On the asymptotic eigenvalue distribution of concatenated vector-valued fading channels

The linear vector-valued channel + with and denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution of the channel’s covariance matrix is given in terms of an implicit equation for its Stieltjes transform as well as an explicit expression for its moments. Additionally, almost all eigenvalues are shown to converge toward zero as the number of factors grows over all bounds. This effect cumulates the total energy in a vanishing number of dimensions. The channel model addressed generalizes the model introduced in [1] for communication via large antenna arrays to -fold scattering per propagation path. As a byproduct, the multiplicative free convolution is shown to extend to a certain class of asymptotically large non-Gaussian random covariance matrices.

[1]  G. Pólya,et al.  Problems and theorems in analysis , 1983 .

[2]  P. Hilton,et al.  Catalan Numbers, Their Generalization, and Their Uses , 1991 .

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[4]  J. W. Silverstein Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices , 1995 .

[5]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

[6]  Simon R. Saunders,et al.  Antennas and Propagation for Wireless Communication Systems , 1999 .

[7]  David Tse,et al.  Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity , 1999, IEEE Trans. Inf. Theory.

[8]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[9]  Shlomo Shamai,et al.  Spectral Efficiency of CDMA with Random Spreading , 1999, IEEE Trans. Inf. Theory.

[10]  David Tse,et al.  Linear multiuser receivers in random environments , 2000, IEEE Trans. Inf. Theory.

[11]  Ralf R. Müller Multiuser receivers for randomly spread signals: Fundamental limits with and without decision-feedback , 2001, IEEE Trans. Inf. Theory.

[12]  David Tse,et al.  Resource pooling and effective bandwidths in CDMA networks with multiuser receivers and spatial diversity , 2001, IEEE Trans. Inf. Theory.

[13]  Ralf R. Müller,et al.  Design and analysis of low-complexity interference mitigation on vector channels , 2001, IEEE J. Sel. Areas Commun..

[14]  Ralf R. Müller,et al.  A random matrix model of communication via antenna arrays , 2002, IEEE Trans. Inf. Theory.

[15]  Kenneth H. Rosen,et al.  Catalan Numbers , 2002 .

[16]  J. Andersen,et al.  Power Distributions Revisited , 2002 .

[17]  O. Johnson Free Random Variables , 2004 .