The original Shannon's capacity equation and limit, as such is applicable for only SISO systems. The capacity equation gets modified for MIMO systems in relation to the number of antennas used at the transmitter and receiver. 

MU is right.

Instead of having the capacity in a SISO system being E{log(1 + |h|^2 * SNR )} where h is the channel coefficient random variable and E is an expectation over h, in the MIMO case you would have:

E{log(1 + H.H^h *SNR)} where H is an Nr x Nt matrix (Nr number of transmit and Nt number of receive antennas) where each entry hij of the matrix H is the link between receive antenna i and transmit antenna j, which is also a random variable and the Expectation is taken over all these random variables.

MIMO makes it possible to exploit "spatial diversity". In other words, each pair of transmitter-receiver antennas see a different wireless channel, for each of which the Shannon bound still holds. The total capacity you can get is then the sum of the capacity of each such channels. However, since the channels are not orthogonal and they interfere one another, the aggregate capacity does not grow linearly with the number of antenna pairs, but according to the formula written by Ahmad Bazzi above. 

In short, Shannon bound is still there!

MIMO capacity can be estimated by "The Extended Shannon Capacity Formula" which is just extended theoretical calculations to the Shannon Formula. Furthermore, The MIMO channel can be easily transformed into min(Nt, Nr) SISO channels and the total capacity is then the summation of the capacities of all the SISO channels.

So, I think the statement is not true.

for more details you can use this book:

The statement "MIMO breaks shannon bound" is completely false. The Shannon bound/capacity is defined as the maximum of the mutual information between the input and the output of a channel. The input and output of MIMO channels are vectors, not scalars as in SISO channels. That is the only difference. The Shannon theory still applies.

I recommend you to read one of the early works on the MIMO capacity: "Capacity of Multi-antenna Gaussian Channels" by E. Telatar (http://mars.bell-labs.com/papers/proof/)

Yes of course MIMO breaks the shannon's bound. Even very fast modem with huge capacity of data transmission is available in today. Shannon's theory was derived in 1940s. Kindly refer the book wireless communication be Andrea Goldsmith

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R.Suresh Babu

@R.Suresh Babu: No, you cannot break the Shannon capacity/bound! The Shannon theory is general and applies to any type of channel, but the final expressions will be different for different types of channels. The Shannon capacity of MIMO channels is higher than the Shannon capacity for SISO channels (if the channel distribution is otherwise the same).

The reasons that we have higher data rates in today's communication systems than in the past are: 1) We use more bandwidth (more data symbols per second), 2) We have closer distances between transmitter and receiver (higher SNR), 3) We use MIMO communications (to send many parallel data streams). These three factors are all covered and explained by Shannon theory!

Dear Emil Bjornson

Sir, I have pointed out that Capacity of MIMO is greater than capacity of SISO (Derived by Shannon)

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Suresh Banu

@R.Suresh Babu: It seems that we are just misunderstanding each other. Shannon developed the capacity concept ("maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution", http://en.wikipedia.org/wiki/Channel_capacity).

Shannon and many others have then derived capacity formulas for different types of channels (e.g., SISO, single-user MIMO, multi-user MIMO, wiretap channels, etc.). You can never beat the capacity, but you can identify that one type of channel that has a higher capacity than another type of channel.

So in my opinion it is correct to say that "MIMO can beat the SISO capacity", but not correct to say that "MIMO can beat the capacity".

To me, "Shannon's bound" is just another word for "channel capacity". It seems that you interpreted it as "channel capacity for SISO channels" instead.

thanks all for your answers