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This is a pretty simple question. [The answer might not be simple :( ]

If I am using a directional antenna, can I used Antenna gain $G_T=1$ as I am considering Rician Fading between transmitter and receiver?

On the contrary, if I am using $G_T>1$, then do I use Rayleigh fading instead of Rician?

Explanations of System Model:

The antenna is mounted under the roof-top in an indoor environment. (e.g. indoor stadiums, warehouses, office building/rooms etc.). The Antenna is directed towards the ground, so that the signal-loss in unwanted direction is minimized, (unlike isotropic antenna where energy is radiated in $360^o$).

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    $\begingroup$ It is not clear what you are asking. In general., whether the _ antenna gain is $1$ or more than $1$, and whether the antenna is directional or not has little to do with modeling the channel fading as Rician or Rayleigh. So, please give some moire details about your system; else your question is likely to get closed as Unclear what you are asking. $\endgroup$ – Dilip Sarwate Sep 25 '18 at 5:34
  • $\begingroup$ I have edited the question. Please let me know if you need more details. $\endgroup$ – Sjaffry Sep 25 '18 at 5:40
  • $\begingroup$ I don't expect that your antenna has significantly high gain to change the channel fading characteristics if you have a fixed antenna with mobile users that can be located in non-specific locations. For users that have line-of-sight proximity to your antenna the channel may likely be more Rician however for the typical user the channel would more likely be better approximated by Rayleigh. See my more detailed answer below. $\endgroup$ – Dan Boschen Sep 25 '18 at 11:43
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The gain is given by the antenna used, and for directional antennas the gain would be much greater than 1. $G_T$ is typically given as the antenna gain compared to an isotropic antenna which radiates or receives equally in all directions. (So $G_T=1$ corresponds to a perfect isotropic antenna, not a directional one).

For example, the azimuth pattern below is for a Yagi antenna with a gain of 15 dBi, which shows the highest gain is achieved when the antenna is pointed in the 90° direction, along with other sidelobes that are also sensitive but significantly less gain (for example approximately -4 dBi at 45° and 135°). Not shown but the elevation pattern also has sidelobes that approach 0 dBi.

Yagi antenna pattern

image source: Cisco white-paper on antenna patters

Rayleigh fading is a statistical model for the channel with multiple reflected propagation paths without any particular path being overly dominant, while Ricean results is the model for the channel that has multiple reflected propagation paths along with a dominant (usually direct) path. Rayleigh fading is typically a reasonable model for heavily urban areas while Rician is often used for SatCom. That said, a highly directional antenna can have the benefit of minimizing reflected paths from other spatial directions and therefore can make an otherwise Rayleigh channel appear to be more Rician, assuming that the antenna is pointed at a propagation path that is significantly strong enough, and the environment is not one that would still result in multiple paths of random delay within the main lobe of the antenna without a single dominant propagation path.

So a highly directional antenna can make a Rayleigh channel into a Rician channel, but that is not guaranteed to do so. It may seem strange at first to state that the antenna can change the channel, but this is really no different than all the buildings, mountains and other objects causing the reflections that also create the channel: the presence or absence of reflections is what creates the channel and the type of antenna is just one of the objects considered in determining the reflection environment.

For further discussion on Rayleigh vs Rician fading see Rayleigh fading with frequency selective fading channel

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  • $\begingroup$ Thanks for the detailed answer. Yes, I understand the difference between Rician and Rayleigh. In one of my research, I claimed that I am using a directional antenna and for this reason, I used Rician Channel but completely ignored directivity assuming it will suffice. Now that I got comments, I am looking at how to integrate directivity of the antenna as well. Thanks again $\endgroup$ – Sjaffry Sep 25 '18 at 21:53
  • $\begingroup$ Can you please comment, what parameters determine the main lobes of an antenna as I understand that as the number of lobes increases, so the gain of antenna decrease. Hope this is not a stupid question :( $\endgroup$ – Sjaffry Sep 26 '18 at 1:33
  • $\begingroup$ I don't have a general quick answer as it depends on the antenna structure, but no there is not a relationship that has the gain decreasing as the number of lobes increases; a linear phased array is a straightforward example that has the gain increasing in the mainlobe as the number of antenna elements increases, which also increases the number of side-lobes. $\endgroup$ – Dan Boschen Sep 26 '18 at 1:37
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    $\begingroup$ Did you mean as the number of "main lobes" increases, the gain decreases? I thought you were referring to total sidelobes with just one main lobe. Ultimately if there are no real losses (and in actual implementation there would be so this would be the theoretically best gain), if you integrate over the entire 3D pattern the total energy would be the same regardless of pattern, so if you have high gain that implies high directivity; narrow main lobe, lower sidelobes. If you have two main lobes of similar shape in different directions then yes the gain in each would be less all else being equal $\endgroup$ – Dan Boschen Sep 26 '18 at 1:41
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    $\begingroup$ I looked and yes those make sense to me (noting that the width of each lobe is reduced when multiple lobes exist, so because of that they can each have the same peak gain). The pattern that would exist depends very much on the type of antenna. You perhaps may be considering antenna array patterns and this link may help you: eceweb1.rutgers.edu/~orfanidi/ewa/ch22.pdf The math to generate the pattern is very similar to the math in the DFT so wtih small modification you can use the DFT to create the patterns, changing the frequency axis to spherical angle! Have fun. $\endgroup$ – Dan Boschen Sep 26 '18 at 2:19

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