This paper focuses on multiuser MIMO channel estimation and data transmission at millimeter wave (mmWave) frequencies. The proposed approach relies on the time-divisionduplex (TDD) protocol and is based on two distinct phases. First of all, the Base Station (BS) sends a suitable probing signal so that all the Mobile Stations (MSs), using a subspace tracking algorithm, can estimate the dominant ...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with respect to Uq(sl(2)) is proved. PACS Nos. 03.65.Fd 05.50+q 75.10.Jm Running Title Closed spin 1 XXZ chain e-mail [email protected] e-mail [email protected] ...

Using a collective field method, we obtain explicit solutions of the generalized CalogeroSutherland models that are characterized by the roots of the classical groups BN and CN . Starting from the explicit wave functions for AN−1 type expressed in terms of the singular vectors of the WN algebra, we give a systematic method to construct wave functions and derive energy eigenvalues for other type...

Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz vectors are derived for various steepest descent/ascent gradient iterations. The analysis shows that poores...

This contribution is complementary to [1] in that it takes a timevarying mode-vector solution as an a priori assumption. The associated dynamic eigenvalue problem is solved by triangularizing the system equations, again accomplished by successive Riccati transforms. It is explicitly shown that equal eigenvalues do not give rise to the Jordan form. Although the mode-vectors are not uniquely dete...

We introduce a simple method to accelerate the convergence of iterative solvers of the frequency-domain Maxwell's equations for deep-subwavelength structures. Using the continuity equation, the method eliminates the high multiplicity of near-zero eigenvalues of the operator while leaving the operator nearly positive-definite. The impact of the modified eigenvalue distribution on the accelerated...

We show that photon coincidence spectroscopy can provide an un-ambiguous signature of two atoms simultaneously interacting with a quantised cavity field mode. We also show that the single–atom Jaynes–Cummings model can be probed effectively via photon coincidence spectroscopy, even with deleterious contributions to the signal from two–atom events. In addition, we have explicitly solved the eige...