If they be placed closer, there will be strong correlation between their signals, therefore the utility of MIMO is reduced.

lambda/2 is somewhat arbitraty, for best performance you should aim for ~4 lambda and for most compact 3/8 lambda may be still marginally useful

Two major constraints are involved. From one side, mutual coupling is inversely proportional to separation between antennas. From other side, at separation distances above lambda/2 main beam is split into several beams, viz. grating lobes appear. Optimal spacing is always a trade-off

In simple words one has to perform trade-off between mutual coupling and the grating lobes that waste power and may appear as source of interference...What about the type of the antennas at the transmitter and receiver i.e their directivity, is there any involvement of array factor for reduction of mutual coupling and grating lobes?

Grating lobes are defined by ratio array pitch to lambda. Mutual coupling, to be more precise, is a function of pitch to lambda and, to some extent, details of element construction. In many cases more inter-element coupling allows to get more bandwidth, for example, in Vivaldi arrays.

Actually, in a MIMO system, grating lobes are not such a problem. In a classical multi-element antenna array the goal is to let all elements work together to cast a focused beam towards the receiver (or to aim the receiver at the transmitter). There is typically only one beam and everything not in it, e.g. in grating lobes, is lost (*). The idea behind MIMO is the complete opposite of this: there is a path from each transmit antenna to each receive antenna and these paths should be as different as possible. This is why the antennas should not be too close together. The paths between transmit and receive antennas are typically non-line-of-sight, with as much scattering as possible. The classical array theory, with the array factor and grating lobes etc isn't really relevant here because this only holds for the line-of-sight situation.

(*) an array may have multiple beams, e.g. communicating with different transceivers, but each of these links has a main beam and side lobes.

"...The classical array theory, with the array factor and grating lobes etc isn't really relevant here because this only holds for the line-of-sight situation...."

Thanks Gert Cuyperts! You have nicely pointed out the difference. Yes, classical array has nothing to do with MIMO antenna spacing.

Hi Gert,

As you mentioned, in MIMO system, the antenna should not be too close together.

I wonder if there is any rule-of-thumb on what is the minimum and maximum distance between adjacent antennas?

Thanks!

A distance of lambda/4 is a minimum to get a significant change in the field distribution. In a standing wave pattern this would be enough to go from a node to an antinode, which would be perfect for MIMO! So that would be my very lower limit. Because of coupling between the antennas a larger spacing is desirable, the lamba/2 mentioned by Mr Lodro would be a good rule-of-thumb. I don't think there is a reasonable upper limit.

(Putting the antennas _very_ far apart would probably complicate the receiver design in case of very high symbol rates, because the symbols arriving at the antennas may no longer be synchronized. For a spacing of 10 meters, this would occur for symbol rates of 30 megasymbols. If this is known in advance, I guess the receiver can take it into account. I am not an expert in this field)

For reduction in mutual coupling, distance between MIMO elements can be less than quarter wave length, but they should be separated by some intermediates parasitic elements whose electrical length/current path length (vertical) is more than quarter wavelength. Some of the popular shapes available in literature are: tree like structures, curve shaped protruded ground plane etc. Papers on these techniques are widely available in IEEE Explorer.

plz,i want to know is there is any limit to the minimum separation distance between element even if there is a structure between them to reduce coupling?

You should avoid inter-element spicing within a MIMO antenna system to be narrow (less than half wavelength) in order to avoid unwanted mutual coupling effects. On the other, inter-element spacing beyond one wavelength is also undesirable in order to reduce multiple sidelobes in the radiation pattern and maintain enough gain in the main lobe. Therefore, an optimum choice for the inter-element spacing within a MIMO antenna system is usually half-wavelength.

to achieve satisfactory isolation

To have acceptable isolation, the minimum distance needs to be maintained in MIMO systems if you are not using any decoupling networks or other sort of techniques.

Grating lobes in an broadside or end fire array can be reduced by maintaining a separation of max lambda/2 or smaller of it between the elements.

I'm sorry, but I have an alternative and marginal point of view.

In my opinion, mutual coupling is not critical for MIMO systems with channel estimation. The question is about the limit of values of this mutual coupling that is dependent on the accuracy of channel estimations.

You can use on receive antennas array Neural Networks (NN) as well. The NNs will automatically take into account the mutual coupling of the transmitting antennas.

On the other hand, you can use electrical small antennas with sizes lambda/10 or less.

Conference Paper 60 years of electrically small antennas theory

In this case, the distance between antennas can be less than lambda/10. And to decrease mutual coupling in this case, you can use metamaterials with cells less than lambda/100:

Conference Paper Metamaterials on antenna solutions

In this regards the limit to the minimum separation distance between transmit antenna elements will be dependent on electrical breakdown (breakthrough, disruption, perforation, rupture) or capacitive short circuit between neighbors elements as well.

I agree with Gert Cuypers that "the paths between transmit and receive antennas are typically non-line-of-sight, with as much scattering as possible". In this regard, we don't have a limit on the maximum distance between transmitting antennas if signals lines can be connected to the antenna elements. By using laser channels for providing signals to transmit radio channels, the MIMO system can have the distance between elements hundreds and thousands of kilometers. As an example, such a very large system can be used to interplanetary MIMO communication in Space. In the general case, the distance between transmitting MIMO antennas can be not-equidistance.

To obtain a smooth antenna gain pattern without grating lobes, a maximum element spacing between the antenna elements is assumed to be λ/2 or less.

It is coming from Bessel function of zero kind that descibe the expectation value between two channel responses with delat(t) time difference. Hence the lambda is measued by Doppler frequency not the carrier frequency of the signal.

Upper Bound to avoid side loops: see below animation (increasing the distance)

https://www.youtube.com/watch?v=YgEg9wMU25E

From EM point of view, to prefent adjacent two anteenas from working in near-field and looks like one antenna (Fraunhofer diffraction and Fresnel diffraction), the recommended distance is lambda over two but no strong proven behind that!