Asymptotic Eigenvalue Moments of Wishart-Type Random Matrix Without Ergodicity in One Channel Realization
نویسنده
چکیده
Consider a random matrix whose variance profile is random. This random matrix is ergodic in one channel realization if, for each column and row, the empirical distribution of the squared magnitudes of elements therein converges to a nonrandom distribution. In this paper, noncrossing partition theory is employed to derive expressions for several asymptotic eigenvalue moments (AEM) related quantities of a large Wishart-type random matrix HH when H has a random variance profile and is nonergodic in one channel realization. It is known the empirical eigenvalue moments of HH are dependent (or independent) on realizations of the variance profile of H when H is nonergodic (or ergodic) in one channel realization. For nonergodic H, the AEM can be obtained by i) deriving the expression of AEM in terms of the variance profile of H, and then ii) averaging the derived quantity over the ensemble of variance profiles. Since the AEM are independent of the variance profile if H is ergodic, the expression obtained in i) can also serve as the AEM formula for ergodic H when any realization of variance profile is available. Index Terms Random matrix, Wishart matrix, variance profile, asymptotic eigenvalue moments (AEM), noncrossing partition. October 6, 2008 DRAFT 2
منابع مشابه
Sujet : Moments Method for Random Matrices with Applications to Wireless Communication
In this thesis, we focus on the analysis of the moments method, showing its importance in the application of random matrices to wireless communication. This study is conducted in the free probability framework. The concept of free convolution/deconvolution can be used to predict the spectrum of sums or products of random matrices which are asymptotically free. In this framework, we show that th...
متن کاملComplex random matrices and Rician channel capacity
The eigenvalue densities of complex noncentral Wishart matrices are investigated to study an open problem in information theory. Specifically, the largest, smallest and joint eigenvalue densities of complex noncentral Wishart matrices are derived. These densities are expressed in terms of complex zonal polynomials and invariant polynomials. The connection between the complex Wishart matrix theo...
متن کاملSpectra of large block matrices
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 ...
متن کاملOn moments of complex Wishart and complex inverse Wishart distributed matrices
This paper addresses the calculation of moments of complex Wishart and complex inverse Wishart distributed random matrices. Complex Wishart and complex inverse Wishart distributed random matrices are used in applications like radar, sonar, or seismics in order to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively. ...
متن کاملBulk Eigenvalue Correlation Statistics of Random Biregular Bipartite Graphs
In this paper, we consider the randommatrix ensemble given by (db, dw)-regular graphs onM black vertices andN white vertices, where db ∈ [N γ , N2/3−γ ] for any γ > 0. We simultaneously prove that the bulk eigenvalue correlation statistics for both normalized adjacency matrices and their corresponding covariance matrices are stable for short times. Combined with an ergodicity analysis of the Dy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/0810.0882 شماره
صفحات -
تاریخ انتشار 2008