Artificial radio signals

In current technology radio signals are essentially always based on carriers of the form Sin[ω t] with frequencies ω/(2 π). When radio was first developed around 1900 information was normally encoded using amplitude modulation (AM) s[t] Sin[ω t]. In the 1940s it also became popular to use frequency modulation (FM) Sin[(1 + s[t]) ω t], and in the 1970s pulse code modulation (PCM) (pulse trains for IntegerDigits[s[t], 2]). All such methods yield signals that remain roughly in the range of frequencies {ω - δ, ω + δ} where δ is the data rate in s[t]. But in the late 1990s—particularly for the new generation of cellular telephones—it began to be common to use spread spectrum CDMA methods, in which many signals with the same carrier frequency are combined. Each is roughly of the form BitXor[u[t], s[t]] Sin[ω t], where u[t] is a pseudonoise (PN) sequence generated by a linear feedback shift register (LFSR) (see page 1084); the idea is that by using a different PN sequence for each signal the corresponding s[t] can be recovered even if thousands are superimposed.

The radio spectrum from about 9 kHz to 300 GHz is divided by national and international legislation into about 460 bands designated for different purposes. And except when spread spectrum methods are used, most bands are then divided into between a few and a few thousand channels in which signals with identical structures but different frequencies are sent.

If one steps through frequencies with an AM radio scanner, one sometimes hears intelligible speech—from radio or TV broadcasts, or two-way radio communication. But in many frequency bands one hears instead either very regular or seemingly quite random signals. (A few bands allocated for example to distress signals or radio astronomy are normally quiet.) The regular signals come from such sources as navigation beacons, time standards, identification transponders and radars. Most have characteristic almost perfectly repetitive forms (radar pulses, for example, typically have the chirped form Sin[(1 + α t) ω t])—and some sound uncannily like pulsars. When there are seemingly random signals some arise say from transmission of analog video (though this typically has very rigid overall structure associated with successive lines and frames), but most are now associated with digital data. And when CDMA methods are used there can be spreading over a significant range of frequencies—with regularities being recognizable only if one knows or can cryptanalyze LFSR sequences.

In general to send many signals together one just needs to associate each with a function f[i, t] orthogonal to all other functions f[j, t] (see page 1072). Current electronics (with analog elements such as phase-locked loops) make it easy to handle functions Sin[ω t], but other functions can yield better data density and perhaps better signal propagation. And as faster digital electronics makes it easier to implement these it seems likely that it will become less and less common to have simple carriers with definite frequencies.

In addition, there is a continuing trend towards greater spatial localization of signals—whether by using phased arrays or by explicitly using technologies like fiber optics.

At present, the most intense overall artificial radio emission from the Earth is probably the 50 or 60 Hz hum from power lines. The most intense directed signals are probably from radars (such as those used for ballistic missile detection) that operate at a few hundred megahertz and put megawatts of power into narrow beams. (Some such systems are however being replaced by lower-power phased array systems.)