What you might think is a single antenna, in MIMO systems, may instead be a radome which contains multiple antenna elements. Constructive and destructive interference are used to steer beams in different directions. Clever stuff. The goal, of course, is to propagate the signal in a given RF channel in multiple directions, carrying different data streams in each direction, and have the receiver(s) be capable of receiving the signal along multiple propagation paths, hopefully highly uncorrelated.

This link shows the design of several different types of MIMO antennas, used for LTE.

http://www.4gamericas.org/documents/MIMO%20and%20Smart%20Antennas_July%202013_FINAL.pdf

I thinks you might find your answer by searching about keyword "directional antennas" which propagate electromagnetic waves in different spatial domains.

Thank you Albert for your useful contribution to answer my question. The link which you supplied contains a highly informative white paper about the different antenna array configurations used in LTE and their conditions of use in the practical system.

ONE important point is the case of MIMOs for spatial multiplexing which i was interested in, the independence between the different paths is  achieved by:

- Cross polarization of the antennas

- Increasing the separation between the antennas to multiple of the wavelengths.

- The presence of rich multipath transmission mode. Rich multipath transmission decorrelates the signals from different paths making them separable.

I would like to thank also the colleagues Abolfazl  and Talha for their contributions

waiting for more answers.

Basically, multiple antenna used for a space diversity. Thus radiation source point and/or receive points are physically placed at different point in a space vertically stacked on a same mast with a space of about a wavelength or multiple of it. This provides two separate journey path to signals. The effect of fading at any point of time is different on different path. Signal is same but devided at transmitter and combined at receiver. This ensures availability of signal at Rx

Dear Abdelhalim,

In MIMO systems or in any multiple sensor system, the aim is to maximize the number of channels waves can propagate through, in this case for communication purposes.

The goal is to have a MIMO matrix H of maximum rank, and it has to do first with the field itself, so the propagation environment, andalso a little bit on the antenna due to mutual coupling (but let's say it's second order, and I don't discuss that here).

So what you want to have is the signals received by each antenna uncorrelated from each other. This has to do with the coherence length of the wave field, namely, the minimal distance between two stastically uncorrelated points of a wavefield.

Namely, if you're in a very complex environment, let's say indoor such as in a house or even worth, in a chaotic cavity, the coherence length of the field tends toward the diffraction limit, that is, half a wavelength, e.g. about 6cm for Wifi. This is due to the fact that waves and scattered and reverberated a lot of time in the medium and the field, which is the superposition of all the scattered/reflected waves, is random (like a speckle in optics), and varies very fast. Yet it cannot vary faster than the diffraction limit since only propagating waves are involved. This is why in most boxes, and routers, antenna spacing for 2.45 GHz Wifi is about 6cm. Note that this assumes same polarization: indeed, playing with polarization adds up degrees of freedom since two orthogonally polarized antennas are naturally uncorrelated.

Now this coherence length can be much higher than the diffraction limit, and in this case using MIMO systems with haklf wavelength spaced antennas is useless. This is the case if you want to communicate between two arrays in free space, let's say for satellite communications separated by distance D. In this case, the coherence length of the field on either array is given roughly by lambda*D/A, with lambda the wavelength, D the distance, and A the typical size of the array. It is roughly the size of the focal spot that could be obtained on one of the array if one focuses waves onto it with the first array. That means that MIMO communications will be useless in this case, unless antennas are spaced by kilometers... A simple way to understand that is if you consider just two wave sources: seen from a short distance they interfere, but seen from large distances (larger then Fraunhofer distance) they behave as a point source, namely they are completely correlated...

Of course in various situations such as urban environment, etc... the coherence length of the field, and hence minimum recommended antenna spacing will vary between the diffraction limit and much larger typical lengths, depending on the complexity of the propagation medium, the density of scatterers, the reverberation time of the waves, etc...

So, long story short, talking about MIMO systems and antenna spacing is meaningless unless you specify the medium in which you use this system. The more complex the medium, the closer you can put your antennas, limited to half a wavelength. This applies by the way to any multiple sensor system based on waves and interference.

For text on coherence and waves, I recommend reading Born and Wolf, "Principles of optics", and for MIMO systems, a book by Pr Paulraj and colleagues, "Introduction to space time wireless communications".

GL

Dear Geoffroy ,

Thank you very much for wonderful explanations.

Conceptually, the path Independence  of different propagating  waves  is the matter of the coherence length. The length between the propagation paths must be greater than the coherence length to be uncorrelated. The coherence length is dependent on the distance between antenna elements in the array, the propagation complexity in the medium in the sense of random reflections and scattering leading to rich multipath propagation a well as the wavelength.

To complete the picture and benefit from the view of Geoffroy Lerosey , a wireless communication channel is characterized by:

- a coherent length, in the space domain,

- a coherent bandwidth, in the frequency domain, and 

- a coherent time, in the time domain.

For multiplexing in the three domain one have to consider these contraints

 I would like to thank also Amipara for his share.

You are welcome

Alamouti's paper might help also

Space codes such as Alamouti, Tarokh and so on can help you to find some information. Also, Sectorization in cellular systems or directional antennas and multi-beam satellite networks are other strategies to find SDMA.