Coherence Based Sufficient Condition for Support Recovery Using Generalized Orthogonal Matching Pursuit

In an underdetermined system,compressive sensing can be used to recover the support vector.Greedy algorithms will recover the support vector indices in an iterative manner.Generalized Orthogonal Matching Pursuit(GOMP)is the generalized form of the Orthogonal Matching Pursuit(OMP)algorithm where a number of indices selected per iteration will be greater than or equal to 1.To recover the support vector of unknown signal‘x’from the compressed measurements,the restricted isometric property should be satisfied as a sufficient condition.Finding the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support recovery.In this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal‘x’using GOMP has been derived.The derived sufficient condition will recover support vectors of P-sparse signal within‘P’iterations.The recovery guarantee for GOMP is less restrictive,and applies to OMP when the number of selection elements equals one.Simulation shows the superior performance of the GOMP algorithm compared with other greedy algorithms.

A New Generalized Complex Orthogonal Space-Time Block Codes

Recent research challenges in the wireless communication include the usage of diversity and efficient coding to improve data transmission quality and spectral efficiency. Space diversity uses multiple transmitting and/or receiving antennas to create independent fading channels without penalty in bandwidth efficiency. Space-time block coding is an encoding scheme for communication over Rayleigh fading channels using multiple transmitting antennas. Space-time block codes from complex orthogonal designs exist only for two transmitting antennas. This paper generalizes a new complex orthogonal space-time block code for four transmitting antennas, whose decoding complexity is very low. Simulations show that the generalized complex orthogonal space-time block code has low bit error rate, full rate and possibly large diversity.

The Related Properties of Generalized Orthogonal Group in Specific Normed Linear Spaces

Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the lp space.

GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS Ⅱ

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE

The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.

Automorphisms of generalized orthogonal graphs of characteristic 2

We determine the automorphism group of the generalized orthogonal graph GO2v＋δ（q, m, G） over Fq of characteristic 2, where 1 〈 m 〈 v.

Generalized Latin Matrix and Construction of Orthogonal Arrays

In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.