The Ultimate Wireless Broadband Speed Limit
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.
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
What is the ultimate physical maximum number of bits that can be communicated via wireless broadband devices within one test region?
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 .
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 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.