The eigenvalues are the ones that characterize the MIMO channel capacity, while the eigenvector does not affect it (for a single-user point-point MIMO channel).

You can have a look at page 6 in the seminal paper på E. Telatar:

http://lthiwww.epfl.ch/~leveque/Projects/telatar.pdf

There you will find an expression of the capacity, C(\mu), that is computed directly from the eigenvalues.

The capacity-achieving transmission strategy is to send one data signal in each of the eigendirections. Hence, the eigenvalues tell us how strong these parallel channels are. This can be utilized to analyze the BER, but you need to make some assumptions on the power allocation and transmission rates in order to define the BERs.

Tanks sir. Can you please give some idea about the relation of rank and eignvalue in correlated channel?

Since the eigenvectors have no impact, spatial correlation will only affect the random distribution of the eigenvalues. More spatial correlation means that it is more probable that a few eigenvalues are large and the rest are small. This might be negative from a a capacity point of view. See the following paper:

E.A. Jorswieck, H. Boche, Optimal transmission strategies and impact of correlation in multi-antenna systems with different types of channel state information, IEEE Transactions on Signal Processing, vol 52, pp. 3440-3453, 2004.

The multiplexing gain is limited by the rank of the matrix H H^H. This is normally equal to min(Nt, Nr), but under very strong spatial correlation you might have a rank loss. He keyhole channel is a common example.

Thanks sir for your kind support.

The eigenvalues can be said as one of the most important aspect in MIMO since this eigenvalues are directly related to the spectral efficiency of the MIMO channel. Take a look an example of 2 by 2 MIMO channel. As the SVD applied to show how the channel matrix of this MIMO system becomes simply an diagonal matrix, whose this diagonal matrix represent the singular values. Take notes that the singular values are the square root of the channel eigenvalues (or if the eigen decompisition apply here, the diagonal values are eigenvalues of the channel.

As previos answer indicated that capacity equation in terms of power are effected by how much the eigenvalues contributing to the capacity (spectral efficiency), through the rank of the channel (number of meaningful eigenvalues.

Hope it helps. Thank you.

Thanks sir

Emil Björnson http://lthiwww.epfl.ch/~leveque/Projects/telatar.pdf link is not working.

Sunil Dhakal The paper that I referred to is "Capacity of multi-antenna Gaussian channels" by Emre Telatar.

Thank you Emil Björnson, I have just sent you a message regarding eigen values.

Dear Dayan Adionel Guimarães ,

Thanks for your response.

Please send me the pdf of the corresponding chapter.

The number of multipath components and their Angular spread in a MIMO channel effects the distribution of the eigen values (or effective rank) and hence the MIMO channel capacity. For example

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7343353

The study below shows that the number of significant eigenvalues of the channel covariance matrix, obtained from the channel impulse response scales linearly with bandwidth

Article Ultrawideband Channel Modeling on the Basis of Information-T...

regards,

Naveed

Thanks sir

Hi..I have been working also lately on MIMO with large number of antenna elements. Eigenvalues (EVs) are very essential in this form of communication. Imagine as the pipe or the cable you have connecting the antenna at TX and RX, the first EV should be biggest and will be decreased (imagine the size of pipe). The conditions of eigenvalues will be varying depends on rank. Rank of the channel means that the meaningful EVs (power higher than the noise). For example, channel will be at its best when the channel has eigenvalues equals to min number of antenna at TX or RX. and will be at equivalent with SISO channel when rank equals to 1. Meaning that there is no diversity.

Hope it helps.

Regards

Thanks Dwi Joko Suroso