Jesús Gutiérrez-Gutiérrez

Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems

For the engineering community, Grays 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.

Block Toeplitz Matrices: Asymptotic Results and Applications

The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide sense stationary processes. Therefore, this monograph is a generalization to block Toeplitz matrices of the Gray monograph entitled “Toeplitz and circulant matrices: A review”, which was published in the second volume of Foundations and Trends in Communications and Information Theory, and which is the simplest and most famous introduction to the asymptotic theory on Toeplitz matrices.

Powers of tridiagonal matrices with constant diagonals

Abstract In this paper, we derive a general expression for the entries of the qth power ( q ∈ N ) of the n × n complex tridiagonal matrix tridiag n ( a 1 , a 0 , a - 1 ) for all n ∈ N , in terms of the Chebyshev polynomials of the second kind.

Positive integer powers of certain tridiagonal matrices

Abstract 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 tridiag n ( 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 tridiag n ( a 1 , a 0 , a 1 ¯ ) for all n ∈ N .

Powers of real persymmetric anti-tridiagonal matrices with constant anti-diagonals

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.

Powers of complex persymmetric or skew-persymmetric anti-tridiagonal matrices with constant anti-diagonals

In this paper, we derive a general expression for the entries of the powers of any complex persymmetric or skew-persymmetric anti-tridiagonal matrix with constant anti-diagonals, in terms of the Chebyshev polynomials of the second kind.

On Combining Distributed Joint Source-Channel-Network Coding and Turbo Equalization in Multiple Access Relay Networks

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.

Positive integer powers of complex skew-symmetric circulant matrices

Abstract 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 circ n ( 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.

Asymptotically Equivalent Sequences of Matrices and Multivariate ARMA Processes

The present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary (WSS) processes. A multivariate random process is said to be asymptotically WSS if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent (a.e.) to the sequence of autocorrelation matrices of some multivariate WSS process. It is shown that this class of processes contains meaningful processes other than multivariate WSS processes. In particular, we give sufficient conditions for multivariate moving average (MA) processes, multivariate autoregressive (AR) processes and multivariate autoregressive moving average (ARMA) processes to be asymptotically WSS. Furthermore, in order to solve multiple-input-multiple-output (MIMO) problems in communications and signal processing involving this kind of processes, we extend the Gray definition of a.e. sequences of matrices and his main results on these sequences to non-square matrices. As an example, the derived results on a.e. sequences of non-square matrices are applied to compute the differential entropy rate and the minimum mean square error (MMSE) for a linear predictor of a multivariate asymptotically WSS process.

Distributed Pseudo-Gossip Algorithm and Finite-Length Computational Codes for Efficient In-Network Subspace Projection

In this paper, we design a practical power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e.g., spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection, where separation of channel coding and computation is assumed, our algorithm combines binary finite-length Computational Coding and a novel gossip-like protocol with certain communication rules, achieving important savings in convergence time and yielding a decrease in energy consumption as the density of the network increases, as compared to a separation scheme.