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

Question

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.

Answer 1

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.

Answer 2

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.