Jesús Gutiérrez-Gutiérrez’s research while affiliated with Universidad de Navarra and other places

For the engineering community, Gray's tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szego theory on large Toeplitz matrices. In this paper, the most important results of the cited monograph are generalized to block Toeplitz (BT) matrices by maintaining the same mathematical tools used by Gray, that is, by using asymptotically equivalent sequences of matrices. As applications of these results, the geometric minimum mean square error (MMSE) for both an infinite-length multivariate linear predictor and an infinite-length decision feedback equalizer (DFE) for multiple-input-multiple-output (MIMO) channels, are obtained as a limit of the corresponding finite-length cases. Similarly, a short derivation of the well-known capacity of a time-invariant MIMO Gaussian channel with intersymbol interference (ISI) and fixed input covariance matrix is also presented.

In this paper, we present an eigenvalue decomposition with an orthogonal eigenvector matrix for any real persymmetric anti-tridiagonal matrix with constant anti-diagonals. Furthermore, we derive a general expression for the entries of the powers of these anti-tridiagonal matrices in terms of the Chebyshev polynomials of the second kind.

In this paper, we derive a general expression for the entries of the qth power (q∈N) of the n×n complex tridiagonal matrix tridiagn(a1,a0,a-1) for all n∈N, in terms of the Chebyshev polynomials of the second kind.

In this paper, we derive a general expression for the entries of the qth power (q∈N)(q∈N) of any complex skew-symmetric circulant matrix, in terms of the Chebyshev polynomials of the first and second kind.

In [J. Rimas, On computing of arbitrary positive integer powers for one type of odd order symmetric circulant matrices – I, Applied Mathematics and Computation 165 (2005) 137–141; J. Rimas, On computing of arbitrary positive integer powers for one type of even order symmetric circulant matrices – I, Applied Mathematics and Computation 172 (2006) 86–90], Rimas derived a general expression for the entries of the qth power (q∈N) of the n×n real symmetric circulant matrix circn(0,1,0,0,…,0,0,1) for all n∈N. In this paper, we present an extension of that interesting work, deriving a similar expression for the entries of the positive integer powers of any complex symmetric circulant matrix.

In [J. Rimas, On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of even order – I, Appl. Math. Comput. 168 (2005) 783–787] and [J. Rimas, On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order – I, Appl. Math. Comput. 171 (2005) 1214–1217] Rimas derived a general expression for the entries of the qth power (q∈N) of the n×n real symmetric tridiagonal matrix tridiagn(1,0,1) for all n∈N. In this paper, we present an extension of that interesting work, deriving a similar expression for the entries of the qth power (q∈N) of the n×n Hermitian tridiagonal matrix tridiagn(a1,a0,a1¯) for all n∈N.

In this paper, we will present diversity gain analysis of a novel channel assignment scheme at the relay for the case in which two non-cooperative independent users communicate with their destination through a single relay and by using only two frequency channels. The analysis of two main relay techniques, namely the amplify-and-forward (AF) and decode-and-forward (DF) will be provided. As the results show, the DF approach provide a higher diversity gain especially in scenarios in which the relay is closer to the receiver.

As data rates are increasing continuously in wireless networks, additional ways of improving system performance and providing higher rates is needed. One scheme that has recently attracted a lot of attention, is using relays in order to provide additional diversity, especially in scenarios that use of multiple antennas may not be practical at transmit or receive sites. In this paper, we will present a novel channel assignment scheme at the relay which will provide full diversity for the case in which two non-cooperative independent users communicate with their destination through a single relay and by using only two frequency channels. As the simulation results show, through use of this approach, significant performance improvement is achieved in comparison with the case in which each user and its corresponding relay use an independent channel for transmission. In addition, the proposed scheme is applied to two main relay-based transmission systems, namely amplify and forward (AF) and decode and forward (DF). As the results show, the performance of DF algorithms is especially superior in scenarios in which the relay is closer to the receiver.

We consider a multiple access relay channel where two sources S₁ and S₂ send their data to a common destination node aided by a shared relay node. In this paper we extend previous work on this topic by assuming that the output of both information sources are correlated with memory. Furthermore, we consider frequency-selective fading channels, which introduce inter-symbol interference among the transmitted symbols. In this context, we propose an iterative receiver which comprises turbo maximum a posteriori (MAP) equalization and distributed source-channel- network decoding in an iterative fashion. Various relaying strategies such as network coding or time multiplexing are analyzed in detail. In addition, a suboptimal but less complex minimum mean square error (MMSE) linear equalizer is also utilized to account for communication scenarios with constrained complexity. Simulation results show that network coding based strategy outperforms, in all cases, the other considered forwarding schemes.

We consider the algebra generated by the principal finite sections of products of multidimensional block Toeplitz operators with bounded symbols. The matrices in this algebra may be regarded as higher-dimensional cubes of increasing side length. We prove that the matrices in the quasicommutator ideal of the algebra have asymptotically no mass in the interior. This observation yields another elementary proof of first-order Szegö-type results. We also determine the corners, edges, and subfaces of the cube that may carry mass asymptotically.