CHAOTIC COMPRESSIVE SENSING OF TV –UHF BAND IN IRAQ USING CHEBYSHEV GRAM SCHMIDT SENSING MATRIX

Cognitive radio (CR) is a promising technology for solving spectrum sacristy problem. Spectrum sensing is the main step of CR. Sensing the wideband spectrum produces more challenges. Compressive sensing (CS) is a technology used as spectrum sening in CR to solve these challenges. CS consists of three stages: sparse representation, encoding and decoding. In encoding stage sensing matrix are required, and it plays an important role for performance of CS. The design of efficient sensing matrix requires achieving low mutual coherence . In decoding stage the recovery algorithm is applied to reconstruct a sparse signal. İn this paper a new chaotic matrix is proposed based on Chebyshev map and modified gram Schmidt (MGS). The CS based proposed matrix is applied for sensing real TV signal as a PU. The proposed system is tested under two types of recovery algorithms. The performance of CS based proposed matrix is measured using recovery error (Re), mean square error (MSE), and probability of detection (Pd) and evaluated by comparing it with Gaussian, Bernoulli and chaotic matrix in the literature. The simulation results show that the proposed system has low Re and high Pd under low SNR values and has low MSE with high compression.

Convergence of NDPP and CSDP Planning Process as a Part of the NATO-EU Strategic Partnership Reinforcing

Over the last few years, a need for reinforcing the NATO-EU mutual coherence has become increasingly apparent. The EU and NATO have recently initiated the steps to consolidate the strategic cooperation where a way ahead to converge NDPP and CSDP planning process was also underpinned. The recent introduction of new tools tailored to get more effective the CSDP process offers new opportunities for facilitating a convergence of EU and NATO planning approaches. Even if it is impossible to assume that the Alliance's and the Union's planning processes would become identical, the implementation of PESCO and other subsequent procedural tools has created a room for potential synchronization and harmonization of respective planning processes. The paper summarises findings on certain parts of both processes which could be brought closer, in terms of time and procedures, without affecting the autonomy of both organizations in any way.

Spatiotemporal non-uniformly correlated beams

We present a new partially coherent source with spatiotemporal coupling. The stochastic light, which we call a spatiotemporal (ST) non-uniformly correlated (NUC) beam, combines space and time in an inhomogeneous (shift- or space-variant) correlation function. This results in a source that self-focuses at a controllable location in space-time, making these beams potentially useful in applications such as optical trapping, optical tweezing, and particle manipulation. We begin by developing the mutual coherence function for an ST NUC beam. We then examine its free-space propagation characteristics by deriving an expression for the mean intensity at any plane $$z \ge 0$$ z ≥ 0 . To validate the theoretical work, we perform Monte Carlo simulations, in which we generate statistically independent ST NUC beam realizations and compare the sample statistical moments to the corresponding theory. We observe excellent agreement amongst the results.

„Ištar“ und „Marduk“ als jüdische Protagonisten, Purim als neues Fest der Befreiung: Zur Theologie und zum historischen Ort des Esterbuches

This article deals with two theological paradoxes in the Book of Esther (Masoretic Text). Arguably, the most striking characteristic of the book is that it does not mention God. At the same time, the two Jewish protagonists bear names that are identical with, or at least strongly reminiscent of, those of the Babylonian deities Marduk and Ištar. While the author of Esther seems to completely ignore the cultic laws of the Pentateuch, at the end of the book he strongly emphasizes the foundation of the Purim feast. Although each of these four topics has been dealt with in scholarship, they are seldomly—and if so, only partly—investigated with regard to their mutual coherence. In aiming to do this, the present article undertakes to reevaluate the theological profile of the Book of Esther (as expressed in the Masoretic Text) as well as its historical location. As for the latter question, the intriguing statement related to “relief and deliverance coming to the Jews from another place” in Est 4:14 provides an important hint.

Tight bounds on the mutual coherence of sensing matrices for Wigner D-functions on regular grids

Many practical sampling patterns for function approximation on the rotation group utilizes regular samples on the parameter axes. In this paper, we analyze the mutual coherence for sensing matrices that correspond to a class of regular patterns to angular momentum analysis in quantum mechanics and provide simple lower bounds for it. The products of Wigner d-functions, which appear in coherence analysis, arise in angular momentum analysis in quantum mechanics. We first represent the product as a linear combination of a single Wigner d-function and angular momentum coefficients, otherwise known as the Wigner 3j symbols. Using combinatorial identities, we show that under certain conditions on the bandwidth and number of samples, the inner product of the columns of the sensing matrix at zero orders, which is equal to the inner product of two Legendre polynomials, dominates the mutual coherence term and fixes a lower bound for it. In other words, for a class of regular sampling patterns, we provide a lower bound for the inner product of the columns of the sensing matrix that can be analytically computed. We verify numerically our theoretical results and show that the lower bound for the mutual coherence is larger than Welch bound. Besides, we provide algorithms that can achieve the lower bound for spherical harmonics.

Universal Measurement Matrix Design for Sparse and Co-Sparse Signal Recovery

Compressed Sensing (CS) avails mutual coherence metric to choose the measurement matrix that is incoherent with dictionary matrix. Random measurement matrices are incoherent with any dictionary, but their highly uncertain elements necessitate large storage and make hardware realization difficult. In this paper deterministic matrices are employed which greatly reduce memory space and computational complexity. To avoid the randomness completely, deterministic sub-sampling is done by choosing rows deterministically rather than randomly, so that matrix can be regenerated during reconstruction without storing it. Also matrices are generated by orthonormalization, which makes them highly incoherent with any dictionary basis. Random matrices like Gaussian, Bernoulli, semi-deterministic matrices like Toeplitz, Circulant and full-deterministic matrices like DFT, DCT, FZC-Circulant are compared. DFT matrix is found to be effective in terms of recovery error and recovery time for all the cases of signal sparsity and is applicable for signals that are sparse in any basis, hence universal.

A New Method of Measurement Matrix Optimization for Compressed Sensing Based on Alternating Minimization

In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence μmax, t-averaged mutual coherence μave and global mutual coherence μall, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces μave and solves the problem that μmax would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

Coherent combining of self-cleaned multimode beams

A low intensity light beam emerges from a graded-index, highly multimode optical fibre with a speckled shape, while at higher intensity the Kerr nonlinearity may induce a spontaneous spatial self-cleaning of the beam. Here, we reveal that we can generate two self-cleaned beams with a mutual coherence large enough to produce a clear stable fringe pattern at the output of a nonlinear interferometer. The two beams are pumped by the same input laser, yet are self-cleaned into independent multimode fibres. We thus prove that the self-cleaning mechanism preserves the beams’ mutual coherence via a noise-free parametric process. While directly related to the initial pump coherence, the emergence of nonlinear spatial coherence is achieved without additional noise, even for self-cleaning obtained on different modes, and in spite of the fibre structural disorder originating from intrinsic imperfections or external perturbations. Our discovery may impact theoretical approaches on wave condensation, and open new opportunities for coherent beam combining.

Measurement Matrix Optimization via Mutual Coherence Minimization for Compressively Sensed Signals Reconstruction

For signals reconstruction based on compressive sensing, to reconstruct signals of higher accuracy with lower compression rates, it is required that there is a smaller mutual coherence between the measurement matrix and the sparsifying matrix. Mutual coherence between the measurement matrix and sparsifying matrix can be expressed indirectly by the property of the Gram matrix. On the basis of the Gram matrix, a new optimization algorithm of acquiring a measurement matrix has been proposed in this paper. Firstly, a new mathematical model is designed and a new method of initializing measurement matrix is adopted to optimize the measurement matrix. Then, the loss function of the new algorithm model is solved by the gradient projection-based method of Gram matrix approximating an identity matrix. Finally, the optimized measurement matrix is generated by minimizing mutual coherence between measurement matrix and sparsifying matrix. Compared with the conventional measurement matrices and the traditional optimization methods, the proposed new algorithm effectively improves the performance of optimized measurement matrices in reconstructing one-dimensional sparse signals and two-dimensional image signals that are not sparse. The superior performance of the proposed method in this paper has been fully tested and verified by a large number of experiments.