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Like ethernet cable, optical fiber. We have a square wave signal, do we just send that squre-wave signal directly down along the cable? If we do send it directly, why we can not send the square-wave signal directly into the air wireless channel? What is the reason behind? Is it because the cable or wire are more stable but wireless is very unstable?

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    \$\begingroup\$ You can send a square wave over wireless also, however, the wireless channel has bandwidth limitations which will cause distortion in the received square wave. Also, if there is any other RF signal around, it the two signals will interfere with each other. \$\endgroup\$ – mkeith Dec 31 '20 at 7:50
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    \$\begingroup\$ Technically you can, but it's not a good idea. For starters, the first problem is that an ideal square wave contains an infinite number of different frequencies (odd harmonics), which makes the communication system pretty inefficient and prone to interference. Spark-gap transmitters have been banned since 70 years ago due to the same reason. \$\endgroup\$ – 比尔盖子 Dec 31 '20 at 7:51
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    \$\begingroup\$ As far as interference goes, maybe the best way to say it is that using a wire or fiber-optic cable gives you a PRIVATE channel. When you transmit in atmosphere or space, that is a PUBLIC channel, so there is much more interference. Square wave brakes all the rules and interferes with other communications which are already on the public channels. \$\endgroup\$ – mkeith Dec 31 '20 at 9:41
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    \$\begingroup\$ @YuanXiao A shielded wired cable belongs to yourself, from 0-10 GHz, the frequencies are all yours. But the wireless spectrum is a limited public resource shared by everyone, you cannot just use whatever frequencies without creating harmful interference to others. The frequencies, bandwidth, and power are limited by both technical and legal standards. For example, 802.11n Wi-Fi, there's only 40 MHz of bandwidth for you. Also, you often have to use your limited power in the most efficient fashion, so you should not waste power to transmit on useless frequencies that contain little information. \$\endgroup\$ – 比尔盖子 Dec 31 '20 at 9:50
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    \$\begingroup\$ @比尔盖子: That's the real answer, and you should write it as an answer rather than just a comment. If a cable can accommodate bandwidth from DC-1MHz, and will harmlessly attenuate anything beyond, potential bandwidth which isn't used by the devices connected to the cable won't be usable by anything else either, so there's no need to avoid wasting bandwidth. By contrast, when communicating wirelessly at non-trivial distances or power levels, it's necessary to avoid generating content at any frequencies one isn't deliberately using, so as to allow others to use those frequencies. \$\endgroup\$ – supercat Dec 31 '20 at 21:16
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Due to the sharp edges, a square wave has a wide spectrum with lots of harmonics.

enter image description here

You could send that over the air with an antenna, but:

1- Signal shape will be distorted at the receiver due to limited bandwidth

2- It will use a lot more bandwidth than it needs to. For radio transmission you want to use as little bandwidth as you can, and not emit any energy at frequencies you don't use, to leave other frequencies available for other users, other channels, etc. So it would have terrible spectrum utilization. This is why digital signals are excellent sources of electromagnetic interference and noise, and a poor way to make an actual useful transmitter. So, pretty good if you want to make a wideband radio jammer, but not an actual transmitter.

3- It would have very poor SNR at the receiver

4- Unlike cables, radio doesn't go down to DC, so if the digital data doesn't contain the same amounts of zeros and ones, the result would be shifted

That's why a much better choice is to use a modulation and encoding suited for radio transmission. A simple encoding would be AM-modulating a carrier, for example.

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    \$\begingroup\$ Note that lots of digital cable connections also balance the zeroes and ones so they can use capacitor or transformer coupling! There are de-facto standard ways of doing this, now. Search for "line coding" \$\endgroup\$ – user253751 Dec 31 '20 at 20:15
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tl; dr: RF needs a carrier, cable can use baseband. Both are band-limited, RF systems using carriers more so.

A perfect square wave has infinite harmonics. A good square wave has a large number of them. Because of this, square waves use a lot of bandwidth for the information they carry. They’re very inefficient. This limits their use to lower speed signaling, even on cables.

Look at serdes protocols like PCI Express or Gbit Ethernet. You will see that they don’t use square waves, but more optimized baseband coding to squeeze more throughput out of the cable.

Similarly, a square wave on an RF carrier is very inefficient use of spectrum (though it’s possible - primitive on-off keying does exactly that.) That said, it’s possible to send very-high bandwidth digital data over RF. The challenge is to do that efficiently, within the limits of the spectrum being used, and over a carrier that a receiver can work with and robustly recover the data.

And finally, wireless systems can’t represent a DC connection or low frequency directly. You can only get an approximate derivative of the changes in flux strength at the receiver side. For RF work need to use a coding system that would behave well as if it were AC coupled onto a wire. Using a carrier overcomes this problem.

That said, look into TEMPEST. This is a group of passive espionage techniques that extract information from emissions leaked digital and analog equipment - that is, from baseband waves (square and otherwise) that find their way into RF.

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Along with all the bandwidth and other considerations mentioned, the main reason you don't transmit your data directly is that everyone would be transmitting at the same frequency.

Take Ethernet. It uses two (or more) pairs of twisted wires to carry two separate channels of information (your Ethernet card sends data on one pair and receives it on the other pair.)

If you just directly broadcast the signals from each pair, then you couldn't separate them.

The wires confine the signals do that they go pretty much only where they are intended to go.

If you just modulate each onto a carrier, you can separate them - but then you have know which carrier frequency is used for what.

That would work for a few channels, but would get difficult really quick as you add more channels (users.)

WiFi gets around that by having multiple channels and using some intelligence to decide who uses which carrier frequency for what and for how long. It also has WiFi routers which coordinate the end users and actively tries to avoid interference from other routers and users.

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  • \$\begingroup\$ When I learned about Ethernet, there was no twisted pair (it used coax), and was transmitting at the same frequency. Usually all machines in the same room used the same cable, and the more machines tried to send at the same time, the more collisions happened and the slower it became. The analogy to sending through the „ether“ is quite obvious. Today’s LAN are usually operating totally different, and I sometimes wonder why the name is still used. Ah, nostalgia! ☺️ \$\endgroup\$ – Axel Dec 31 '20 at 16:19
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    \$\begingroup\$ I am not knocking your answer. But gigabit ethernet uses all the pairs for simultaneous transmit and receive. Yes. It can transmit and receive at the same time on the same pair. \$\endgroup\$ – mkeith Dec 31 '20 at 19:21
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The physics of antennas plays a large part. To understand this, you must consider the Fourier transform of your signal. For a simple binary NRZ code, where 0 is 0V and 1 is some voltage, Most of the Fourier energy is contained within the frequency range 0-B/2, where B is your bitrate. But antennas are frequency-selective: at the high end, an efficient non-directional antenna has an effective signal collecting area that declines as the square of frequency. At the low end, efficiency suffers if the antenna is much less than a wavelength in dimension. The entire story is much more complicated than above, but any attempt to ameliorate the frequency dependence in some parameters increases the frequency dependence in other parameters. However, an antenna where the ratio of the highest to lowest frequency of operation is small can have nearly constant parameters over that narrow frequency range. Unfortunately, the NRZ signal has a infinite ratio, since the lowest frequency is zero! Any attempt to send a NRZ signal directly through a pair of antennas will yield an extremely distorted signal.

The usual cure is to modulate a wave that has a frequency, f, that is at least several times your bitrate. This moves the Fourier energy up to a band, perhaps f±B/2, with a small ratio of highest to lowest frequency. Then, antennas are well behaved, and you may recover the received data with a demodulator.

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The voltage or current you apply at one end of a pair of wires can be detected directly at the other end. It's like pulling on one end of a tight string -- you can feel the pull at the other end.

When communicating wirelessly there is no quality of the source that can be directly felt or measured at the other end. It's like you're standing in one end of a pool. You can hold your hand at any height and the water at the other end is unchanged -- the height of your hand is undetectable. If you move your hand up and down rapidly, however, you can make a wave that propagates to the other side of the pool where it can be felt and measured.

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True square waves do not exist because they require an infinite frequency range, in the real world they will always get rounded off a bit.

Copper and fiber have an awful lot more frequency range than anything you can send over a radio signal and thus they don't get rounded off as much.

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None of them are actually a square wave. They all are approximations. It would take a noise free channel with infinite bandwidth to transmit a true square wave.

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