Radio Free Meredith

It's been a busy week for comments over here at Radio Free Meredith, and there have been some exciting discussions going on. I'd like to break yet another comment thread out into a post of its own: heron61 and I got to talking about some freedom-of-speech stuff, which you can go read if you want to, and I'm going to continue that discussion here.

Why? Well, it's been two weeks since we started our discussion of Claude Shannon's "A Mathematical Theory of Communication". However, instead of moving on to Part 2 of that paper, I'm going to talk about the history of telecommunications, from both a technical and an economic standpoint. I'll explain some fundamentals -- many of which were driving forces behind Shannon's research -- and we'll explore the problems of bandwidth scarcity, how they got started, how information theory has helped to address them, and why they're still relevant today. I also have a modest proposal, but that will be a separate post.

I'm going to offer a counter-proposal to heron61's proposal of reintroducing the Fairness Doctrine, but to do so I'm going to need to step back in time and give a sort of technological history of broadcast media and why it works the way it does today. Hopefully enochsmiles will also jump in and put in his $.028 (he gets paid in euros) about the telecom side of things -- he was right there in the thick of it for a lot of what was going on between the big telecom providers in the late '90s and he's got a lot of good domain knowledge.

So. In the beginning, there was radio. (Actually, the telegraph came before radio, as did the telephone, and those will be important in the big picture, but we're talking about how mass media came to be, so we're going to start with radio.) At first, radio was just wireless telegraphy using Morse code, which is still well-loved by hams like me. Every radio signal that conveys something other than a continuous tone has a bandwidth, which is literally how wide a piece of spectrum the signal needs in order to be transmitted and received effectively. Bandwidth is measured in hertz, abbreviated Hz. One Hz is one cycle per second: the wave starts at zero, rises to its peak, falls back down past zero to its trough, then rises back up to zero.

For wireless telegraphy, also known as CW, the bandwidth can be as little as 20 Hz, which is a really narrow slice -- if I'm transmitting that signal using a 28.000000 MHz carrier wave or "transmitting on 28 MHz", with a 20 Hz modulation frequency, if someone else in range is simultaneously transmitting at, say, 28.000010 MHz, also with a 20 Hz modulation frequency, our signals will interfere with each other, but if the other guy moves up to a carrier wave at 28.000040 MHz, we're fine. (Modulating one frequency with another frequency gives you what's called "sidebands" which are the sum and difference of the two signals, so the other guy has to move all the way up to 28.000040 to keep his lower sideband from overlapping with your upper sideband.) With the amount of bandwidth allocated for 10-meter (that is, signals with a wavelength of around 10 meters) narrow CW on the current ITU region 1 amateur bandplan, there's room for 1750 simultaneous 20 Hz signals: that band goes from 28.000 MHz to 28.070 MHz and each transmission would use a carrier wave that is separated from its neighbours by 40 Hz to either side. (I'm oversimplifying this a lot, because there are a bunch of things that come into play when figuring out how wide a CW signal is, but they're not hugely relevant here.)

I didn't explain what CW stands for yet because now I'm going to explain AM radio: the two are interlinked. CW stands for Continuous Wave. It's a carrier signal of constant amplitude and constant frequency, and to use it to communicate, you turn it on and off. Shannon talked about this a little bit in Part 1, Section 1 when he described the signals used in telegraphy: a dot is ON for one unit of time and OFF for one unit of time, a dash is ON for three units of time and OFF for one unit of time, a letter space is OFF for three units of time, and a word space is OFF for six units of time. (Clever readers may be thinking, "Hmm, is this units-of-time stuff important?" Yes, it is. We'll get to that, though it'll be a bit.) Since the signal is of constant frequency and constant amplitude, each dot or dash sounds the same when represented as a human-audible signal, i.e., a sound wave; they're just longer or shorter in duration. (Humans can't hear radio-frequency waves, but we can mathematically -- and electrically! -- map those waves down to a range of frequencies that people can hear.) But a CW signal is really just a special case of an AM, or Amplitude Modulated, signal.

Amplitude modulation just means changing, or modulating, the amplitude (informally, the height of the wave) of that carrier signal in order to produce variations in sound. This was originally invented for the telephone. When you speak into an analog telephone, the sound waves of your voice create pressure on a membrane in the mouthpiece, causing the membrane to vibrate. Those vibrations are mapped to the DC voltage (voltage, as a measurement, is just the amplitude of an electrical current) on the phone line -- the voltage rises and falls in sync with the vibration of the membrane caused by the pressure of the sound waves of your voice. The varying amplitude of your voice modulates the voltage (amplitude!) of the current on the telephone line, and that current travels over wires between you and whoever you're talking to. On the other end, the receiver translates that varying voltage into vibrations of a membrane in the earpiece, and the sound waves from that little buzzing membrane travel down the other person's ear canal to the person's eardrum, where they make the eardrum vibrate, the nervous system translates that vibration into nerve signals which the brain can interpret, and the other person hears what you're saying. Phew!

AM radio works in a very similar fashion, but instead of modulating DC amplitude (voltage!) going over a wire, we modulate the amplitude of a radio signal. The thing is, in order to transmit a voice signal, you need much more bandwidth than you do for CW. Here's why. See, the frequency of the modulation signal determines just how quickly you can raise or lower the amplitude of the carrier signal. A guy named Harry Nyquist proved back in 1928 that a wave of B cycles per second can be used to transmit 2B code elements per second (if anyone's interested, we could read that paper sometime -- for now, just remember you have two sidebands to work with), so with a 20 Hz modulation frequency we actually have 40 code elements per second or 2400 code elements per minute. For somewhat obscure reasons, the word PARIS is used as a baseline for establishing transmission speed. (Like in typing, a "word" is really "five characters".) PARIS in Morse code is [.--. .- .-. .. ...] -- so let's look at how many times we could transmit PARIS in a minute.

By Shannon's reckoning (which is a little different from how hams do it, but let's go with Shannon), a dot takes up 2 time units, a dash takes up 4 time units, the space between two letters takes up 3 time units, and the space between two words takes up 6 time units. So we've got (2+4+4+2+3+2+4+3+2+4+2+3+2+2+3+2+2+2+6) = 54. 2400 code elements per minute divided by 54 code elements per word gives us roughly 44 words per minute. That's the absolute maximum words per minute we can possibly transmit using a 20 Hz modulation frequency -- the maximum capacity of the channel. If we could key Morse faster than that -- like Ted McElroy, who could do over 70 words per minute -- we'd need a higher modulation frequency, which would eat up more bandwidth because the sidebands to either side of the carrier would have to be larger.

But this is just dots and dashes. You have to make the amplitude fluctuate (the technical term for this is sampling, which I'll use from here on out) much more rapidly in order to reproduce audio. CD-quality audio uses a sampling rate of 48 kHz. In AM bandwidth terms, 48 kHz is a huge modulation frequency. Today's FCC regulations limit the AM modulation frequency to 10.2 kHz (before 1989 it was 15 kHz), which is why AM radio doesn't sound anywhere near as good as a CD. And the FCC really hasn't allocated very much of the broadcast spectrum for commercial broadcasting; it never has.

( History break! Also, why we can't have nice things. )

Through all this time, the federal government has not changed the spectrum allocation for AM radio. But what about FM radio? What about television? We'll look at those as well -- but first, let's look at how FM works.

If amplitude modulation means raising or lowering the amplitude of a carrier wave to produce changes in sound, then frequency modulation is raising or lowering the frequency of a carrier wave to produce changes in sound. If you look at the waveform of an audio signal in the time domain (using, say, a program like Audacity), you'll see a sinusoidal wave of varying frequency and varying amplitude. The job of a frequency modulator is to combine this waveform with a sinusoidal carrier wave of fixed frequency and amplitude, to be sent out by a transmitter, and the job of an FM receiver is to tune in the modulated signal (by locking onto the carrier wave), strip out the carrier, and convert the modulating signal back into audio in much the same way that an AM receiver does, i.e., by turning it into a fluctuating voltage (amplitude!).

FM turns out to be much more robust against interference than AM, as you've no doubt noticed if you've ever listened to either of them while driving. If an AM receiver picks up two signals at or near the same carrier frequency, it can't determine which shifts in amplitude correspond to which signals, so it just demodulates everything it picks up at the tuned-in frequency and you end up hearing talk radio and the baseball game garbled together. Since the amplitude of an FM signal is constant, the signal strength is constant as long as you and the transmitter stay in the same place. This makes it easy for an FM receiver to pay attention to only the stronger of two carriers at or near the same frequency (known as the capture effect, so the weaker signal is attenuated (diminished) at the receiver, and only the stronger signal gets demodulated. This is a really nice property to have in a radio -- remember the problems back in the '20s with stations colliding on the air -- but it comes at a cost: FM requires more bandwidth than AM.

Rather than try to shoehorn FM into the 520 kHz-1610 kHz AM band, the FCC originally decided to put it in the VHF (Very High Frequency) part of the spectrum -- originally 42-50 MHz, later 88-106 MHz, and eventually the 87.8-108 MHz that it is today. That's nearly 20 times the allocation available to AM -- and for good reason, since each FM channel is 200 kHz wide, as opposed to the mere 10.2 kHz bandwidth per channel of AM. But that's only 101 channels. It was a lot back in the early days, but the spectrum filled up quickly, and broadcasters rapidly figured out that spectrum real estate was an incredibly valuable resource. So did the FCC. Licenses to operate a radio station are sold at auction, and the process is expensive and complicated. (As a concrete example, 122 licenses across the country are going up for sale this September 9th. The lowest opening bids are $1500 apiece, for stations in Peach Springs, AZ [pop. 600], Oak Grove, LA [pop. 2174], Rocksprings, TX [pop. 1285], San Isidro, TX [pop. 270], and Spur, TX [pop. 1088]. At the high end, $200,000 apiece, we've got stations in Lamont, CA [pop. 13,296] and Murrieta, CA [pop. 44,282]. So this should give you some idea of just how much Clear Channel has had to shell out for its 900-some stations in markets nationwide, both large and small.)

If you've read this far, you may be wondering what happened to all the information theory -- we started out so well, with Shannon and Nyquist and everything! Well, this is what Shannon had to work with back in 1948: analog transmission media over channels that could easily be polluted with crosstalk and environmental interference (i.e., weather). Building on Nyquist's work, he wanted to formally represent the notion of how much information could reliably be transmitted over a channel, with or without noise -- and in order to do that, he first had to characterise what information is.

After Shannon's groundbreaking work, engineers suddenly had the tools to figure out ways to represent information so that it could be transmitted more reliably, e.g., error-correcting codes. Also -- and this is the important part with respect to the FCC -- they had the tools to figure out how to interleave channels over the same carrier, thereby exploiting a single carrier frequency to transport multiple independently tunable channels.

Tune in next post, where we'll talk about the history and future of television, multiplexing, multiple-access protocols, software-defined radio, and some possible futures for the broadcast spectrum -- and the role information theory plays in all of them.

Comments are open -- have at.