’s surface. Line-of-sight communication has the transmitter and receiver antennas in visual contact with each other. Assuming both antennas have height h above the earth’s surface, maximum line-of-sight distance is

dLOS = 2 2hR + h2 ≈ 2√2Rh (6.19)

where R is the earth’s radius ( 6.38 × 106m).

Exercise 6.4 (Solution on p. 255.)

Derive the expression of line-of-sight distance using only the Pythagorean Theorem. Generalize it to the case where the antennas have different heights (as is the case with commercial radio and cellular telephone). What is the range of cellular telephone where the handset antenna has essentially zero height?

Exercise 6.5 (Solution on p. 255.)

Can you imagine a situation wherein global wireless communication is possible with only one transmitting antenna? In particular, what happens to wavelength when carrier frequency decreases? Using a 100 m antenna would provide line-of-sight transmission over a distance of 71.4 km. Using such very tall antennas would provide wireless communication within a town or between closely spaced population

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