Spacing between antennas in an antenna array for ind. fading

[senaydud]

Hello people,
I have previously asked this question on the board but in a different section, however I couldnt have received a satisfactory reply. I want to take a chance in this section that is more related with Antennas. Please read that follows;

The fact is: "for independent fading, spacing between antennas should be much greater than half wavelength in an antenna array".
My question is; What is the mathematical explanation for that? I need some Maths please.

 

[RF-OM]

Re: Spacing between antennas in an antenna array for ind. fa

You may check any book on radio link or channel modeling. There are different type of fading and different bands, modulations and so on. There probably no one answer that will fit any situation.

 

[Jone]

Re: Spacing between antennas in an antenna array for ind. fa

Yes, check any book on wireless communications, Molisch, Rappaport, Tse, Goldsmith. See especially the the sections on diversity.

In a Rayleigh channel where all waves have a uniform azimuthal distribution, a separation of 0.5 wavelengths or more gives uncorrelated data. Knowing this, you then have to find an antenna array where the elements can be placed this close (azuming you want to minimize the antenna).

For cases where the angular spread is much less, like outdoors, 0.5 wavelengths is not enough. For example base station array elements are separated by 10-20 wavelengths because of little scattering at the top mast.

 

[vfone]

Re: Spacing between antennas in an antenna array for ind. fa

After a lot of experiments using different small antennas I found that the minimum spacing between antennas (to get diversity), its a “magic number” of minimum 20dB isolation between antennas.

 

[Jone]

Re: Spacing between antennas in an antenna array for ind. fa

After a lot of experiments using different small antennas I found that the minimum spacing between antennas (to get diversity), its a “magic number” of minimum 20dB isolation between antennas.

Don't mix up coupling (isolation) and correlation. Good isolation doesn't necessary give you independent signals since this depends on the pure channel properties (i.e. antenna is not a part of the channel). For good diversity performance one need equal MEGs on the different branches.

So first you look at the channel properties for and see what element distance is required. This depens on teh angular spread. Then you find an antenna for this.

I'd say an isolation of 10 dB can be good enough if the compactness comes into play.

 

[vfone]

Re: Spacing between antennas in an antenna array for ind. fa

Of course you need correlation, but 10dB coupling will make antennas to behave more or less like only one, whatever correlation you have.
20dB is the minimum coupling to be in the “headache free zone”.

 

[Mustafa_Engineer]

Re: Spacing between antennas in an antenna array for ind. fa

hi

 

[senaydud]

The documents you have uploaded, do they have the answer to my question or what?

 

[RF-OM]

Re: Spacing between antennas in an antenna array for ind. fa

There are at least two phenomena that require antenna diversity: fading and multipath. Today multipath is probably more popular because contemporary urban and in-building communications link are more affected by multipath. Fading is noticeable for long HF links. For multipath distance between antennas may be relatively short and depends heavily on antennas heights. For fading the process is totally different. It creates when wave traveling trough ionosphere for long way. Fading requires much longer distance between antennas. I designed diversity stations for HF radio links and we used receiving stations with about 100 or 200 km separation. Received signals were then translated trough long distance phone coaxial cable systems and adding together with special circuit which allows adjusting of signals amplitude and phase. For most critical links there were more than two stations.

 

[senaydud]

Wow, I didnt know that the distance is sometimes kept that long, thanks for that valuable information. However my concern is for small scaled devices, where the spacing is in millimeters and it is always accepted as half the wavelength of transmitted signal.

 

[RF-OM]

Re: Spacing between antennas in an antenna array for ind. fa

I put this distance just for an example. It is real for HF radio lines but not for multipath. The underlying mechanisms in fading and multipath are different but both of them independent from your radio. They depend on radio path properties. If your devices are so close they probably into near field zone and in this case you need to use filed solver to determine the real picture what is going on around your antennas. Any way the first step is to answer the question what do you have: fading, multipath or both? Sometimes both are possible especially for moving radios. And keep in mind what vfone told you about 20 dB. It is reasonable practical consideration.

 

[senaydud]

No, my concern is fading. If you take a look at many and many journals related to antenna arrays which are built to obtain independent fading channels, then you will encounter that the spacing is always mandated to be kept at the half of the wavelength. Especially for MIMO, this is the rule of thumb. I am just trying to find out the fact behind it. there should be a derivation for this lambda/2 constraint.

 

[RF-OM]

Re: Spacing between antennas in an antenna array for ind. fa

I have practical experience only with HF fading. There the distance of half of the wavelength often (if not always) is not enough. MIMO applications suggest much higher frequencies. If you will model your radio link or channel with corresponding model you will see how the resulting Pr is changing with variable parameters and it may be much easier to make some conclusion.

In my GHz applications multipath is the major problem, but sometimes I have a fading from the human who crosses the line-of-sight. This is actually the random process, but even in this case it is possible to model it. Therefore, I think that modeling the link will help you.

Sorry, but I have no formulas that you asked.

 

[Jone]

Re: Spacing between antennas in an antenna array for ind. fa

Just have to comment on the article "CONSIDERATION OF MUTUAL COUPLING" in Progress In Electromagnetics Research, uploaded by Mustafa.

Seems like the opponents are not really reading through these articles before they're published. In this article the authors haven't understood the logarithmic nature of decibels, when they claim that -40 dB is much better than -30 dB in return loss of an antenna. It's sad that the quality of publications seem to decrease over the years. Too many people publish something, just to publish.

 

[vfone]

Re: Spacing between antennas in an antenna array for ind. fa

It's sad that the quality of publications seem to decrease over the years. Too many people publish something, just to publish.

“Writers don't need love; all they require is money.” - - John Osborne