# MIMO: How Can Two Antennas So Close Together Receive Different Signals?

I'm trying to understand how MIMO (as used by 802.11n wi-fi and some upcoming cellular data standards) works in practice. I understand at least the gist of the theory of spatial multiplexing. What I don't get is how it works in practice. Let's say you have two TX antennas ~30 cm apart, two RX antennas ~30 cm apart and the distance between the transmitter and receiver is about 30 meters. The angular separation of the transmit antennas as seen from the receiver is tiny. From the perspective of each RX antenna the two TX antennas are about the same distance away. How is the difference between the signals at the two RX antennas measurable and not buried in noise? I would think that in such a configuration they would be nearly identical.

EDIT: Both answers I've received have mentioned phase. This doesn't make sense to me. Assume a coordinate system where the two TX antennas are separated only along the X-axis. The Y component of their separation is zero. As the Y-axis distance between the transmitter and receiver goes to infinity, the difference in distance between the two TX antennas as seen from the receiver goes to zero. If the distance between the TX antennas is 30 cm and most of the distance between the transmitter and receiver is along the Y-axis, then 30 m is for all practical purposes infinite separation between the transmitter and receiver.

• Don't know enough about the specifics to list this as an answer, but I was under the impression that there was typically some directionality involved with the orientation of the antennas, so the multiple antennas would not necessarily be exposed to the same signal levels. Jan 23, 2012 at 20:24
• @TevoD WiFi tends to use antennas that are fairly omni-directional so there isn't much signal strength difference. In the cell phone world, directional antennas are used, but the MIMO antennas are pointed in the same direction so the signal strength is still about the same. Jan 24, 2012 at 0:04
• Most of what (little) I've read about MIMO talks about explicitly using multipath as a way to increase bitrate. Each path becomes spatial reuse, and if there isn't anything for the signal to bounce off and create multipath, the throughput doesn't go up much. It relies on the path length being different for each path because the signal bounces off different objects along the way. Jan 24, 2012 at 19:08
• @dsimcha Regarding your edit, I still have more research to do on the other types of MIMO, but for precoding it doesn't matter how far away from the receiver you are, the delay will be fixed for any given angle. I understand your point about as far as the receiver is concerned, it looks only like 1 antenna, but this doesn't come to play in precoding. Like I said in my answer, in precoding acts the same way as MISO. Jan 24, 2012 at 22:15
• It is worth noting that multipath can be cleaned up some by using a RAKE receiver, and this is separate from MIMO but still along the same lines. Jan 24, 2012 at 22:21

There are different types of MIMO. Those are Precoding, Spatial multiplexing, and Diversity Coding.

Precoding

The idea behind MIMO is that at the frequencies being used, the wavelength is small enough that even 30 cm apart is enough to receive the signal at different phases. As Brain said, the wavelength is about 12.5cm for 2.4 GHz. This means that regardless of how far you are from the two antennas, the delay (or phase delay) between the two antennas will always be fixed for any given angle.

You are able to take advantage of this phase difference to create beam steering. The math and actual implementation of this is complex, but the general idea is actually relatively simple. If the two signals are in phase, then you know that the source of that signal is the same distance from each antenna which means that your source has to be somewhere along the line of symmetry.

As the source begins to move around, the signal will get to one or the other antennas first and the angle from the receiver can be determined based off of the amount of delay between the two. This then allows you to setup "sectors" or beams based of off how much delay is applied to the incoming signal.

Now technically the drawing I showed is only MISO (Multi in single out), but the logic holds true when you add another antenna to create a full MIMO. Also, on the transmitting side, you can do the same thing I talked about with receiving, but instead a delay is applied to one or the other antenna to create a beam in specific direction out of the transmitter.

The accuracy of the angle in and out of each pair of antennas is determined by both the spacing of the antenna and the accuracy of electronics to produce and detect a specific phase shift.

Also things get more complex as you start to account for the fact that at some locations the signal might appear to get to the antennas at the same time but are actually 1 full cycle apart. Also there has to be a control system setup to know what direction you should be directing you beam at, especially when you have a moving device.

But to get to your question directly, it doesn't matter if your source has 2 antennas or not, it is treated the same on the receiving end. What maters is the angle that the source is from the destination. You essentially end up with a source directing its beam in the general direction of the receiver and then the receiver is steering its beam in the general direction of the transmitter.

The big advantage of using MIMO is that you are not creating a lot of extra noise for neighboring devices and so you are able to get more devices in to a small area. Also, since the signal is more directional there is less to bounce off of which results in less issues with multipath.

• Do you know offhand what angular resolution one can expect with today's consumer technology, and/or how it relates to carrier frequency? Jan 24, 2012 at 0:45
• @tyblu scratch what I said before (if you even saw it) I am not sure. I will be looking into it though. Jan 24, 2012 at 0:50
• Maybe I am wrong but I was under impression the MIMO scheme did not use beam steering but rather a) exploit multipath to send more data or b) by creating spatial diversity mitigate fading problems due to multipath. (The difference compared to beam forming is that transmitted signal is omnidirectional in MIMO scheme compared to directional in beam forming scheme) Jan 24, 2012 at 10:04
• @mazurnification I was basing everything I knew off of a class I took in college. It looks like I was only taught the "precoding" form of MIMO while 2 other forms exist. I have edited my question some. I hope to be able to go back and add more detail about the other forms, but it will take me a bit to read up on them enough to teach them. Jan 24, 2012 at 13:48

At 2.4 GHz, the wavelength is about 12.5 cm. So the receive antennas are at different phases of the source signal.

The environment for MIMO does not consist simply of N transmitters and M receivers, it also consists of R reflectors of signal creating multipath signal dispersion. These reflectors between the Tx and Rx, and close to them, consist of things like buildings, walls, trees, filing cabinets, cars, people etc. Any communication that takes place other than on an uninterrupted plain will have various reflectors around causing multipath signals at the receivers.

Multipath creates the effect of there being many received signals from many different directions. As such, once the receive antennae are λ/2 apart, their signals are essentially uncorrelated.

Now that the Rx antennae are uncorrelated, it's possible to create two signals at the Tx such that each Rx antenna receives just one of the signals. This is spatial division multiplexing.

If this sounds fanciful, consider the following. Two signal sources are connected by two coaxial cables to two receivers. Each signal gets received uncontaminated. This is what MIMO is trying to emulate. Now consider that the two cables are leaky, and have crosstalk. The two signals will be contaminated by some of the other signal. If the cables' positions are fixed, then the amount of crosstalk can be measured, then the transmit signals can be matrixed together such that the crosstalk will be removed on reception. If the cables move, then the crosstalk must be remeasured, and new matrices constructed.

The multipath MIMO environment is like a number of very leaky cables. Over a sub-ms time frame, the channel path remains stable enough to be measured, then matrices constructed at Tx and Rx, such that it looks like several independent channels. Error correction allows there to be small changes in the channel gain which result only in a small degradation of the channels, rather than it stopping working.

Consider a MIMO system with two antennas in transmitter and two in receiver and let the channel coefficients be h11, h12, h21, h22. Assume that the transmitter transmits x_1 and x_2 from its antennas 1 and 2 at the same time. The receiver receives two signals in the antennas y_1=h11*x_1+h21*x_2 and y_2=h12*x_1+h_22*x_2 assuming that the system is noise free. Assuming that the channel coefficients have been obtained at the receiver using prior pilot signals, we can extract x_1 and x_2, transmitted by the transmitter, if these two equations are independent. That would be possible if the channel coefficients are uncorrelated. The antennas are to be spaced apart to get this. Then the MIMO system is said to have achieved spatial multiplexing. A probable distance could be at least 10*lambda, the wavelength.

• Where do you get your 10*lambda from?
– Mast
Aug 30, 2016 at 17:21

Spatial multiplexing MIMO depends mathematically on 2 factors: 1-The rank of the channel matrix and 2-Its condition number Physically now this translates into two factors as well: The resolution of the antenna array on both RX and Tx and the angular spread or angular difference between different multipaths. As long as the angular difference expressed in terms of cosines is larger than the resolution of the array which is inversely proportional to the array length normalized to the frequency then streams carried by different multipaths can be resolved and separated in an almost orthogonal way . In a rich scattering ( wide power angular spread) environment half a wavelength antenna separation is enough for distinguishing between different signatures.

You're assuming TX is sending similar signals from it's antennas so they would be same in 30 meters. This is not true.TX does not transmit 2 similar signals each time from it's antennas.So RX is not receiving similar signals either.Its the relationship between those signals that MIMO is taking advantage of.

• What are you talking about? Sep 8, 2020 at 3:11
• @doubleE ali khalil has trouble understanding what you are trying to convey technically. He may wish to be somewhat clearer about what he does not understand. Sep 9, 2020 at 11:16