# Brother, can you spare a theorem?

A theorem is not, indeed, a fact.  It is rather, an idea which is deduced and supported by other proven facts.  Thus, a theorem is generally believed a truth.  It should be of interest to the “All Digital” AM (AKA Medium Wave) proponents that noise on the digital channel will reduce data throughput as a function of channel bandwidth and Signal to Noise Ratio.  This is known as the Shannon-Hartley theorem:

$C = B \log_2 \left( 1+\frac{S}{N} \right)$

Where:
C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz (passband bandwidth in case of a modulated signal);
S is the average received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watts (or volts squared);
N is the average noise or interference power over the bandwidth, measured in watts (or volts squared); and
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels).

With this equation, one can discern a fundamental flaw in the all digital logic.  One of the main issues with AM Medium Wave broadcasting is the ever increasing noise floor.  Our society has changed drastically in the last one hundred years or so since AM was invented.  Electrical noise generators; computers, plasma screen monitors, mobile phones, appliances, energy efficient lighting, data over power line, street lights, poor utility line maintenance, even electric cars, it seems, generate a cacophony of noise in the Medium Wave frequency band. A digital modulation scheme, be it HD Radio or DRM, will mask the noise to a certain extent, that is true.  However, once the SNR exceeds the ability of the receiver to decode the necessary bits, the receiver will mute.  While it is true, the listener will not hear noise, they may not hear anything at all.

I will also note; none of the current “AM improvement” schemes under consideration by the FCC addresses the noise issue on the AM band.  Without addressing the noise issue, any digital modulation scheme will be a temporary fix at the very best.  The noise floor will continue to rise and after it gets high enough, the all digital modulation will simply not work.

It will be interesting to see the data from the all digital HD Radio testing that is being done in various locations.  That is, if the NAB, et al. does not decide to treat that data like some kind of state secret; they have become reticent of late.  When somebody acts like they have something to hide, it makes me think they have something to hide…

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### 17 comments to Brother, can you spare a theorem?

• Peter

Time to let the AM band go. Time to let go! It’s over people! It doesn’t work anymore!

When a factory worker loses a job to technology people will say “get over it, move on, learn new skills, blah blah blah”. When an industry like AM is threatened people argue how to keep the life support on! How fair!

AM is the telegraph to the telephone. It’s over.

• Dave Dybas

The AM band remains relevant to the Baby Boomers, but their children/grandchildren have little attachment to it. Once the Boomers have all left this earth, then the AM band will become irrelevant. But up to that point in time, I suggest we do whatever is necessary to provide the best transmitted signal and best reception of that signal. The technology exists to improve analog AM reception and provide a quality experience.

• Lorne

I still think the primary ingredient that is missing from all these discussions is that stations need to provide programming that listeners want to tune into. Regardless of any technical issues, if AM radio is used as a dumping ground for programming that no one wants to listen to, it won’t matter what else is done. If the programming is compelling to listen to, then you’re more likely to have listeners. Of course the same goes for FM (or internet, satellite, etc)

• spinetingler

I’m slightly younger than the baby-boomers and I listen to AM every day (two different stations) – sports talk. One of the stations is even simulcast on FM, but for some reason the AM sounds more “right” to me for sports.

• Nick Straka

AM will become the home of religious and/or ethnic programming. Even more than it is now. That is still programming that certain groups will want to hear, and will put up with the technical limitations.

All digital AM is a waste of time. The band can be left to analog only, and those that want a digital channel should get one in a new band. Whether it is VHF Channel 6, slightly above or below the current band doesn’t matter. Owners could replicate their current coverage for a fraction of the cost and hassle. Maintaining multiple tower DA’s is not cheap or easy. Takes a lot of capital and a lot of land to do it right. Contrast that with hanging a couple bays off a tower and renting the space.

Now couple that expense with the further expense of the all-digital equipment that only reaches a portion of the population with “HD” radios and it is a recipe for licenses being turned in.

After all that, the noise and bandwidth are a problem. Trying to do all digital AM is like cramming 5lbs of crap in a 2lb bag that also leaks.

• StvCmty

Why does the medium wave band need to be amplitude modulated? If an all-digital solution is on the table, requiring new receivers for most consumers, then any and all modulations should be looked at.

Could narrow band FM work at 530 to 1700 kHz? Would a switch to narrow band FM provide some distant station rejection thanks to the capture effect?

If every station went single side band (all using the same, nationwide either upper or lower) many of the adjacent channel problems would vanish.

• Paul Thurst

One of our AM clients is broadcasting High School football play-by-play. Guess who is listen to the AM radio? Programming, or rather, bad programming is the larger part of the “decline” of AM radio. If people want to hear something, they will put up with some noise, static, lightning crashes, power line noise, etc.

Medium wave does not necessarily need to be amplitude modulated. My point is, if broadcasters are going to spend hundreds of thousands of dollars on a new system, it should at least work right. Narrow band FM, sure, why not?

• chuck gennaro

” if broadcasters are going to spend hundreds of thousands of dollars on a new system, it should at least work right.”

Can I nominate you to have a talk with whatever governmental genius thought CAP alerts over the internet was a splendid idea?
Internet service goes down faster than the cellphones when the weather gets bad around here. But anyway..
We’ve been assured the death of the newspaper is just around the corner as well….for the last 25 years. Yet they live on with a smaller footprint, as will AM. Dead on about programming being the key issue.

• Bill Frahm

I’ve been tempted to restrict the audio bandwidth on our FM sports station as part of the effort to mimic the “AM” sound. I can’t quite put my finger on what makes up the entire sound tho.

• StvCmty

@Bill
I am not sure if you are being serious or joking, but there is something to what you are saying. I am able to listen to Q1370 on AM or on a FM translator 99.9. For some classic rock songs the FM is clearly better. But some songs sound “right” on the AM signal and they are too harsh on the FM signal; Hotel California for example.

***
Q1370 does it right for an AM station, they have music that appeals to older people but enough of it has been in rock band that younger people can listen to it. They promote their FM signal and AM signal enough that people might find them on FM but go to AM when the translator signal is unusable. Their daytime AM signal is very directional so most of Harford county is poorly covered from nulls in their pattern. Just from where the full power 99.9 FM’s are, the translator does a good job covering Harford county even if only a tiny area is in the translators primary service area.

***
Another example of a decent local AM is kHz TV, a network of AM stations. In Harford County MD I listen to WAMD, 970. They play a song to death. For about 3 weeks, if I wanted to hear All about that bass or Bang Bang, I could tune to 970 AM and have a really good chance of hearing one or the other. kHz TV’s playlist is stuff that went high on the charts, and they are aggressive with squeezing commercials in, a song will fade out early for a commercial to start, then a new song will fade in as the commercial is ending. Their commercials are local and targeted to the area, so at least they are doing that right. The audio quality sucks, but since they play newer songs part of it may be how music is being mixed down. The same programing is on 810, and depending on where I am sometimes 810 comes in clearer depending on where I am, where noise sources are (power lines), and where I am in relation to each stations directional patterns.

***
The only AM stations near me that are authorized to do IBOC are talk and religious. I don’t listen to the religious stations. I don’t think IBOC would benefit talk.

• Bob Roe

1) Get rid of IBOC, drops out on impulse noise or lightning strikes and it’s real good at generating hash noise on either side. Makes distant listening impossible at night thanks to the FCC for allowing IBOC at night. IBOC sounds like crap anyway.

2) Get rid of the NRSC bandwidth adoption, let stations go back to 15KHz and if some adjacents have to go, move them to expanded AM band or LPFM’s, or translators. With only 10KHz, today’s AM audio is mostly lousy. AM C-QUAM stereo kicked ASS!.

3) Make radio manufacturers design products that can utilize the wider AM audio, better sensitivity and selectivity. They are a big reason for AM’s destruction, cut corners on the AM side and today’s radios suck.

AM radio used to sound so good 20 years ago, always remember listening to Monday Night Football and it sounded so good, it was like you were at the game. With the right processing AM sounds fantastic. The FM station that carries the local football sounds so god awful, whoever setup the processing must be deaf!.

AM radio can be saved and it should be!.

• Rob

Brother, can you spare some numbers? Wait, got some right here: WGSO 990 AM New Orleans, 1000 Watts, received approximately 50 miles away. Total measured signal strength was varied from S7-S8 on my Yaesu FT-450D, while noise on adjacent empty frequencies was in the S3-S4 range. This is about at the level of “comfortably listenable.” Yes a DX enthusiast can pick out far weaker signals, but this is more of a S/N level that most people will find acceptable, and frankly even this sounds pretty rough.

Take the difference of the lower signal level and the higher noise level, i.e. the worst case, is dS = 3. Convert to dB, assuming 1 S-unit = 6 dB (I know, I know… just go with me here): S/N = 18 dB, or a factor of 63. Assume we’re still going with 10 kHz channel widths, and stick a 1 kHz guard band on either side, so now we’re down to 8 kHz for B. Plug it all into the Shannon-Hartley theorem and we get C = 8 * log2(1 + 63) = 48 kHz. That is enough for a very good mono signal.

OK, so let’s chop it down even more: S/N = 3 dB, which is about anybody’s rock-bottom for listenability. Even that gives a 12.7 kHz channel bandwidth, which is PLENTY for talk or sports radio content.

For comparison, here’s a link to a DRM demo page: http://www.drm.org/?page_id=25 On the bottom right of the map, there’s a music clip at 16 kbps. According to the S-H theorem, this requires only a 4.8 dB S/N. Not exactly CD quality, but far, far better than anything heard on AM radio today. Listen to its AM counterpart. Pretty bad, eh?

All-digital is not only feasible, it is on the way. US broadcasters and regulators just haven’t woken up to this yet. Now if we can push these hybrid schemes overboard and get serious about adopting a full-digital standard, we’ll be getting somewhere.

• Paul Thurst

Rob, You are correct, 48 kpbs will produce pretty good audio, depending on the CODEC being used. BTW, AM HD Radio has a data rate of either 40 or 60 kbps. I understand your point of view, but there are a few things to correct:

First of all, you are using a high quality stationary receiver. I very much doubt the average AM listener has or will have a receiver that matches the quality of a Yaesu FT-450D. Part of the issue with analog AM is the poor quality of the receivers.

Secondly, in a mobile listening environment, an 18 dB signal to noise ratio is not a realistic goal, especially in city environments. You will have to acknowledge that most radio listening these days is done in an automobile. In city environments, the defacto listenable coverage area is within the 2.5 mV/m contour. Areas outside of this contour are often okay, but overpasses, steal truss bridges, power lines, street lights and other electrical noise will be present from time to time.

Thirdly, As it is currently configured, AM HD Radio at 60 kbps requires approximately 9 dB SNR, at 40 kbps, 6 dB SNR.

Forth, in my opinion, 12.7 kbps audio will not sound very good at all. I have tried to listen to a few web streams running at 22.5 kbps and ended up with a headache.

Fifth, you seem to be implying some type of adaptive data rate being used, lower data rates with higher noise levels. With DRM and HD Radio, the data rate is fixed and much faster than 12.7 kbps, thus when the receiver moves into an area of high noise and high BER, it will mute. The data rate does not slow down for those in high noise areas.

I know there are several people out there that are chomping at the bit to convert the AM band to all digital HD Radio. Based on past performance, it seems to be an expensive boondoggle designed to make one company wealthy.

• Bob Roe

I don’t need numbers!. The only numbers are my EARS. A station here operates IBOC all night and blows away an adjacent station 45 miles away. When it happens to be off for whatever reason, no problems hear 830KHz and 840KHz just fine. I don’t care what anyone says, properly processed, wide band bandwidth AM is superior, even to an all digital only broadcast. The analog signal will hold up during a decent electrical storm, enough to copy what is being broadcast. So when there is a tornado coming down my street and the lightning crashes cause the digital signal to dropout, mind as well ask Siri on my IPHONE, assuming the cell network is up where it is.

• Rob

Paul, I think that we’re largely in agreement, with a few minor things around the edges.

I used my 450D because it was the best S-meter I had at hand. Usually I listen to this station on my two year old Ford’s stock, base model radio. It does a surprisingly good job, almost on par with the Yaesu base. Impressive radios they’re putting into cars these days, especially when few buyers actually care.

Yeah, 18 dB is a pretty clean signal. Even so, current AM sounds a little rough there, and as you point out, there’ll be a lot of bad spots in city driving. Still, that 16 kbps DRM demo clip, which would only require a 5 dB S/N level, was very listenable. The math supports this data rate, and it does sound better than most current AM.

No, I’m not expecting any kind of adaptive data rate, just batting around numbers. For talk and sports radio, it wouldn’t take much.

It is unfortunate that the US seems wedded to iBiquity’s IBOC standard, because hybrid broadcast AM was a turkey from the get-go, and as you pointed out, seems more designed to deliver money to a sweetheart company than to actually deliver listenable signal to radios. My guess is that we’ll all be stuck on this particular dime until AM band usage completely crashes, at which point who knows what’ll happen. An open standard seems like the way to go here. How open of a standard is DRM? Maybe we’ll get there in 20 years, once things crash out and IBOC is as forgotten as Beta video tapes. Anyway, I still hold out hope for a digital standard, eventually, but only after the US has tried everything else.

• Jim Seaman

@StvCmty

Early experiments indicated that very little capture effect is evident with narrow-band FM signals. NBFM is not just a narrow bandwidth version of FM broadcast, it is best suited for two-way radio. The high-fidelity found in FM broadcasting would not be possible. Also forget about stereo and subcarriers. If any alternative to AM voice were to be used on MW, it would have to be some digital mode.

While not quite the same thing, but interesting nonetheless, the Voice of America has been experimenting with digital on HF by transmitting their “Radiograms” using MFSK which is a mode generally used in ham radio. They transmit digital news and still images at the end of a program, and encourage listeners to decode it using the fldigi software app. I believe they have also used some slow-scan TV or Fax.

• Kari K.

http://swradiogram.net/ today – not via VOA anymore

### Axiom

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