Sampling of stochastic operators

We develop sampling methodology aimed at determining stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function. The data that we use to reconstruct the operator (or, in some cases only the autocorrelation of the spreading function) is based on the response of the unknown operator to a known, deterministic test signal

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

BER of MRC for M-QAM with imperfect channel estimation over correlated Nakagami-m fading

In this contribution, we provide an exact BER analysis for M-QAM transmission over arbitrarily correlated Nakagami-m fading channels with maximal-ratio combining (MRC) and imperfect channel estimation at the receiver. Assuming an arbitrary joint fading distribution and a generic pilot-based channel estimation method, we derive an exact BER expression that involves an expectation over (at most) 4 variables, irrespective of the number of receive antennas. The resulting BER expression includes well-known PDFs and the PDF of only the norm of the channel vector. In order to obtain the latter PDF for arbitrarily correlated Nakagami-m fading, several approaches from the literature are discussed. For identically distributed and arbitrarily correlated Nakagami-m channels with integer m, we present several BER performance results, which are obtained from numerical evaluation and confirmed by straightforward computer simulations. The numerical evaluation of the exact BER expression turns out to be much less time-consuming than the computer simulations

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.Comment: 11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theor