Third generation mobile radio systems will employ TD-CDMA in their TDD mode. In a TD-CDMA mobile radio system, jointdetection is equivalent to solving a least squares problem with a block-Toeplitz system matrix. By extending this matrix to a block-circulant matrix, it is possible to blockdiagonalize the matrix with Fast Fourier Transforms. For the typical system scenario of a TD-CDMA system, th...

An equitable vertex coloring for the splitting of block circulant graphs is investigated. The comprises matrices, where each itself a matrix. These blocks in row are cyclically shifted one place to right from those previous row. We approached such matrix representation and derived their independent sets using neighbourhoods vertex. This classification makes process be simpler most cases. In thi...

In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graphG of order n is a Cayley graph over the cyclic groupZn: Equivalently, G is circulant i its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent con guration A and, in particular, a S...

In this paper, we discuss the solutions to a class of Hermitian positive deenite system Ax = b by the preconditioned conjugate gradient method with circulant preconditioner C. In general, the smaller the condition number (C ?1=2 AC ?1=2) is, the faster the convergence of the method will be. The circulant matrix C b that minimizes (C ?1=2 AC ?1=2) is called the best conditioned circulant precond...

Discrete body of revolution (DBOR) codes can accelerate moment method (MoM) solutions for scattering geometries possessing discrete circular symmetry. Traditional DBOR formulations require modifications to the incident field, such as decomposition into circular modes. While appropriate for methods employing direct solvers, approaches employing iterative solvers are disadvantaged by this dramati...

In this paper, a recently introduced block circulant preconditioner for the linear systems of the codes for ordinary differential equations (ODEs) is investigated. Most ODE codes based on implicit formulas, at each integration step, need the solution of one or more unsymmetric linear systems that are often large and sparse. Here, the boundary value methods, a class of implicit methods for the n...

1 Abstract In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graph G of order n is a Cayley graph over the cyclic group Z n : Equivalently, G is circulant ii its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent connguration A and, in...

We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that these matrices are expected to be very well conditioned. Our probabilistic estimates for the norms of standard Gaussian random Toeplit...

A new method of obtaining a sequence isolated complex Hadamard matrices (CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is presented. We discuss, several analytic examples resulting from modification the Sinkhorn algorithm. In particular, we present orders $9$, $10$ and $11$, which elements are not roots unity, also multiparametric families order $10$. note novel conne...

Properties and potential applications of the block pulse response circulant matrix (PRCM) and its singular value decomposition (SVD) are investigated in relation to MIMO control and identification. The SVD of the PRCM is found to provide complete directional as well as frequency decomposition of a MIMO system in a real matrix form. Three examples were considered: design of MIMO FIR controller, ...