Phorgy Phynance

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60 GHz Wireless – A Reality Check

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The wireless revolution has been fascinating to watch. Radio (and micro) waves are transforming the way we live our lives. However, I’m increasingly seeing indications the hype may be getting ahead of itself and we’re beginning to have inflated expectations (c/o the hype cycle) about wireless broadband. In this post, I’d like to revisit some of my prior posts on the subject in light of something that has recently come to my attention: 60 GHz wireless.

Wavelength Matters

As I outlined in Physics of Wireless Broadband, the most important property that determines the propagation characteristics of radio (and micro) waves is its wavelength. Technical news and marketing materials about wireless broadband refer to frequency, but there is a simple translation to wavelength (in cm) given by:

\begin{aligned} \lambda(cm) = \frac{30}{f(GHz)}. \end{aligned}

Ages ago when I generated those SAR images, cell phones operated at 900 MHz (0.9 GHz) corresponding to a wavelength of about 33 cm. More recent 3G and 4G wireless devices operate at higher carrier frequencies up to 2.5 GHz corresponding to a shorter wavelength of 12 cm. Earlier this month, the FCC announced plans to release bandwidth at 5 GHz (6 cm).

This frequency creep is partially due to the issues related to the ultimate wireless bandwidth speed limit I outlined, but is also driven by a slight misconception that can be found on Wikipedia:

A key characteristic of bandwidth is that a band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum.

Although this is true from a pure information theoretic perspective, when it comes to wireless broadband, the transmission of information is not determined by Shannon alone. One must also consider Maxwell and there are far fewer people in the world that understand the latter than the former.

The propagation characteristics of 2G radio waves at 900 MHz (33 cm) are already quite different than 3G/4G microwaves at 2.5 GHz (12 cm) not to mention the newly announced 5 GHz (6 cm). That is why I was more than a little surprised to learn that organizations are seriously promoting 60 GHz WiFi. Plugging 60 GHz into our formula gives a wavelength of just 5 mm. This is important for three reasons: 1) Directionality and 2) Penetration, and 3) Diffraction.


As I mentioned in Physics of Wireless Broadband, in order for an antenna to broadcast fairly uniformly in all directions, the antenna length should not be much more than half the carrier wavelength. At 60 GHz, this means the antenna should not be much larger than 2.5 mm. This is not feasible due to the small amount of energy transmitted/received by such a tiny antenna.

Consequently, the antenna would end up being very directional, i.e. it will have preferred directions for transmission/reception, and you’ll need to aim your wireless device toward the router. With the possible exception of being in an empty anechoic chamber, the idea that you’ll be able to carry around a wireless device operating at 60 GHz and maintain a good connection is wishful thinking to say the least.


If directionality weren’t an issue, the transmission characteristics of 60 GHz microwaves alone should dampen any hopes for gigabit wireless at this frequency. Although the physics of transmission is complicated, as a general rule of thumb, the depth at which electromagnetic waves penetrate material is related to wavelength. Early 2G (33 cm) and more recent 3G/4G (12 cm) do a decent job of penetrating walls and doors, etc.

At 60 GHz (5 mm), the signal would be severely challenged to penetrate a paperback novel much less chairs, tables, or cubical walls. As a result, to receive full signal strength, 60 GHz wireless requires direct unobstructed line of sight between the device and router.

Photon Torpedoes vs. Molasses

The more interesting aspects of wireless signal propagation are diffraction and reflection, both of which can be understood via Huygen’s beautiful principle and both of which depend on wavelength. Wireless signals do a reasonably good job of oozing around obstacles if the wavelength is long compared to the size of the obstacle, i.e. at low frequencies. Wireless signal propagation is much better at lower frequencies because the signal can penetrate walls and doors and for those obstacles that cannot be penetrated, you still might receive a signal because the signal can ooze around corners.

As the frequency of the signal increases, the wave stops behaving like molasses oozing around and through obstacles, and begins acting more like photon torpedoes bouncing around the room like particles and shadowing begins to occur. At 60 GHz, shadowing would be severe and communication would depend on direct line of sight or indirect line of sight via reflections. However, it is important to keep in mind that each time the signal bounces off an obstacle, the strength is significantly weakened.

What Does it all Mean?

The idea that we can increase wireless broadband speeds simply by increasing the available bandwidth indefinitely is flawed because you must also consider the propagation characteristics of the carrier frequency. There is only a finite amount of spectrum available that has reasonable directionality, penetration, and diffraction characteristics. This unavoidable inherent physical limitation will lead us eventually to the ultimate wireless broadband speed limit. There is no amount of engineering that can defeat Heisenberg.

There are ways to obtain high bandwidth wireless signals, but you must sacrifice directionality. The extreme would be direct line of sight laser beam communications. Two routers can certainly communicate at gigabit speeds and beyond if they are connected by laser beams. Of course, there can be no obstacles between the routers or the signal will be lost. I can almost imagine a future-esque Star Wars-like communication system where individual mobile devices are, in fact, tracked with laser beams, but I don’t see that ever becoming a practical reality.

We still have some time before we reach this ultimate wireless broadband limit, but to not begin preparing for it now is irresponsible. The only future-proof technology is fiber optics. Communities should avoid the temptation to fore go fiber plans in favor of wireless because those who do so will soon bump into this wireless broadband limit and need to roll out fiber anyway.


Written by Eric

January 21, 2013 at 9:15 am

WSJ: “Culprit in Wi-Fi Failures: Chicken Wire”

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On Thursday, the Wall Street Journal published an article

Culprit in Wi-Fi Failures: Chicken Wire

that is consistent with the theme I’ve been talking about lately. This is a perfect example of what I outlined in

The Ultimate Wireless Broadband Speed Limit

where I wrote:

Now consider two people trying to communicate via radio waves, but they are separated by a wall of metal. No dice. The radio waves cannot penetrate. Now, puncture a small hole in the wall. To be concrete, lets say we are communicating at a frequency of 3 GHz with a corresponding wavelength of 10 cm. If the hole is 1 cm in diameter, it is difficult for the radio signal to “ooze” through that tiny hole. Remember, the “size” of anything as far as a radio wave is concerned is only as a ratio of its wavelength. In this case, the hole is .1\lambda.

The ability of a wave to ooze through the hole depends on the size of the hole relative to its wavelength. Roughly speaking, when the size of the hole is greater than .5\lambda it has a much easier time oozing through it.

This example is actually pretty close to the situation described in the Wall Street Journal article. Wi-Fi operates at a frequency of roughly 2.5 GHz with a wavelength of roughly 13 cm. I’m guessing the holes in chicken wire are probably close to 3 cm in diameter or roughly .25\lambda. Since the hole is smaller than .5\lambda, the Wi-Fi signal cannot easily penetrate the chicken wire.

The photo in the Wall Street Journal illustrates another point I was trying to make. Although the 2.5 GHz Wi-Fi signal cannot penetrate the chicken wire, the MUCH higher frequency visible light does easily penetrate it, i.e. you can see through the chicken wire. The physics here is similar to why AM radio signals in underground parking lots are much worse than FM radio signals. The radio can see the FM radio signals, but the lower frequency AM radio signals get blocked.

Written by Eric

January 3, 2010 at 12:26 pm

Posted in Broadband

The Ultimate Wireless Broadband Speed Limit

with 7 comments

This is a follow-up to my previous posts

as well as some of the comments those posts generated.

First of all, I was pleased that loganb (Comment on 12/29, 9:27 PM EST) brought Shannon into the picture because information theory is important. As Rod pointed out, “information is physical” so the limits of wireless broadband communications will involve a knowledge of both Maxwell and Shannon. In fact, if any grad student out there was interested in both information theory and wireless communications, it would be a fun project to try to determine this ultimate wireless broadband speed limit.

The Problem

If two computers were to communicate via laser beam and they had direct line of sight access, the speeds at which those two computers could communicate over the airwaves should approach those possible via fiber optics.

Of course that is not what one means by wireless broadband. We do not think of a PC communicating to a tower via laser beam with direct line of sight. So this is not the “ultimate speed limit” I’m talking about.

Instead, we want to think of a region of space containing multiple wireless broadband devices. What is the maximum “density of information” available in the air within this region. For concreteness, we could consider

\text{1 unit} = 10 m\times 10 m\times 10 m


\text{1 test region} = \text{10 units}\times\text{10 units}\times\text{10 units}

What is the ultimate physical maximum number of bits that can be communicated via wireless broadband devices within one test region?

My Guestimate

My “guestimate” is that in a test region the ultimate wireless broadband speed limit, i.e. the maximum number of bits that can be communicated via wireless broadband devices is 1,000 Mbps. This is the total number of bits available to everyone within the test region. To get the speed available to any one wireless broadband user, we simply take this speed limit and divide by the number of users simultaneously downloading (or uploading) content.

For example, if my guestimate is correct and there were 100 people simultaneously using their wireless broadband devices, then with a perfectly design wireless network (*cough*) each person would have access to speeds of 10 Mbps. This is still pretty high and most in the US would drool for these speeds (although people in Korea, Japan, and parts of Europe would yawn).

I don’t ever expect routine wireless broadband access in excess of 10 Mbps in crowded tech savvy cities and even this speed assumes perfect network design. It will take a while for us to reach this ultimate speed limit as determined by fundamental physics, but we will eventually. With bandwidth demands doubling every couple of years, it is easy to imagine running into this speed limit within 5 years.

A Note on Radio Wave Oozing

Here is a comment from Zathras:

“The behavior of a wave depends on its frequency. At low frequencies, radio waves are kind of like molasses. They can ooze around corners and through buildings.

As frequencies increase, the waves start acting more like laser beams.”

This is absolute nonsense. For starters, go into a parking garage and compare your AM radio reception to your FM. The AM won’t come in, despite being lower frequency than the FM. There is no “molasses effect” here. Yes, I realize that these are lower frequencies than the cell phone ones, but since the above quote is stated in such absolute terms, it is still an effective counterexample.

The reasons for the interference are more complex. It has to do with the interference with vibrational frequencies that the molecules in the barriers have. The multi-GHz range is full of resonant frequencies for molecules. It also has to do with the fact that higher frequencies attenuate more in conducting metals than lower frequencies do. It certainly has nothing to do with any laser beam/molasses nonsense.

The actual physics of radio waves is more complex than can be communicated in a few paragraphs.  However, the “oozing” analogy does take you some distance in understanding what is going on. Unlike molasses, radio waves can ooze through some materials such as glass, dry wall, wood, etc. One material that radio waves cannot penetrate is metal. In fact, the better the material is at conducting electricity, the worse radio waves are at penetrating it. For example, the earth is fairly good at conducting electricity so it is difficult to send radio waves through the earth.

Now consider two people trying to communicate via radio waves, but they are separated by a wall of metal. No dice. The radio waves cannot penetrate. Now, puncture a small hole in the wall. To be concrete, lets say we are communicating at a frequency of 3 GHz with a corresponding wavelength of 10 cm. If the hole is 1 cm in diameter, it is difficult for the radio signal to “ooze” through that tiny hole. Remember, the “size” of anything as far as a radio wave is concerned is only as a ratio of its wavelength. In this case, the hole is .1 \lambda.

The ability of a wave to ooze through the hole depends on the size of the hole relative to its wavelength. Roughly speaking, when the size of the hole is greater than .5\lambda it has a much easier time oozing through it.

Keep in mind that most buildings have some kind of metal exterior and especially underground parking lots are surrounded by rebar, etc.

Now, an AM radio wave is roughly 1,000 kHz (or .001 GHz) with a corresponding wavelength of 300 meters. For an AM radio wave to ooze through a hole, that hole would have to be more than 150 meters wide. This is why AM does not penetrate very far into a tunnel.

On the other hand, an FM radio wave is roughly 100 MHz (or .1 GHz) with a corresponding wavelength of 3 meters. Although still fairly big, FM radio waves can still ooze through garage doors in underground parking lots, through building windows, into tunnels, etc.

Wireless broadband at 2.5 GHz or 12 cm can  “ooze” though windows etc, but as I said, they ooze too fast and have a harder time turning corners. Hence, at these higher frequencies, we begin to see shadowing etc.

Written by Eric

December 31, 2009 at 12:34 pm

Posted in Broadband

Physics of Wireless Broadband

with 2 comments

With a title like the one I’ve chosen, I’m sure only the die hards will get even this far, so this post will be a somewhat technical follow-up to my informal post yesterday that was picked up by Felix Salmon and also noted by Paul Krugman.

In graduate school, I had fun building large-scale simulations where I modeled the propagation of radio waves transmitted from a cell phone through a 1 cubic millimeter resolution model of a human head

SAR distributions for the sagittal slice

SAR distributions for the frontal slice

SAR distributions for the coronal slice

These simulations are generally extremely accurate. The physics is well understood and can be modeled with a high degree of confidence. One of my favorite stories is when my office mate was modeling an aircraft and comparing results to measurements, he noticed the angle seemed off by .5 degrees. He called up the lab and, sure enough, the measurement was off by .5 degrees from what was specified. The simulation was more accurate than the measurement.

As mentioned yesterday, the behavior of a radio wave depends on its frequency and hence its wavelength. The two are related by

\lambda = \frac{c}{f},

where \lambda is the wavelength, f is the frequency, and c is the speed of light. To simplify things, we can write that formula as

\lambda (cm) = \frac{30}{f(GHz)}.

For example, if the frequency is 1 GHz, i.e. f(GHz) = 1, then the wavelength is 30 cm, i.e. \lambda(cm) = 30. When we double the frequency to 2 GHz, the wavelength reduces by half to 15 cm.

The wavelength is an important number to keep in mind because radio waves interact more strongly with objects whose size is roughly on the order of the wavelength of the radio wave. When I was in grad school, the frequency we were looking at was 900 MHz (.9 GHz) with a corresponding wavelength of roughly 33 cm. In a comment on Felix’s blog, Mark states:

It’s amazing that Phorgy can make so many technical errors and still make you worry that he’s right. For example:

“That is why the…7-800 MHz range is so valuable for cell applications.”

The 700 MHz band has never been used for cell phone communications in the US. It was auctioned off, but the spectrum is unused at present.

There is a big difference between what is valuable and what is available. Things are valuable sometimes precisely because they are not available. My statement was about the frequencies at which cell applications would be better off. I could have and maybe should have made the range a little broader, say 700-900 MHz, but that was not the point I was trying to make. The point is that radio waves propagate nicely, i.e. they ooze well, in the 700-800 MHz range. Higher than that and we begin to see directionality creep in, i.e. the radio waves begin to have preferred directions and the coverage becomes less uniform. For a very nice interactive demonstration of this, have a look at this:

Radiation Pattern of a Linear Antenna

The important number in that demonstration is the “Dipole Length (Wavelength)”. This is the length of the antenna relative to the wavelength. So in that demo, setting the slider t0 .5 means the antenna is half the length of the wave. For numbers up to 1.0, the pattern is fairly uniform, but once you get above 1.0, you start to see nulls where there is no radiation. This is one source of directionality in wireless signals.

From Felix’s article, we have:

For one thing, Phorgy’s limit of 1,000mps in total for a few city blocks is I think far higher than anything AT&T is currently able to provide. With what Baruch calls “compression, prioritisation, all that level 4-7 stuff you can do at the packet level” (don’t ask me), you can serve a lot of people with that kind of bandwidth.

The number I gave (1,000 mbps) was a “guestimate”, but it wasn’t a wild guestimate. When/if the formal studies are done, I am confident the number will not be too far off from this. This number includes “compression, prioritisation” and even polarization and modulation. I’m not talking about spectrum here, I am talking about the total availability of bits to everyone within a given vicinity. The number available to any one person will be simply this number divided by the number of people simultaneously downloading stuff within this vicinity. This is similar to the early days of cable modems. You could tell your neighbor was downloading a pirated movie because your connection drops to a crawl.

To be sure, my note was meant to convey an important message and sometimes a degree of license is warranted. No one should believe that any phone company has built out enough towers to reach the ultimate wireless speed limit, but how many people knew there was a wireless speed limit?

A couple years ago, I was telling people that in a few years, we would begin to see the limits of wireless broadband. I think we are beginning to see it, but we still have a way to go before we truly hit that ultimate speed limit. But we will.

There is no number of towers or “Wi-Fi” hot spots that will overcome this physical limitation. For one thing, you cannot put Wi-Fi hotspots too close together or they start to interfere with one another. You can be clever and switch to a neighboring channel, but that again only delays the inevitable.

Like another comment by loganb on Felix’s blog points out:

The real limit isn’t Heisenberg’s, it’s (Claude) Shannon’s, and those limits only apply to limits on the capacity of a given base station.

This is a great point, but I would say the two go hand in hand. Shannon and Heisenberg together determine the ultimate limit of how much information can by communicated via wireless broadband within a given vicinity.

One day, in the not too distant future, instead of going into a cafe and hopping online via a Wi-Fi hotspot, that same cafe will have a fiber optic plug next to the salt shaker.

Written by Eric

December 30, 2009 at 10:28 am

Posted in Broadband

Hello Heisenberg: “New York City not ready for the iPhone”

with 12 comments

Interesting story from The Consumerist:

AT&T Customer Service: “New York City Is Not Ready For The iPhone”

Recall an earlier article of mine (from July 2007):

I chose a technically incorrect term “Wi-Fi” because that is what most people were talking about back then, but the subject was more generally about “wireless broadband”.

It is not that NYC isn’t ready for the iPhone. It is that NYC was the first to bump up against the inherent physical limitation of wireless broadband. There is no number of towers that will be able to accommodate hundreds or thousands of people within a small vicinity all expecting reasonable wireless bandwidth. There is a little thing called the Heisenberg uncertainty principle that no amount of marketing or engineering will be able to get around.

Edit: Here is a copy of a comment below in response to the questions:

I’ll try to write a separate article, but this is about the physics of waves.

Unlike finance, the physics of electromagnetic waves is well understood. Computer programs can be written to model radio waves to many digits of accuracy.

The behavior of a wave depends on its frequency. At low frequencies, radio waves are kind of like molasses. They can ooze around corners and through buildings. That is why the (relatively low frequency) 7-800 MHz range is so valuable for cell applications.

In recent years, the frequencies of cell phones and even more recently, smart phones, has increased from a little over 1 GHz to over 2.5 GHz (and beyond).

(Note: Your microwave oven operates at the same frequency as most smart phones now.)

As frequencies increase, the waves start acting more like laser beams. They no longer ooze around corners. You start to get “shadows” or dead spots with no signal. It becomes more difficult for the signals to penetrate walls etc. These problems get worse the higher you go in frequency.

An extreme case is an actual laser. Here, it becomes more difficult to distinguish the wave dynamics from particle dynamics. Like in Star Wars, the laser beams can bounce around like particles.

So we have two extremes: low frequency molasses waves and high frequency laser beams. As bandwidth demands increase, we begin moving the dial away from molasses (where we have good wireless signals) to laser beams (where we have dark spots, shadows, with no signal, etc).

There are many clever modulation tricks that delay the inevitable, but the basic rule is that you cannot defeat Heisenberg. This is an imprecise (but I hope effective) analogy that relates to the fact that at lower frequency (and longer wavelength, i.e. larger “effective size” of the wave), you have more certainty as to “where the photon is” (because it is coming from a relatively smaller antenna) you have more uncertainty about where it goes, i.e. it goes everywhere like a good wireless signal should. At higher frequency (and shorter wavelength), the antenna is relatively larger (compared to the wave) so we know less precisely where the photons are, hence we have more certainty as to where they are going, i.e. in a straight line instead of around a corner, which is undesirable for a wireless signal.

This physical fact does not deter marketing people. You can easily set up a demonstration on a van driving down the highway at 65 mph with an antenna mounted on top downloading web content at 100-1000 mbps. Don’t fall for this trick! They are essentially shining a laser beam at the van and tracking it down the road. Ask them to do the same demo with 1000 vans stuck in LA traffic. Forget about it.

I’d guestimate that a practical limit for the available wireless bandwidth in the air in a vicinity of say a couple square NYC blocks would be 1000 mbps. This is the TOTAL BANDWIDTH AVAILABLE FOR EVERYONE WITHIN A FEW NYC BLOCKS. So now divide 1000 mpbs by the number of people downloading stuff wirelessly taking into consideration highrise buildings, etc. That is probably a decent estimate of what the long term limits of wireless broadband would be.

So you can see, for the early adopters, wireless bandwidth is great! “Geez! This wireless is faster than my ethernet!” But once you start adding some real traffic, say 100 or 1000s of people all downloading stuff wireless within a small vicinity and you can imagine that we will easily bump up against the basic physical limitations as communicated by my good friend James Clerk Maxwell.

Written by Eric

December 27, 2009 at 4:42 pm

Posted in Broadband

The new corporate trend: “onshoring”

with 2 comments

Ha! What did I tell you? It is wayyy past my bedtime and I should be sleeping (especially since I’m sick and feel like I’ve been run over by a truck), but just stumbled on an interesting article from one of my favorite economic development blogs: Design Nine. He points to an article in the

Recall that in the midst of all the market doom and gloom, I recently said:

I’m actually ironically optimistic about the outlook for suburban and rural economic development. A weaker dollar will make outsourcing less attractive. That will bring manufacturing jobs back home. I can imagine a boon in suburban and rural development. Just imagine if communities developed decent broadband via fiber-to-the-home/business. Suddenly, there will be attractive jobs and living standards in affordable places.

I admit that the quote is a bit misleading because Andrew Cohill has influenced the way I think about things, but still timely I think. Here is an excerpt from the article:

Small-town America: The new Bangalore?


Onshoring, in fact, is becoming trendy.

Some U.S. companies recently have pulled back from India to set up shop in rural areas where access to high-speed broadband connections isn’t the problem it was just a few years ago and where lower real-estate prices and wages are attractive.

Note that the key to onshoring is an investment in telecommunications infrastructure. In particular, fiber-to-the-home. It is quite sad to see so many municipalities rest their hopes on wireless broadband. That will only end in tears as the reality of wireless broadband becomes apparent. Any community that is not investing now in fiber will lose out on an important opportunity that is now beginning to present itself: onshoring. As Andrew will tell you more eloquently than I could, an intelligent investment in a communities future MUST involve a combination of both fiber and wireless and I would put wireless as a distant second. I can explain in gory detail why wireless will fail if you like (I did my PhD in the subject), but for now need to hit the sack.

Go onshoring! Go USA!

Written by Eric

December 4, 2007 at 12:50 am

WP: Japan’s Warp-Speed Ride to Internet Future

with 2 comments

An important factor for long term economic growth is technological innovation. An important factor for technological innovation is increasingly access to high speed internet connections. The US has been falling behind Japan, South Korea, and parts of Europe in terms of access to fiber optic connections to the home. I alluded to this here and here and probably elsewhere.

In the next couple of years, I suspect you’ll see the number of articles like the one pointed out by Barry Ritholtz over on The Big Picture

Japan’s Warp-Speed Ride to Internet Future

TOKYO — Americans invented the Internet, but the Japanese are running away with it.

Broadband service here is eight to 30 times as fast as in the United States — and considerably cheaper. Japan has the world’s fastest Internet connections, delivering more data at a lower cost than anywhere else, recent studies show.

Written by Eric

September 1, 2007 at 5:13 pm