Say we have the technology to broadcast a signal from an antenna to receivers, with some bandwidth B. Without getting clever, we can only send or receive one signal, since any others would interfere with each other.
The trick is, can we do something to shift the bandwidth B to some other base frequency F such that B + F > B? Or B + (N - 1)F > B? And if we can do that, and then downshift from B + NF back to B, it means we can broadcast to multiple channels, and receivers can tune their antennas to F and downshift the decoded signal to 0 and receive it at the original bandwidth B.
A cheap way to do this is amplitude modulation, where multiplying a signal with bandwidth B by a carrier signal of frequency F shifts it up to the range F +/- B and we can space channels apart by 2B to get however many channels our antennas allow for.
The real question is, why is it 2B and not B? Well that lies in some Fourier analysis, where the bandwidth of a signal extends into negative frequency ranges. But neverless, there is another trick, called single-side-band modulation (SSB) where we can shift a signal into the range F + B instead of F +/- B, and demodulate it into -B, B to get the original.
And that gets us to the 1950s in terms of radio technology.
The trick behind FM is to understand we can get more bandwidth by shifting the frequency response not into a series of non-overlapping channels centered at carrier frequencies like AM, but to distribute most of the information across many non overlapping bands over the entire spectrum of the antennas. To do this we don't modulate the amplitude of the carrier, but its frequency. This makes it possible to distribute far more bandwidth across a wide range of frequencies, and it's how FM radio works today.
These concepts create the foundation for modern radio communication, We can modulate data signals to different bandwidths and receive them, provided we know where to tune to. And these bandwidths can either be continuous chunks of spectrum (AM), or interleaved (FM). The next step is to think in terms of time, which is to say that we can have receivers negotiate not only which ranges in frequency they care about, but which time frames they want to listen before waiting for their next time slot.
For those interested in the theory, the fundamental problem is that we can design antennas that can transmit or receive at some fixed maximum bandwidth, bounded by physics. The engineering problem is to find out how to share that bandwidth to maximize the number of receivers and/or senders by sharing the same bandwidth. Amplitude modulation is excellent, but it divides the bandwidth up into a fixed number of channels of maximum individual bandwidth. FM is a bit more efficient in how it can allow many broadcasters to even more receivers choose which channels they receive. But for modern communications, where we need high bandwidth for distinct transmitter/receiver connections, we need protocols to figure out how to share the bandwidth over the air and the two tricks are to divide that bandwidth by frequency (like AM and FM) or time (sharing the same frequency channels, but only picking the frames that we care about), or both.
And for those even deeper into the theory, one question you might ask is, if we can divide spectrum and time to get some bandwidth B per channel, how many bits can we send/receive over a distinct channel?
The answer is C = Blog2(1 + S/N) where B is the bandwidth and S/N is the signal to noise ratio determined by the environment (how much noise is present relative to the signal being transmitted). The crazy thing is this was proven in the 1940s and everyone interested should go read The Mathematical Theory of Communication by Claude Shannon. This is referred to as the Shannon-Hartley theorem, and it determines the channel capacity (C, in bits/second) of any communication channel in the presence of noise.
The math concepts might seem heady, but it's actually fairly approachable and available online. It's fascinating that the fundamentals were proven out in one work nearly 80 years ago by a handful of people, and the math is not that bad.
The thing that makes this nuts is that if an engineer picks some target bitrate for a device, say a cellphone watching video, they can work backwards to determine the channel capacity they need, do some experiments to figure out noise, and then determine what the target their modem protocol needs to reach to be suitable. And this is how we get 5G and fiber or whatever comes next.
Shannon was pretty ridiculous. He basically invented information theory, proved all the major theorems involved, and applied it to communications and error-correction codes. If you work in RF you can't do much without encountering his work. (It did take a while before anyone figured out how to get close in practice to the limits he proved, though)
And before his work on information theory, his master's thesis showed that Boolean algebra could be used to design digital circuits and invented logic gates:
> divide that bandwidth by frequency (like AM and FM) or time
Ah. The real magic is when we separate by space (beyond just frequency or time). The ability to do this was discovered relatively recently, in 1996, by a guy called Foschini, though radio astronomers will say "Meh". By adding multiple antennas and doing space-time coding engineers found they could pump an order of magnitude more data through a radio channel. The maths involved is high school level (linear simultaneous equations), and it's magic to understand Foschini's work and think "Why didn't we do that before?"
The other bit of radio magic is error control coding. This is the stuff that lets us reliably talk to Voyagers I and II.
Fascinating how we keep being inspired by fundamental physics and astronomy to keep cramming mode information in our channels. I'm still trying to understand Orbital Angular Momentum multiplexing https://en.m.wikipedia.org/wiki/Orbital_angular_momentum_mul...
I'd agree with the Wikipedia article, that it sounds like MIMO, in that it requires the beam to have a spatial extent.
From the Wikipedia article:
> can thus access a potentially unbounded set of states
That's what people originally thought about MIMO. MIMO's not unbounded. The limit to the number of states is related to the surface area of the volume enclosing the antenna, with the unit of distance being the wavelength. A result radio astronomers already knew when the comms people derived it. With absolutely no evidence to back it up, I'd guess that the same limit applies to OAM multiplexing.
As an aside, when one expresses physics in terms of information theory my understanding is that the maximum the number of bits that can be stored in a volume of space (also the number of bits requited to completely describe that volume of space) is related to the surface area of the volume with the linear unit being Plank lengths. Is MIMO capacity in some way a fundamental limit in communications?
Say we have the technology to broadcast a signal from an antenna to receivers, with some bandwidth B. Without getting clever, we can only send or receive one signal, since any others would interfere with each other.
The trick is, can we do something to shift the bandwidth B to some other base frequency F such that B + F > B? Or B + (N - 1)F > B? And if we can do that, and then downshift from B + NF back to B, it means we can broadcast to multiple channels, and receivers can tune their antennas to F and downshift the decoded signal to 0 and receive it at the original bandwidth B.
A cheap way to do this is amplitude modulation, where multiplying a signal with bandwidth B by a carrier signal of frequency F shifts it up to the range F +/- B and we can space channels apart by 2B to get however many channels our antennas allow for.
The real question is, why is it 2B and not B? Well that lies in some Fourier analysis, where the bandwidth of a signal extends into negative frequency ranges. But neverless, there is another trick, called single-side-band modulation (SSB) where we can shift a signal into the range F + B instead of F +/- B, and demodulate it into -B, B to get the original.
And that gets us to the 1950s in terms of radio technology.
The trick behind FM is to understand we can get more bandwidth by shifting the frequency response not into a series of non-overlapping channels centered at carrier frequencies like AM, but to distribute most of the information across many non overlapping bands over the entire spectrum of the antennas. To do this we don't modulate the amplitude of the carrier, but its frequency. This makes it possible to distribute far more bandwidth across a wide range of frequencies, and it's how FM radio works today.
These concepts create the foundation for modern radio communication, We can modulate data signals to different bandwidths and receive them, provided we know where to tune to. And these bandwidths can either be continuous chunks of spectrum (AM), or interleaved (FM). The next step is to think in terms of time, which is to say that we can have receivers negotiate not only which ranges in frequency they care about, but which time frames they want to listen before waiting for their next time slot.
For those interested in the theory, the fundamental problem is that we can design antennas that can transmit or receive at some fixed maximum bandwidth, bounded by physics. The engineering problem is to find out how to share that bandwidth to maximize the number of receivers and/or senders by sharing the same bandwidth. Amplitude modulation is excellent, but it divides the bandwidth up into a fixed number of channels of maximum individual bandwidth. FM is a bit more efficient in how it can allow many broadcasters to even more receivers choose which channels they receive. But for modern communications, where we need high bandwidth for distinct transmitter/receiver connections, we need protocols to figure out how to share the bandwidth over the air and the two tricks are to divide that bandwidth by frequency (like AM and FM) or time (sharing the same frequency channels, but only picking the frames that we care about), or both.