This paper proposes a mathematical model that studies the fuel consumption of a jet engine aircraft during the climbing and descent flight phases. Such problem is addressed by providing a closed-form formula of the aircraft’s rate-of-climb and rate-of-descent, which then enables obtaining a closed-form formula of the aircraft’s fuel consumption that provides the closed-form relationship between the aircraft’s fuel consumption and aerodynamic, engine and design parameters. In order to validate our mathematical model, a comparison is made between our results and results provided by Piano-X software and accuracy between both is proven. Furthermore, our mathematical model is applied to the calculation of pollutant gas emissions, specifically, we present a closed-form expression that provides the dependency between the mass of pollutant gas emitted and the aircraft’s aerodynamic, engine and design parameters.

Structural health monitoring (SHM) using wireless sensor networks (WSN) has become a popular implementation, due to low maintenance and installation costs. These networks commonly use a centralized approach and battery-powered sensors, leading to energy consumption limitations, in both the central unit and the sensors. Therefore, it is of interest to consider the use of passive sensors and distributed processing in the network. In this paper, we present a distributed algorithm for SHM using wireless passive sensor networks (WPSN) that allows any passive sensor in the network to obtain the distance to its neighbours via backscattering, and hence to detect and signal changes in the monitored structure.

In this paper the Pisarenko spectral estimation method for wide sense stationary (WSS) 1-dimensional (scalar) processes is extended to autoregressive (AR) multidimensional (vector) processes.

Using some recent results on asymptotically equivalent sequences of matrices, we present in this paper, a new derivation of the capacity formula given by Brandenburg and Wyner for a discrete-time Gaussian multiple-input-multiple-output channel with memory. In this paper, we tackle not only the case considered by them, where the number of channel inputs and the number of channel outputs are the same, but also when both numbers are different.

In this paper we prove the asymptotic formula that has been recently used as a numerical integration method to approximate the relative entropy (or Kullback-Leibler distance) between two probability density functions with bounded support in terms of functions of Hermitian Toeplitz matrices. To prove that asymptotic formula we use the Gray concept of asymptotically equivalent sequences of matrices.

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.

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.

Toeplitz matrices and functions of Toeplitz matrices (such as the inverse of a Toeplitz matrix, powers of a Toeplitz matrix or the exponential of a Toeplitz matrix) arise in many different theoretical and applied fields. They can be found in the mathematical modelling of problems where some kind of shift invariance occurs in terms of space or time. For the engineering community, R. M. Gray's tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szego distribution theory on the asymptotic behavior of continuous functions of Toeplitz matrices. His asymptotic results, widely used in engineering due to the simplicity of its mathematical proofs, do not concern individual entries of these matrices but rather, they describe an "average" behavior. However, there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a Toeplitz matrix. To gain insight into the solutions of this sort of problems, the present paper introduces new theoretical results regarding the convergence of these entries, that can be derived by using similar mathematical tools.

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.

Toeplitz matrices and functions of Toeplitz matrices (such as the inverse of a Toeplitz matrix, powers of a Toeplitz matrix or the exponential of a Toeplitz matrix) arise in many different theoretical and applied fields. They can be found in the mathematical modeling of problems where some kind of shift invariance occurs in terms of space or time. R. M. Gray's excellent tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szegö distribution theory on the asymptotic behavior of continuous functions of Toeplitz matrices. His asymptotic results, widely used in engineering due to the simplicity of its mathematical proofs, do not concern individual entries of these matrices but rather, they describe an “average” behavior. However, there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a Toeplitz matrix. Using similar mathematical tools and to gain insight into the solutions of this sort of problems, the present correspondence derives new theoretical results regarding the convergence of these entries.