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Ignoring quantum effects, there's no upper limit in theoretically perfect radio conditions, even for a single radio channel, where there is absolutely no backgr

Ignoring quantum effects, there's no upper limit in theoretically perfect radio conditions, even for a single radio channel, where there is absolutely no background noise or interference, and the antennae and electronics are literally perfect. However, nothing can be built like that, and there is always background noise. The real life limit is complicated. For each single radio channel the limit depends on other characteristics of the channel than just the (temporal) radio bandwidth, for example the antenna, background radio noise, interference, and power level. The Shannon-Hartley theorom covers capacity of a single noisy channel with fixed characteristics; it depends on the signal to noise ratio as well as the bandwidth. Radio channels used for mobile communications are typically "fast-fading", which means the conditions keep changing, and both ends have to continuously measure those conditions and adapt dynamically how they encode and decode the data. This complicates a measure of the theoretical limit, and also means the limit is changing with time, for example as the user moves the handset around. https://en.wikipedia.org/wiki/Channel_capacity#Channel_capacity_in_wireless_communications https://en.wikipedia.org/wiki/Channel_capacity#Channel_capac... The highest rate encoding used in 802.11be is "4096-QAM" which carries 24 bits/sec per Hz when noise is sufficiently low, and decreases the more error correction is required. I'm not sure if 4096-QAM is chosen because the signal-to-noise level is such that a larger number wouldn't improve thoughput enough to matter, or if it's limited by the electronics, non-linearity and calculations at those high speeds. That bit rate is for a single radio channel. Multiple channels overlapping the same frequencies are also possible, as long as the antennae are sufficiently spread out in space and/or polarisation. When something large enough like a laptop (which has multiple antenna in the display) talks to a base station, it is combined with beamforming and diversity, or in a general mathematical description, polarisation modes and spatial bandwidth. That is equivalent to having multiple radio channels using the same frequencies to the same device, but the channels are not physically distinct, they are combined and separated mathematically with linear algebra. As with MHz bandwidth, spatial and polarisation are also limited. You can't add more channels with no limit to a single device of fixed size. But if you have no limit on device size so can add more antenna spread out, and/or many base stations cooperating, you can increase the total bits/second by using those. 4G LTE does the multiple base stations thing to some extent already, to maintain channels to multiple user handsets at the same time inside a cell. It's not that each handset talks to a separate base station. It's that the signals are combined with linear algebra in such a way that each handset can decode different information from the multi-spatial-channel signal that they all receive slightly differently.

H8crilA 5y ago
Thank you for the detailed response! I just recently picked up an RTL-SDR, and for a moment though that I have this bandwidth thing figured. Nope, more learning ahead. I'll probably write some simple demodulator to better understand this stuff.
- H8crilA 5y ago
  PS. I think I can see how to send unbounded data rates through a narrow bandwidth, assuming perfect conditions with no noise. If you want to transfer N bits per second, for half a second transmit plain carrier, then for half a second transmit carrier multiplied by x/2^N DC, where x is the sequence of bits to be transferred in that second. Then repeat the process. The receiver can establish the max reading when pure carrier is being transmitted, and do a readout when the multiplied carrier is transmitted.
  - jlokier 5y ago
    That's exactly right, although if you take the Fourier transform of that modulated signal you'll see that it uses infinite bandwidth due to the square-wave modulation steps at each half second. That can be sent through a narrow bandwidth channel, which will filter out the higher harmonics. But then, as the Fourier transform suggests, you'll see at the receiver a different signal, with rounded edges instead of steps in the modulated amplitude. Those half second intervals set what's called the symbol rate to 2sym/s, and the Nyquist frequency for them is 1Hz. If your channel bandwidth (the filter) is > 1Hz, the information will still be there in the modulated, filtered signal to recover, but you'll have an interesting time doing it if the bandwidth is close to 1Hz. If your channel bandwidth is < 1Hz (the filter strictly removes all frequencies above 1Hz), you won't be able to recover all the transmitted bits. I recommend building a demodulator and varying the channel bandwidth to get an intuition for how it gets trickier to demodulate close to 1Hz. Note that making the strict bandwidth filter is also quite an interesting challenge, especially close to 1Hz; this is called a brick wall filter. Doing the Fourier transform on the entire signal before and after filtering is a good way to visualise the bandwidth taken by a modulation scheme and the effects of a channel, and to see if it's correctly removed everything above the threshold frequency. Modifying those Fourier values in the frequency domain then using an inverse Fourier transform to construct a filtered version of the entire signal is a good way to construct an ideal filter for testing the demodulator.

H8crilA 5y ago

Thank you for the detailed response! I just recently picked up an RTL-SDR, and for a moment though that I have this bandwidth thing figured. Nope, more learning ahead. I'll probably write some simple demodulator to better understand this stuff.

H8crilA 5y ago
PS. I think I can see how to send unbounded data rates through a narrow bandwidth, assuming perfect conditions with no noise. If you want to transfer N bits per second, for half a second transmit plain carrier, then for half a second transmit carrier multiplied by x/2^N DC, where x is the sequence of bits to be transferred in that second. Then repeat the process. The receiver can establish the max reading when pure carrier is being transmitted, and do a readout when the multiplied carrier is transmitted.
- jlokier 5y ago
  That's exactly right, although if you take the Fourier transform of that modulated signal you'll see that it uses infinite bandwidth due to the square-wave modulation steps at each half second. That can be sent through a narrow bandwidth channel, which will filter out the higher harmonics. But then, as the Fourier transform suggests, you'll see at the receiver a different signal, with rounded edges instead of steps in the modulated amplitude. Those half second intervals set what's called the symbol rate to 2sym/s, and the Nyquist frequency for them is 1Hz. If your channel bandwidth (the filter) is > 1Hz, the information will still be there in the modulated, filtered signal to recover, but you'll have an interesting time doing it if the bandwidth is close to 1Hz. If your channel bandwidth is < 1Hz (the filter strictly removes all frequencies above 1Hz), you won't be able to recover all the transmitted bits. I recommend building a demodulator and varying the channel bandwidth to get an intuition for how it gets trickier to demodulate close to 1Hz. Note that making the strict bandwidth filter is also quite an interesting challenge, especially close to 1Hz; this is called a brick wall filter. Doing the Fourier transform on the entire signal before and after filtering is a good way to visualise the bandwidth taken by a modulation scheme and the effects of a channel, and to see if it's correctly removed everything above the threshold frequency. Modifying those Fourier values in the frequency domain then using an inverse Fourier transform to construct a filtered version of the entire signal is a good way to construct an ideal filter for testing the demodulator.