On Construction of Hadamard Rhotrix using a Special Type of Mn- Matrix

The Hadamard matrix H is a square matrix with all the entries +1’s or -1’s which satisfies the property HHT = n In. Rhotrix is a new concept for mathematical enrichment with much scope for research and has a wide range of applications in coding theory and cryptography. Mn–matrix is also a matrix with  1 entry, like the Hadamard matrix, but the orthogonality property is not satisfied. It is shown in this paper that Hadamard matrices and thereby Hadamard rhotrices can be constructed by using a special type of Mn-matrix, named N- matrix, which is a unique approach

Mitigating Pilot Contamination with Scrambling Sequences

In this letter, we advocate that it is possible to mitigate Pilot Contamination in Massive MIMO systems by scrambling the pilot sequences with a Base Station (BS) scrambling sequence. It is possible if a set of sequences is carefully designed to meet the orthogonality property defined in this letter. Each BS possesses its own scrambling sequence that can be reused the same way frequency reuse is applied to cell deployment. The main advantage of the prosed pilot generation scheme is that the frequency reuse factor can be set to 1, the most aggressive one, while the scrambling sequences can be reused with much less aggressive reuse factors (e.g. 4, 7, 9, 12, etc.), which in consequence results in pilot contamination mitigation and increased system's performance.

On generalisation of H-measures

In some applications it is useful to consider variants of H-measures different from those introduced in the classical or the parabolic case. We introduce the notion of admissible manifold and define variant H-measures on Rd x P for any admissible manifold P. In the sequel we study one special variant, fractional H-measures with orthogonality property, where the corresponding manifold and projection curves are orthogonal, as it was the case with classical or parabolic H-measures, and prove the localisation principle. Finally, we present a simple application of the localisation principle.

Support Recovery of Greedy Block Coordinate Descent Using the Near Orthogonality Property

In this paper, using the near orthogonal property, we analyze the performance of greedy block coordinate descent (GBCD) algorithm when both the measurements and the measurement matrix are perturbed by some errors. An improved sufficient condition is presented to guarantee that the support of the sparse matrix is recovered exactly. A counterexample is provided to show that GBCD fails. It improves the existing result. By experiments, we also point out that GBCD is robust under these perturbations.

The Research into Biorthogonal Six-Variable Wavelet Packets with Two-Scale and Applications in Material Science

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, the notion of orthogonal nonseparable six-variable wavelet bundles is introduced. A new method for designing them is presented by iteration process. A nice approach for constructing six-variable biorthogonal wavelet bundles is developed. The bi-orthogonality property of six-variable wavelet packets is discussed. Biorthogonality formulas con-cerning these six-variable wavelet packets are obtained. A constructive method for affine frames is presented. Moreover, it is shown how to get new Riesz bases of from the wavelet bundles.