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From the top of my knowledge in the theory of EM propagation, two antennas show the same gain if used to transmit from A to B or viceversa, provided that they use the same transmission gain (reciprocity principle). And this holds regardless of reflections, directionality of the antenna and obstacles.

But is it true in practice, at least from an engineering point of view?

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A linear antenna has the same gain receiving or transmitting. Likewise, the path loss is the same in either direction. This property is called reciprocity.

However, most but not all antennas are linear. Some may have losses that increase non-linearly with increasing power. For example, the loopstick antenna is a small loop antenna made of many turns of fine wire around a ferrite rod. The ferrite rod helps concentrate the magnetic flux through the loop, giving the antenna an effective aperture much larger than its physical size. However, the ferrite saturates at even modest transmit powers. Reciprocity does not hold.

It's also likewise possible to construct a propagation medium in which reciprocity does not hold, but it requires a non-linear material. Since most propagation occurs in air which is quite linear, this is more a theoretical problem than a practical one.

However, the path and the antenna are not the whole system. There are practical issues that make wireless communication links not symmetrical, meaning if A can hear B, B may not hear A. It's not an uncommon case for one station to have a higher power transmitter, especially when one of the devices is battery powered (cell phones, Wi-Fi, ...). The receivers or transmitters on either end may likewise not have identical sensitivity or selectivity.

Furthermore, the different location of each station can lead to asymmetric communications. The hidden node problem you mention is one case. It can also be that there is a source of noise that's close to A, but far from B. In this case, B may hear A, but A may not hear B due to the higher noise floor in A's location. Related is the exposed node problem.

These issues of asymmetric link quality are very significant in the design of wireless communications in practice. A common solution is to have the station with the likely biggest, tallest, highest power antenna arbitrate access to the medium. Cellular networks take this approach: the tower tells the phones when they may transmit. Cellular towers also have wired links to each other to further improve their cooperation. It's a much more difficult problem when a central authority does not exist. See for example version two of B.A.T.M.A.N. which was developed primarily to address this problem in its mesh protocol.

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Nice answer! However, IMO the exposed node problem is not exactly affecting the link itself but the "perception" that the TX has of the channel. But in case of CSMA and the like it can cause collisions indeed. –  clabacchio Feb 13 at 15:26
    
@clabacchio true, but I say it's related because if you change "node that wants to transmit" to "node that wants to receive", you have a very similar problem that's applicable to a broader class of protocols. The interfering node not even need be an intentional transmitter: it can be noise. –  Phil Frost Feb 13 at 15:38
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Just after posting the question I though about a phenomenon that can make the link, if not physically, practically asymmetrical. It's the hidden node problem.

Image courtesy of wikipedia

If A transmits to B while also C is transmitting, there will be an interference at the receiver, in this case B. When the signal goes the other way around (from B to A), the interference may prevent B from transmitting but won't affect the quality of the signal at the receiver A.

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Yes, it is true. This is a fundamental property from physics. If it were not true, you could construct a perpetual motion machine by exploiting the assymetry.

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You can't really argue this way, since a system of two antennas is by no means closed. Energy isn't conserved but most of it is "lost in space" either way. It's not obvious on that level that the loss is the same in both directions, and indeed not true in general: as Phil Frost said, it requires that everything has a linear response. –  leftaroundabout Feb 13 at 20:08
    
@left: I took the original question to be much simpler and more basic. Anything you do to antenna A to change its gain transmitting to antenna B also effects the gain equally when B transmits to A. This is assuming the rest of the universe is passive. By envoking "gain", it also says everything is linear. It is important to first understand this basic rule, then you can make it more complicated by adding other active sources, non-linear materials, etc, but that's not what I understood the question as asking. –  Olin Lathrop Feb 13 at 20:22
    
Yeah maybe I could have specified it better, but I'm fairly aware of transmission theory. I was more interested in practical issues, including interference but not only, possibly. –  clabacchio Feb 17 at 13:46
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I noticed that fast fading was not mentioned. Spatially distributed constructive/destructive interference patterns exist from multi-path reflections between transmitter and receiver. For a device in motion, these manifest as temporal dips in the channel gain (fast fades). Whether fast-fading on forward and reverse path are the "same" depends on several things, among them, whether forward and reverse channel are on the same radio frequency, and whether forward and reverse channel are used at the same time. The question asked about symmetry "in practice". Re fast fading, the answer is No and Yes. Modulation, coding and scheduling strategies are highly optimized to be aware of fast fading. So propagation path asymmetry may indeed be present in the system, but clever designs are immune to this and even take advantage of it so that it is not noticed by end users.

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