Deduction of Lorentz Transformation from the existence of absolute rest. Deduction of the speed of light in any frame of reference

We begin by admitting the following: (i) there is a frame of reference where the speed of light is the same in any direction (that speed is c) (ii) the average speed of light on a two-way journey is c in every frame of reference. From this two premises we obtain an expression for the speed of light which implies the speed of light depends on the motion of the frame of reference. Also from this two premises solely we deduct Lorentz Transformation.Comment: 6 pages, 0 figure

The Energy-Entropy Principle

In this paper, through a criticism of what we call the paradigmatic view of thermodynamics, we aim at showing a new perspective attained in this matter. The generalization of heat as internal energy (generalization of the kinetic energy concept of heat) permits the generalization of the Kelvin postulate: "It is impossible, without another effect, to convert internal energy into work" (no reference to heat or to heat reservoir).Comment: 18 pages, 1 figur

The physical meaning of synchronization and simultaneity in Special Relativity

Based on two previous papers, the physical meaning of synchronization and simultaneity as is presented in Einstein's Special Relativity paper of 1905 is reconsidered. We follow Einstein's argumentation to introduce a criterium of synchronization and for the same arguments we arrive at a different criterium for synchronization. From that we conclude that simultaneity is absolute.Comment: 11 pages, 0 figure

Joint Power Adjustment and Interference Mitigation Techniques for Cooperative Spread Spectrum Systems

This paper presents joint power allocation and interference mitigation techniques for the downlink of spread spectrum systems which employ multiple relays and the amplify and forward cooperation strategy. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to an individual power constraint and the design of linear receivers for interference suppression. We derive constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problem efficiently, we develop joint adaptive power allocation and interference suppression algorithms that can be implemented in a distributed fashion. The proposed stochastic gradient (SG) and recursive least squares (RLS) algorithms mitigate the interference by adjusting the power levels across the relays and estimating the parameters of the linear receiver. SG and RLS channel estimation algorithms are also derived to determine the coefficients of the channels across the base station, the relays and the destination terminal. The results of simulations show that the proposed techniques obtain significant gains in performance and capacity over non-cooperative systems and cooperative schemes with equal power allocation.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1301.009

Distributed Low-Rank Adaptive Algorithms Based on Alternating Optimization and Applications

This paper presents a novel distributed low-rank scheme and adaptive algorithms for distributed estimation over wireless networks. The proposed distributed scheme is based on a transformation that performs dimensionality reduction at each agent of the network followed by transmission of a reduced set of parameters to other agents and reduced-dimension parameter estimation. Distributed low-rank joint iterative estimation algorithms based on alternating optimization strategies are developed, which can achieve significantly reduced communication overhead and improved performance when compared with existing techniques. A computational complexity analysis of the proposed and existing low-rank algorithms is presented along with an analysis of the convergence of the proposed techniques. Simulations illustrate the performance of the proposed strategies in applications of wireless sensor networks and smart grids.Comment: 12 figures, 13 pages. arXiv admin note: text overlap with arXiv:1411.112

Low-Rank Signal Processing: Design, Algorithms for Dimensionality Reduction and Applications

We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed to introduce the reader to the fundamentals of reduced-rank signal processing and to describe how dimensionality reduction is performed on an observed discrete-time signal. A unified treatment of dimensionality reduction algorithms is presented with the aid of least squares optimization techniques, in which several techniques for designing the transformation matrix that performs dimensionality reduction are reviewed. Among the dimensionality reduction techniques are those based on the eigen-decomposition of the observed data vector covariance matrix, Krylov subspace methods, joint and iterative optimization (JIO) algorithms and JIO with simplified structures and switching (JIOS) techniques. A number of applications are then considered using a unified treatment, which includes wireless communications, sensor and array signal processing, and speech, audio, image and video processing. This tutorial concludes with a discussion of future research directions and emerging topics.Comment: 23 pages, 6 figure

Study of Sparsity-Aware Distributed Conjugate Gradient Algorithms for Sensor Networks

This paper proposes distributed adaptive algorithms based on the conjugate gradient (CG) method and the diffusion strategy for parameter estimation over sensor networks. We present sparsity-aware conventional and modified distributed CG algorithms using $l_{1}$ and log-sum penalty functions. The proposed sparsity-aware diffusion distributed CG algorithms have an improved performance in terms of mean square deviation (MSD) and convergence as compared with the consensus least-mean square (Diffusion-LMS) algorithm, the diffusion CG algorithms and a close performance to the diffusion distributed recursive least squares (Consensus-RLS) algorithm. Numerical results show that the proposed algorithms are reliable and can be applied in several scenarios.Comment: 1 figure, 7 page

Joint Iterative Power Allocation and Linear Interference Suppression Algorithms in Cooperative DS-CDMA Networks

This work presents joint iterative power allocation and interference suppression algorithms for spread spectrum networks which employ multiple hops and the amplify-and-forward cooperation strategy for both the uplink and the downlink. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to individual and global power constraints and the design of linear receivers for interference suppression. We derive constrained linear minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problems, we develop cost-effective algorithms for adaptive joint power allocation, and estimation of the parameters of the receiver and the channels. An analysis of the optimization problem is carried out and shows that the problem can have its convexity enforced by an appropriate choice of the power constraint parameter, which allows the algorithms to avoid problems with local minima. A study of the complexity and the requirements for feedback channels of the proposed algorithms is also included for completeness. Simulation results show that the proposed algorithms obtain significant gains in performance and capacity over existing non-cooperative and cooperative schemes.Comment: 9 figures; IET Communications, 201

Interference Suppression and Group-Based Power Adjustment via Alternating Optimization for DS-CDMA Networks with Multihop Relaying

This work presents joint interference suppression and power allocation algorithms for DS-CDMA networks with multiple hops and decode-and-forward (DF) protocols. A scheme for joint allocation of power levels across the relays subject to group-based power constraints and the design of linear receivers for interference suppression is proposed. A constrained minimum mean-squared error (MMSE) design for the receive filters and the power allocation vectors is devised along with an MMSE channel estimator. In order to solve the proposed optimization efficiently, a method to form an effective group of users and an alternating optimization strategy are devised with recursive alternating least squares (RALS) algorithms for estimating the parameters of the receiver, the power allocation and the channels. Simulations show that the proposed algorithms obtain significant gains in capacity and performance over existing schemes.Comment: 2 figures. arXiv admin note: substantial text overlap with arXiv:1301.5912, arXiv:1301.009

Is the assumption of a special system of reference consistent with Special Relativity?

In a previous work we have shown that the null result of the Michelson-Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its `equivalence' of all inertial frames, but as well as in Lorentz-Poincar\'e scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a "special system of reference experimentally inaccessible" is indeed compatible with Einstein's Special Relativity, as beautifully outlined and discussed by John Bell [1]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks.Comment: 16 pages, 6 figure