What's with a negative SNR?

Foundations of Amateur Radio

We describe the relationship between the power of a wanted signal and unwanted noise as the signal to noise ratio or SNR. It's often expressed in decibels or dB which makes it possible to represent really big and really small numbers side-by-side, rather than using lots of leading and trailing zeros. For example one million is the same as 60 on a dB scale and one millionth, or 0.000001 is -60.

One of the potentially more perplexing ideas in communication is the notion of a negative signal to noise ratio. Before I dig in how that works and how we can still communicate, I should point out that in general for communication to happen, there needs to be a way to distinguish unwanted noise from a desired signal and how that is achieved is where the magic happens.

Let's look at a negative SNR, let's say -20 dB. What that means is that the ratio between the wanted signal and the unwanted noise is equivalent to 0.01, said differently, the signal is 100 times weaker than the noise. In other words, all that a negative SNR means is that the ratio between signal and noise is a fraction, as-in, more than zero, but less than one. It's simpler to say the SNR is -30 dB than saying the noise is 1000 times stronger than the signal.

Numbers like this are not unusual. The Weak Signal Propagation Reporter or WSPR is often described as being able to work with an SNR of -29 dB, which indicates that the signal is about 800 times weaker than the noise.

To see how this works behind the scenes, let's start with the idea of bandwidth.

On a typical SSB amateur radio, voice takes up about 3000 Hz. For better readability, most radios filter out the lower and upper audio frequencies. For example, my Yaesu FT857d has a frequency response of 400 Hz to 2600 Hz for SSB, effectively keeping 2200 Hz of usable signal.

Another way to say this is that the bandwidth of my voice is about 2200 Hz, when I'm using single side band. That bandwidth is how much of the radio spectrum is used to transmit a signal. For comparison, a typical RTTY or radio teletype signal has a bandwidth of about 270 Hz. A typical Morse Code signal is about 100 Hz and a WSPR signal is about 6 Hz.

Before I continue, I should point out that the standard for measuring in amateur radio is 2500 Hz.

This is significant because when you're comparing wide and narrow signals to each other you'll end up with some interesting results like negative signal to noise ratios. This happens because you can filter out the unwanted noise before you even start to decode the signal. That means that the signal stays the same, but the average noise reduces in comparison to the 2500 Hz standard.

This adds up quickly. For a Morse Code signal, it means that turning on your 100 Hz filter, will feel like improving the signal to noise ratio by 14 dB, that's a 25 fold increase in your desired signal.

Similarly, filtering the WSPR signal before you start decoding will give you roughly a 26 dB improvement before you even start.

But there's more, since I started off with claiming that WSPR can operate with an SNR of -29 dB. I'll note that -29 dB is only one of the many figures quoted. I have described testing the WSPR decoder on my system and it finally failed at about -34 dB. Even with a 26 dB gain from filtering we're still deep into negative territory, so our signal is still much weaker than the noise.

There are several phenomena that affect the decoding of a signal.

To give you a sense, consider using a limited vocabulary, like say the phonetic alphabet, or a Morse character, the higher the chance of figuring out which letter you meant. This is why it's important that everyone uses the same alphabet and why there's a standard for it. To send a message, WSPR uses an alphabet of four characters, that is, four different tones or symbols.

Another is how long you send a symbol. A Morse dit sent at 6 words per minute or WPM lasts two tenths of a second, but sent at 25 WPM lasts less than 5 hundredth of a second This is why WSPR uses two minutes, actually 110.6 seconds, to send 162 bits of data, lasting just under one and a half seconds each.

If that's not enough, there's a processing gain. One of the fun things about signal processing is that when you combine two noise signals, they don't reinforce each other, but when you combine two actual signals, they do. Said in another way, signal adds coherently and noise adds incoherently.

To explain that, imagine that you have an unknown signal and you pretended that it said VK6FLAB.

If you combined the unknown signal with your first guess of VK6FLAB and you were right, the unknown signal would be reinforced by your guess. If it was wrong, it wouldn't. If your vocabulary is small, like say four symbols, you could try each in turn to see what was reinforced and what wasn't.

There's plenty more, things like adding error correction so you can detect any potentially incorrect words. Think of it as a human understanding Bravo when the person at the other end said Baker.

If you knew when to expect a signal, it would make it easier to decode, which is why a WSPR signal starts at one second into each even minute and each symbol contains information about when that signal was sent, which is why it's so important to set your computer clock accurately.

Another is to shuffle the bits in your message in such a way that specific types of noise don't obscure your entire message. For example, if you had two symbols side-by-side that when combined represented the power level of your message, a brief burst of noise could obliterate the power level, but if they were stored in different parts of your message, you'd have a better chance of decoding the power level.

I've only scratched the surface of this, but behind every seemingly simple WSPR message lies a whole host of signal processing magic that underlies much of the software defined radio world.

These same techniques and plenty more are used in Wi-Fi communications, in your mobile phone, across fibre-optic links and the high speed serial cable connected to your computer.

Who said that Amateur Radio stopped at the antenna connected to your radio?

I'm Onno VK6FLAB