V/U Packet Rate Limits

Question

I'm studying for the General exam and I've encountered some questions about maximum baud rates on various bands. They seem... extremely optimistic. Given the trouble I've had investigating 9600 baud on 2m, I had to wonder if people are actually managing anything like the limits.

Secondarily, how would I go about setting up a 19.6k connection on 2m or a 56.6k connection on 70cm? Are there radios that offer this as a capability, or specific TNCs, or is this just a lot of legal headroom and nobody's actually doing it?

Answer 1

As mentioned above, you should make a distinction between the legal limits, and the technical feasibility, and the theoretical maxima in rates.

To illustrate: Shannon's channel capacity says that over a channel with bandwidth $B$ and SNR $\frac SN$, you can do at most the bit rate $C$:

$$C = B\log_2\left(1+\frac SN\right)\,\text.$$

What Shannon does not say is how you do that, and in fact, that problem is often unsolved, so most transceiver systems stay considerably below that rate limit.

Let us, however, plug in some numbers here of a rather idyllic scenario:

We go for a channel width of $B= 3\,\text{kHz} \approx 35\,\text{dBHz}$, and let's assume some ~S8 scenario, so $S=-80\,\text{dBm}$, as well as letting your receiver run at room temperature and have a Noise Figure $N_F=4\,\text{dB}$:

$$\begin{align} C &= 3\cdot10^3\frac1{\text s} \cdot\log_2\left(1+\frac{-80\,\text{dBm}}{-174\,\text{dBm/Hz}\cdot 35\,\text{dBHz}\cdot4\,\text{dB}}\right)\\ &= 3\cdot10^3\frac1{\text s} \cdot\log_2\left(1+\frac{-80\,\text{dBm}}{\left(-174+35+4\right)\,\text{dBm}}\right)\\ &= 3\cdot10^3\frac1{\text s} \cdot\log_2\left(1+(-80-(-174+35+4)\,\text{dB})\right)\\ &= 3\cdot10^3\frac1{\text s} \cdot\log_2\left(1+(-80+135)\,\text{dB})\right)\\ &= 3\cdot10^3\frac1{\text s} \cdot\log_2\left(1+55\,\text{dB}\right)\\ &\approx 3\cdot10^3\frac1{\text s} \cdot\log_2\left(10^{5.5}\right)\\ &\approx 3\cdot10^3\frac1{\text s} \cdot18.27\\ &= 54.81\,\text{kb/s} \end{align}$$

In other words, no matter what modulation, channel code you use, there's no chance you'll get more that 54810 bits per second error-free through that channel. So, restricting you to about $\frac13$ of that still makes no sense from an RF perspective (regulator doesn't actually care how fast you transmit, but how much spectrum you occupy with that), but it's not inherently too optimistic – on a short range scenario, the receive powers might be much higher (calculate Free Space Path loss for 5 km with 2 m waves, how much power do you get when someone blasts out 750 W? My rough head calculation says you get about 20 times the capacity).

Answer 2

There are two questions in the General exam dealing with bandwidth in the VHF and UHF bands (G1C09 and G1C11). Both of these questions are dealing with the regulatory, not technical, limits of data communications.

From a practical perspective the limiting technical factor will be the radio you use to try to obtain 19.6 or 56 kbaud on these bands. Most FM and SSB transceivers for have modulators that are restricting the output bandwidth to that required for voice communications (about 3 kHz). Any attempt to use these modulators at the higher signaling rates required for higher speed digital communications will result in significant distortion to the modulated signal rendering the received signal useless.

You can overcome the modulation bandwidth restrictions by using a radio purposely designed for higher speed data communications or by modifying or building a radio to suit your needs. This is one of the great joys and privileges of having an amateur radio license - you are encouraged by the FCC to experiment in this way!

Good luck on your General exam!

Edit: I should add that some off the shelf UHF/VHF radio's have accessory connectors that allow a wider bandwidth. Examples are the FT-7900, the TM-V71, and the IC-208H. None of these are wide enough for the data limits of UHF and they all still use FM as the modulation method.