How does two way communication between a baseband modem (on a phone) and a mobile phone mast work?

Question

I've been thinking absent-mindedly about how mobile phone communication works when I wondered how something as power efficient as a mobile phone can have such a powerful radio. I am guessing that most celltowers have a transmit power of, say, 100w (I have no evidence, but the point is that it's a lot), and they have a range of >6km. What I want to know is how can such a power constrained radio (I'm guessing max 2w) transmit a receivable signal to the phone tower?

I have tried googling it but of course it just comes up with a bunch of very basic and irrelevant descriptions of how a celltower works.

Of course I have absolutely no knowledge of radio stuff besides the highschool physics stuff, so I am not able to do any calculations to see whether my question is unjustified.

Answer 1

Cell towers only transmit around 10 watts usually. Sometimes up to 50 or so in urban areas. Your phone can transmit up to 2 watts.

Transmit power does obviously have a big effect on the range of a signal, but it is not nearly as much as you would think due to the 1/r2 relationship of radio waves propagating out from the source. If your transmitter puts out 4 times as much power, you only get twice the range. 16 times the power, only 4 times the range. 100 times the power... 10 times the range.

The main advantage a cell tower has over your phone is in the size, power, complexity, and quality of the low-noise amplifier in its receiver. Since the tower is not limited so much by size and cost, they can put a really high quality amplifier in the tower (probably a noise figure of 1-2 dB...) and very effective low-loss filters in front of the amp (probably a cavity filter which is 10x the size and weight of a cell phone all by itself). This has a huge effect on the quality of the received signal compared to the cheap, small stuff that has to fit into the cell phone.

You might think that the tower's big antenna means it can "hear" small signals better compared to the phone's tiny antenna, but this is not true. The path from the cell tower to the phone is 100% symmetrical to the reverse path. In other words, when the tower transmits to the phone it gets a big benefit from its large antenna because the power is transmitted mostly in the direction of the phone, but this same benefit is in effect when the tower is receiving signals from the phone. The phone's tiny antenna has equally lousy performance when receiving signals from the tower as it does when it is transmitting back out to the tower.

Answer 2

Here what we call propagation equations : https://en.wikipedia.org/wiki/Friis_transmission_equation.

To explain it with hands, the Base Station (BTS) (your celltower) is emitting a signal with a power of 100 W (+50 dBm) using an anisotropic antenna ( all directions). But this is attenuated ( power decreased) with the square of the distance to your cell phone . Suppose the attenuation is 75 dBm. This meens your cellphone will receive +50 dBm - 75 dBm = -25 dBm.

Suppose your cellphone has a sensitivity of -100 dBm (can detect any signal above this level). So your phone can easily receive the -25 dbm.

If you think about it in the other side, from Cellphone to BTS : Suppose a emitting power of 1 mW ( 0 dBm) , the BTS will receive 0 - 75 dBm = -75 dBm ( attenuation is the same as the fist case) and suppose the sensitivity of this BTS is -120 dBm . The -75 dBm received by the BTS is fare above it limit and the signal will be detected easily.

Sorry for my English.

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