Last Updated on June 4, 2026 by John Berry
Are paths reciprocal? It’s reasonable to assume they are, but we need to be more specific because in some cases, they’re not. Here’s an analysis supporting the assumption. And does it matter? Understanding about reciprocity matters if we want to be accurate about the reasons for received signals.
Here’s a clip from Dr Kate Zawdie’s presentation at HamSCI 2024. She’s a research physicist at the US Naval Research Laboratory. Her topic was HF propagation modelling by ray tracing, and the clip is from a question at the end.
Kate’s answer sets the context, at least for HF paths. Reciprocity is a reasonable assumption in this context, but we need to understand some of the exceptions.
One approach to answering this question fully is to break it down, to analyse each primitive on its own. We can then draw conclusion when primitives are aggregated to determine the path loss for each geometry and mode.
Just before diving in though, the economist’s adage, ‘all other things being equal’ applies. I’ve expanded on this as an annex below in this page. All the technical parameters that so often get forgotten in the analysis must be normalised.
We also need to know what we mean by ‘reciprocal’: about the same, or exactly the same? And if about the same, how much difference in path loss between go and return paths is permissible? I’ll include some thoughts on this below.
Given the above, here’s the analysis with a few examples.
Free Space component
All propagation modes and geometries have a free space component.
Two stations, A and B, communicating through the troposphere typically do so by diffraction. But we talk of diffraction loss as a loss over free space. The free space component depends only on frequency and distance. And hence the free space component is the same from A to B as from B to A.
Two stations communicating via chordal hop propagation typically do so with several discernible segments:
- a lower atmosphere component comprising a free space loss up to the ionosphere,
- an excess loss (over free space) component as the wave enters the ionosphere,
- then an excess loss (over free space) as the wave transits the ionosphere, being reflected and refracted,
- an excess loss (over free space) component as the wave exits the ionosphere, and
- then a lower atmosphere free space component down to the distant station.
Of course, the portion of the path through the ionosphere may experience absorption. But there’s still a free space component. And if the total path distance is the same A to B and B to A, the free space loss component will be the same.
Multiple paths
The Free Space Loss equation contains the term 20logd, where d is distance. This gives the fact that loss rises by 6dB per doubling distance. If a chordal hop path is 7,000km from A to B say, it’s unlikely to be more than 10% greater distance in the other direction. This allows for a different point of entry to the ionosphere and a different point of exit and some different return distances. At 14MHz, a 7,000km path has a free space loss of 132.3dB while at 10% more, a 7,700km path has a loss of 133.1dB. Just 0.8dB different – not discernible on an S-meter, with no discernible readability change.
If we then add the inclusion of multiple rays describing the signal path to, and through, the ionosphere, and that the signal received is the aggregate of that from all paths, reciprocity seems even more likely. The idea of having two distinct and different paths A-B and B-A that would result in different path losses might be possible, but low in probability. Yes, there will be a difference, but that difference will be small. I contend therefore that over all but the most diverse paths, the free space component of path loss is reciprocal.
Excess loss components
Diffraction
For diffraction loss (over Free Space) for smooth Earth and beyond the horizon tropospheric propagation cases, the wave encounters the same terrain, buildings and vegetation in each direction. It’s the same (bulging) Earth after all. And the path profiles will be nearly identical. All just the other way round. The diffraction loss will therefore be about the same whether propagating A-B or B-A. ITU-R Rec. P.526-15 illustrates this in formulae and nomographs for smooth Earth and beyond the horizon diffraction loss calculations.
For diffraction loss (over free Space) over a VHF rough tropospheric path, the path can be modelled as a series of cylinders laid across the path, each a separate obstruction. Each cylinder can be considered as a knife edge, then modified for roundness. Importantly its contribution to the total loss is independent of where in the path it occurs. The cylinder model also accounts for sub-path losses between the cylinders. It does however uniquely identify the loss due to the first sub-path intrusion forward of the transmitter. This does mean that the A-B (TX-RX) path can exhibit slightly different loss compared with the B-A. But the maximum value of sub-path loss is low, even for a fully obstructed lower half of the Fresnel zone. So, the difference will mostly be small (and under 6dB) compared to the total path loss.
The two diagrams above give the ideas, first of the cylinders, and then of the sub-path losses.
Absorption
For absorption loss as an HF wave enters and propagates the ionosphere, the A-B path and the B-A path will likely differ. Ray tracing and the many possible modes suggest that there are many possible paths into and through the ionosphere, even in either direction. For prevalent simple modes like 1F1 or even chordal hop, it’s unlikely that the absorption distances will differ much and hence the absorption loss will be about the same. But, yes, a 1F1Es1F1 mode has plenty of chance for difference A-B over B-A, but the occurrence of such a mode is low.
I therefore contend that differences in the excess losses caused by diffraction, absorption, and reflection are small and hence the excess loss component of path loss is reciprocal.
Paths are reciprocal
It’s easy to argue that for simple paths in the troposphere and ionosphere, paths between two stations are reciprocal – that for the same technical conditions at each terminal, the same signal level will be received at each receiver.
It’s also easy to see that for complex paths, and where the ionosphere is different at one end of the link, it may be that some slight differences in received signal will be encountered. I’ve argued here that in most cases, the differences will be low. But equally, in a small number of cases, they may be significant.
The one exception to all of this is where paths are victim to polarisation distortion because of the Earth’s magnetic field – the Faraday effect. EME signals, for example, suffer significant distortion as the polarisation rotates under the influence of the field, and this loss can be over 20dB. Strictly it’s not a path loss, but its effect is still felt!
So to conclude
It’s a reasonable assumption that paths are reciprocal. And to make such a generalisation, I am not having to reduce the number of unique path geometries much. Those instances where differences are apparent will be of low frequency of occurrence.
I’d assert that around 90% of all paths will result in a received signal that is within 3dB (half an S-point), and perhaps 95% within 6dB (one S-point).
So absent an exhaustive study to catalogue all possible paths and ionospheres to trap the errors and probabilities, there’s my summary: paths are reciprocal.
Technical parameters
Decibels
When building evidence, the same conditions must be used. The power at the antennas at both ends must be the same. If one station is running 1kW and the other 100W, it’s no surprise when one path is, apparently, less lossy than the other. There will be 10dB difference – the difference between the powers. All sensitivities, noise figures and other RF parameters that determine how well a signal will be transmitted and received must be normalised.
Time
When building evidence, the same point in time must be used. The nature of fading shows that a path may fade seconds after a transmission is made. In meteor scatter, seconds become milliseconds. So, the return ‘over’ may well be several decibels – even 10s of decibels – below (or above) the original used as reference. Since time marches on in propagation, it’s impossible to assess a path at the same time. It is however possible to understand if fading is present, appropriately questioning conclusion validity. And it’s possible to assess if the path itself has changed. An extreme example would be HF propagation by short path, then by long path a few minutes later.
Frequency
The same is true of frequency. The frequency must be about the same. Path loss in free space, by diffraction, and via ionised media is a function of frequency. And fading is frequency dependent. It would be wrong to use one frequency for the go, and another for the return.
Antennas
Simply, for the same frequency, antenna responses are reciprocal. There’s no concept of the transmit polar response and the receive polar response, or the transmit gain and the receive gain. It’s simply the (singular) polar response, the (singular) gain. Consider the case where one station is running a 5-element HF beam and the other a short, trapped vertical using a poor ground plane. The total loss or gain is the same in each direction. One antenna generates a poor effective radiated power and the other a good received signal, and vice versa. The decibels add on each side to give balance.