# How did old mobile phones amplify signals lower than the noise floor?

In the early days of GSM in around 2000 when the network was still not fully deployed, it was common for me to receive very low signal, even sometimes No Signal due to out of network.

I used to use a Nokia phone which was equipped with a built in NetMonitor so sometimes I checked the signal level in certain areas I visited. Sometimes I got -80 dBm, -90 dBm, or even -100 dBm. Nowadays I never meet again such that area.

As shown in the picture 1, the RxLevel sometimes is -101 dBm. This RxLevel is lower than the noise floor of electronic devices, which is around -90 to -80 dBm.

With this noise floor and the RxLevel = -101 dBm, the signal to noise ratio (SNR) is less than 1. As we see in picture 2, the Agilent measurement result, a signal below the noise floor can't be measured.

How can the electronic equipment operate with such a low signal? How could the mobile phone amplify a signal that is lower than the noise floor? Bear in mind that the shown RxLevel is the received signal in the mobile phone, not the received signal on the antenna.

• A 200kHz(GSM) wide channel has a thermal noise power of around -120dBm, significantly smaller than -85dBm. Commented Apr 6, 2023 at 19:51
• But what's that -85dBm graph a measurement of though - it's the noise floor of a random spectrum analyser with no context. The phones receiver will have its own characteristics. Commented Apr 6, 2023 at 20:07
• I know what the noise floor is, and it's not just to do with thermal noise. My point is each device has electronic circuitry with different sources of noise. Each amplifier will inherantly add noise, power supplies will add noise, resistors will add thermal noise. Just because the noise floor of that particular model of spectrum analyser is -85dBm doesn't mean that every device has the same noise floor. Commented Apr 6, 2023 at 20:12
• To improve the noise floor on that analyzer, reduce its resolution BW (RBW) currently set to 10kHz, see bottom left. I have a spectrum analyzer whose RBW goes down to 3 Hz. Much lower noise, but takes an age to make a plot. (And it won't do GHz)
– user16324
Commented Apr 6, 2023 at 21:12
• @AirCraftLover no, you're the one totally out of line here, as I'm the sixth expert to tell you... Your understanding is wrong. Commented Apr 7, 2023 at 0:32

As shown in the picture 1, the RxLevel sometimes is -101 dBm. This RxLevel is lower than the noise floor of electronic devices, which is around -90 to -80 dBm.

Well there's your problem, the assertion that 'electronic devices' have a noise floor of -90 to -80 dBm.

The graph from the wikipedia article you quote1 shows a noise floor of -85 dBm in a 10 kHz (40dBHz (noise bandwidth is power remember, so it's 10log10, not 20log10)) resolution bandwidth, ie -125 dBm/Hz (give or take 2.5dB for peak log), for some random unspecified thing it's connected to. Although spectrum analysers generally have an atrocious noise figure, this is so high that it's probably measuring a high gain amplifier generating quite a high level of noise at its output, rather than its own input noise.

The fundamental physics 'rules of the universe' lower limit for noise is -174 dBm/Hz, at room temperature. All systems will exhibit at least this.

Any practical receiver will have a higher noise floor than the fundamental limit. A good receiver may be able limit that degradation to a dB or so.

A GSM signal has a bandwidth of 200 kHz, or 53dBHz, which gives a fundamental noise floor of -121dBm in the GSM channel. IIRC, GSM receivers need to have a better floor than -118dBm to be approved for use on the network (someone who knows their stuff please correct me?), and are generally a bit better.

With a GSM signal power of -101dBm, the SNR could approach 20dB, and will be substantially better than 15dB, plenty for excellent reception.

1 - that's a very poor article. I'll look at the talk, and see whether it can be improved without a rewrite.

• What do you think about baseband/unspread bandwidth as citied by @jpa in his/her commend below my post. I remember a BTS machine by a Finnish company, there is module called baseband module. It was exist with 900/1800MHz. It is related on a very top of the BTS shelf. Is it related? Commented Apr 7, 2023 at 10:14
• @AirCraftLover Processing gain seems magical until you realise it's another way of accounting for power. Frequency and time are the two common bases to project signal energy onto, and then frequency naturally gives rise to the concept of noise bandwidth. You can also project onto orthogonal 'sequencies', typically called spreading at the transmitter and despreading at the receiver. You can generalise noise bandwidth slightly to work with these. Even if you call it averaging or correlation when you can, the maths works the same, and the noise drops while the signal doesn't, improving SNR. Commented Apr 7, 2023 at 10:40
• So, based on your understanding, what is the allowed minimum received signal level (RxLevel) and what bandwidth a system may received and proceed? I am curious about how the Voyager-1 and Voyager-2's signals received and proceed by NASA from the brink of our galaxy, which I guess the signals are very weak. Commented Apr 7, 2023 at 14:55
• @AirCraftLover The Shannon-Hartley theorem (1) says that with suitable source coding, you can transmit 1 bit per Hz bandwidth even with a 0dB SNR in the channel without error. We still don't know how to code a source that well, though both Turbo (2) codes and Low Density Parity Check (3) codes can get within about 1dB of Shannon. LNAs can get to 1dB noise figure comfortably. There's a lot of info out there, wikipedia 1, 2 and 3. The Voyagers, they crank up transmit power, use good source coding, reduce the data rate, use large antennas on earth, until they hit Shannon. Commented Apr 7, 2023 at 15:59
• @AirCraftLover Can you please explain what answer would satisfy you? It seems you're looking for something and not finding it. Come up with an answer you'd like, and then look carefully for why it's wrong :) Commented Apr 7, 2023 at 16:41

Not a full answer, but some general ideas.

I will suppose digital signal in "logic level". The reasoning could be extended to analog signals, but it's a bit more complicated.

Let's suppose each bit is (ideally) represented by either 0V or 5V. If your noise is always less than 2.5V, then you can always be 100% sure about the value of the bit.

Now let's suppose noise up to 4V. If you measure something <1V, you are sure it is supposed to be a 0, it is above 4V, you are sure it is supposed to be a 1. In between, you are unsure (but usually, the nearer you are to 5V, the more likely it is that it is supposed to be a 1).

So, for example, if you decide that each bit is repeated 10 times, then you can average the values, and be quite sure about the result (supposing noise is independent, so it cancels out in the average).

Now suppose you have a very high gaussian noise, for example 100V standard deviation with no time correlation (ie the value of the added noise is independent on each measurement).

Your 5V signal is well below the noise level. But if your signal is slow enough, you can make multiple measurements. If measurements are independent, then the noise of the average has a standard deviation of 1/sqrt(N), where N is the number of measurements. So if you take 100 measurements, the noise on the average is divided by 10, so 10V (still not enough). If you take 10,000 measurements, the noise is divided by 100, so you have 1V of noise - this time, you clearly see your 5V signal.

So, there is no issue with a signal below noise level: you just have to average it over a long enough duration to retrieve it (which means, you are quite limited in the amount of data you can transmit).

To give you a completely different example: if you try to measure the sea level, in order to sea how it changes due to global warming, you are looking into a signal in the centimeter range, yet your noise (waves and tides) is several meters. It's still done without problem, simply by averaging over several weeks.

• How did you still talk 2.5V while the RxLevel is around -100dBm? -100dBm is 0.1pico watt. Commented Apr 6, 2023 at 20:07
• This is just an example with an "easy" situation (simple logic signals, usual voltages, ...) to show you that some "averaging" is all it takes to get a signal "lost" in noise. In the case of "radio" communication, the "averaging" becomes more complicated (and I have no idea how it is done), but the main idea remains the same : each measurement carries some very small amount of information, so if you do enough measurements, you can retrieve some useful information Commented Apr 6, 2023 at 20:13
• @AirCraftLover This answer simplifies things, since your question is based on a premise that breaks down even in this simple example :) So getting simple things right is important. You can scale this answer to any level you want. Even levels below the theoretical limit - that's what averaging is good for. Ask anyone working with radiotelescope signals :) Commented Apr 7, 2023 at 16:43
• @Kubahasn'tforgottenMonica, "Ask anyone working with radio telescope signals," actually, it was on my mind but hard for me to phrase it. I was wonder how the signal frpm Voyager1 & Voyager2 that travel to the brink of our Galaxy but the the signal they transmit to the earth still proceed-able. But I don't have any idea about what is the signal level received in Earth Station. Then I remember when around 2 decades ago I used to used Nokia with NetMonitor installed on it which I used to check the received signal when I was surveying location for microwave transmission link. Commented Apr 7, 2023 at 17:47
• The signals from Voyager 1 or 2 have traveled nowhere close to the brink of our galaxy. Commented Apr 7, 2023 at 19:48