scholarly journals Asymptotic Performance Analysis of the MUSIC Algorithm for Direction-of-Arrival Estimation

2020 ◽  
Vol 10 (6) ◽  
pp. 2063
Author(s):  
So-Hee Jeong ◽  
Byung-kwon Son ◽  
Joon-Ho Lee
Keyword(s):  
Performance Analysis ◽  
Closed Form ◽  
Covariance Matrix ◽  
Estimation Error ◽  
Closed Form Expression ◽  
Simultaneous Estimation ◽  
Music Algorithm ◽  
Form Expression ◽  
Sample Covariance ◽  
Future Work

We consider the performance analysis of the multiple signal classification (MUSIC) algorithm for multiple incident signals when the uniform linear array (ULA) is adopted for estimation of the azimuth of each incident signal. We derive closed-form expression of the estimation error for each incident signal. After some approximations, we derive closed-form expression of the mean square error (MSE) for each incident signal. In the MUSIC algorithm, the eigenvectors of covariance matrix are used for calculation of the MUSIC spectrum. Our derivation is based on how the eigenvectors of the sample covariance matrix are related to those of the true covariance matrix. The main contribution of this paper is the reduction in computational complexity for the performance analysis of the MUSIC algorithm in comparison with the traditional Monte–Carlo simulation-based performance analysis. The validity of the derived expressions is shown using the numerical results. Future work includes an extension to performance analysis of the MUSIC algorithm for simultaneous estimation of the azimuth and the elevation.

On the three-state weather model of transmission line failures

2007 ◽  
Vol 221 (3) ◽  
pp. 217-228 ◽  
Author(s):  
A Csenki
Keyword(s):  
Transmission Line ◽  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Rate Matrix ◽  
Reliability Indices ◽  
Matrix Operations ◽  
Weather Model ◽  
Adverse Weather ◽  
Future Work

Recent work by Billinton et al. has highlighted the importance of employing more than one adverse weather state when modelling transmission line failures by Markov processes. In the present work the structure of the modelling Markov process is identified, allowing the rate matrix to be written in a closed form using Kronecker matrix operations. This approach allows larger models to be handled safely and with ease. The MAXIMA implementation of two asymptotic reliability indices for such systems is addressed, exemplifying the combination of symbolic and numerical steps, perhaps not seen in this context before. It is also indicated how the three-state weather model can be extended to a multi-state model, while retaining the scope of the proposed closed-form expression for the rate matrix. Some possible future work is discussed.

scholarly journals Secrecy capacity optimization artificial noise: the ergodic secrecy capacity lower bound and optimal power allocation

2020 ◽  
Author(s):  
Yebo Gu ◽  
Zhilu Wu ◽  
Zhendong Yin ◽  
Bowen Huang
Keyword(s):  
Lower Bound ◽  
Channel Estimation ◽  
Closed Form ◽  
Power Allocation ◽  
Estimation Error ◽  
Closed Form Expression ◽  
Artificial Noise ◽  
Secrecy Capacity ◽  
Capacity Optimization ◽  
Form Expression

Abstract The secure transmission problem of MIMO wireless system in fading channels is studied in this paper. We add a secrecy capacity optimization artificial noise(SCO-AN) to the transported signal for improving the security performance of the system. The closed-form expression of secrecy capacity's lower bound is obtained. Base on the closed-form expression of secrecy capacity's lower bound, We optimize the power allocation between the information-bearing signal and the SCO-AN. By calculating, the optimal ratio of power alloation betwenn the information-bearing signal and the SCO-AN is obtained. Through simulation, the results shows the secrecy capacity increases with more receiving antennas and less eavesdropping antennas.And more power should be allocated to the SCO-AN with the increase of the colluding eavedroppers.More over, we study the effect of channel estimation error on power allocation between information-bearing signal and SCO-AN and find that more power should be allocated to decrease eavesdroppers capacity if the channel estimation is not perfect.

scholarly journals Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 263
Author(s):  
Claudia Fassino ◽  
Giovanni Pistone ◽  
Maria Rogantin
Keyword(s):  
Closed Form ◽  
Covariance Matrix ◽  
Sufficient Conditions ◽  
Closed Form Expression ◽  
Gaussian Vector ◽  
Form Expression ◽  
Singular Covariance Matrix

Given a multivariate complex centered Gaussian vector Z = ( Z 1 , ⋯ , Z p ) with non-singular covariance matrix Σ , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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