Techreport,
Spectra of large block matrices
(2006)
Abstract
In a frequency selective slow-fading channel in a MIMO system, the channel
matrix is of the form of a block matrix. This paper proposes a method to
calculate the limit of the eigenvalue distribution of block matrices if the
size of the blocks tends to infinity. While it considers random matrices, it
takes an operator-valued free probability approach to achieve this goal. Using
this method, one derives a system of equations, which can be solved numerically
to compute the desired eigenvalue distribution. The paper initially tackles the
problem for square block matrices, then extends the solution to rectangular
block matrices. Finally, it deals with Wishart type block matrices. For two
special cases, the results of our approach are compared with results from
simulations. The first scenario investigates the limit eigenvalue distribution
of block Toeplitz matrices. The second scenario deals with the distribution of
Wishart type block matrices for a frequency selective slow-fading channel in a
MIMO system for two different cases of $n_R=n_T$ and $n_R=2n_T$. Using this
method, one may calculate the capacity and the Signal-to-Interference-and-Noise
Ratio in large MIMO systems.
