In my opinion,If you want to extract the information transmitted by N transmitting antennas , the number of receiving antennas M should be greater ie M>=N. Then only

rank of channel matrix is 'N' . this makes to extract information through some linear operations

I believe this is true. If we want to have a low Bit Error Ratio (BER) performance and use linear detectors at the same time, then the number of receive antennas M should be at least equal to the number of transmit antennas N.

Linear detectors may also be used in the case where M

Two

Hallo,

First, the use of a common definition, even designation of MIMO is necessary. I consider some definition based on an example taken from "4G americas":

"An operator uses 2 Tx antennas and 4 RX antennas in the base station (BS), while the terminal uses 2 RX antennas and 1TX antenna, so the DL is 2*2 MIMO and the UL is 1*4 SIMO".

I will try to give an answer (from antenna's engineering point of view):

As illustrated in the example, we must refer to two different things: the terminal and the BS which have completely different characteristics, features and capacities. It's enough to mention that the sizes are different that have some major implications (number of antennas implanted, processing, memory capacity ...).

We have more antennas in the BS (transmitter and receiver) than in the terminal (transmitter and receiver).

The number of antennas (whether transmitting or receiving) must be referred rather to the BS supposed to serve more than 1 terminal or to the terminal itself. Normally, the BS contains more antennas in both ends (DL and UL) than the terminal.

Regards

It all depends on what you transmit from your antennas. I would say that the number of receive antennas, M, is not limited by the number of transmit antennas, N, but the rank of the transmitted signal, R (i.e., the rank of the N x N signal covariance matrix). In other words, we want to have M>=R because otherwise the detector doesn't have enough observations to decode the complete signal.

I would have started from another from another point of view. For given values on N and M, how should we select the rank R to balance between high capacity (high rank) and higher reliability and simpler detection algorithms (low rank).

It is two.

The simplest MIMO system is the 2x2 one that comprises two transmitting and two receiving antennas. However, you should keep in mind that, In general, diversity increases with the number of receiving antennas. Therefore, the answer on your question depends on what you are really asking for your system.

A SISO telecommunication system is composed by a transmitting and a receiving antenna SISO means single input / single output. So only two antennas are necessary.

Then you can have a SIMO system single input multiple output , this means that you have only one TX antenna and two RX antennas, for a SIMO system three antennas is the minimum number for this kind of system. Also for a MISO system you need at least three antennas since you have multiple input and single output (at least two TX antennas and one RX antenna).

Finally you have a MIMO system this means that you have multiple input and multiple output (at least two TX and RX antennas) so the minimum antenna number for a MIMO system is four antennas.

Hi. The smart antenna M (transmit antenna elements) and N (Receive antenna elements) can be of any size (theoretically). This depends on your objectives from the antenna system. Practical issues limit the number of antenna elements at the mobile terminal side due to its size. However, we can have M>N or M

2x2 tx-rx antennas is considered to be mimo.

Minimumm numbers of antennas required areTWO on receiver side.

The minimum number of antennas in MIMO system is depending on the rank of the channel, namely the environments. If the rank is lower, such as 4, so the useful configuration of MIMO should only be 2*2. If a larger MIMO is employed in such environment, no improvement will be introduced.

In general, the 2*2 MIMO configuration is the safest.

The min. is 2. The optimum depends on the rank of the channel. In Smart Phones I would expect 2, because of space and cost limitations.

Nan Zhang: Even if the rank of the channel is limited, you can achieve an array gain by having more antennas. This will improve the SNR if you do Beamforming.

Two

It's 2.

I agreed with the mini is 2. The more antennas can receive more energy but cause much more complicated design and signal processing as well as higher cost.

In order to obtain a MIMO system, the minimum number of Rx antennas is 2. With only one Rx antenna we have a MISO system ! However, as mentioned before, 2 is just the minimum numver. You may increase the number of Rx antennas, depending on the expected performance of the system.

Hi, when you talk about MIMO and specified it as MInmum, It is 2, and More than 2

for Maximum.

Agree with all opinions. On the transmitter side, usually there would be no power constraints and hence can opt for more than 2 antennas. While on the receiver side, the power constraint is a critical measure and hence 2 would be efficient. Generally speaking 2x2 would be the minimum requirement. In case of linearity, MIMO configuration and associated data processing algorithms are always considered linear. Hence, the base of nonlinearity doubt is not so clear, unless some nonlinear coding schemes were referred to and under such situations have nothing to do with the number of antennas.  

To form a minimum MIMO configuration, there should be two receive antennas. It depends on the rank of the channel matrix. So for a 2x2 MIMO case if the rank of the channel matrix is less than 4, the receiver shall not have sufficient content to recover the transmitted data. Of course channel non-linearity and fading will increase the complexity of a practical scenario.    

Should be dependent on your objectives. You have to take into consideration the status of your system, Is it under-determined or over-determined? and hence, the complexity.