scholarly journals Linear Regression with Optimal Rotation

Stats ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 416-425 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Linear Regression ◽  
Correlation Coefficient ◽  
Rotation Angle ◽  
Outer Region ◽  
Optimal Angle ◽  
Optimal Rotation ◽  
Optimal Value ◽  
The One ◽  
Optimal Rotation Angle ◽  
Selection Of

The paper shows how the linear regression depends on the selection of the reference frame. The slope of the fitted line and the corresponding Pearson’s correlation coefficient are expressed in terms of the rotation angle. The correlation coefficient is found to be maximized for a certain optimal angle, for which the slope attains a special optimal value. The optimal angle, the value of the optimal slope, and the corresponding maximum correlation coefficient were expressed in terms of the covariance matrix, but also in terms of the values of the slope, derived from the fitting at the nonrotated and right-angle-rotated axes. The potential of the new method is to improve the derived values of the fitting parameters by detecting the optimal rotation angle, that is, the one that maximizes the correlation coefficient. The presented analysis was applied to the linear regression of density and temperature measurements characterizing the proton plasma in the inner heliosheath, the outer region of our heliosphere.

scholarly journals Comparison of iterative angular spectrum and optimal rotation angle methods in designing beam-fanners

2009 ◽  
Vol 17 (17) ◽  
pp. 14825 ◽  
Author(s):  
Seyyed H. Kazemi ◽  
Mir M. Mirsalehi ◽  
Amir R. Attari
Keyword(s):  
Rotation Angle ◽  
Angular Spectrum ◽  
Optimal Rotation ◽  
Optimal Rotation Angle

scholarly journals Selection of Features on Mining Techniques for Classification

2018 ◽  
Vol 7 (S1) ◽  
pp. 108-111
Author(s):  
Gurrampally Kumar ◽  
S. Mohan ◽  
G. Prabakaran
Keyword(s):  
Feature Selection ◽  
Linear Regression ◽  
Gaussian Process ◽  
Statistical Method ◽  
Correlation Coefficient ◽  
Euclidean Distance ◽  
Experimental Results ◽  
Selection Of

Feature selection has been developed by several mining techniques for classification. Some existing approaches couldn’t remove the irrelevant data from dataset for class. Thus it needs the selection of appropriate features that emphasize its role in classification. For this it consider the statistical method like correlation coefficient to identify the features from feature set whose data are very important for existing classes. The several methods such as Gaussian process, linear regression and Euclidean distance have taken into consideration for clarity of classification. The experimental results reveal that the proposed method identifies the exact relevant features for several classes.

Low Complexity Channel Estimation Algorithm Using Paired Spatial Signatures for UAV 3D MIMO Systems

2020 ◽  
Author(s):  
Peizhong Xie ◽  
Yingqing Wan ◽  
Ting Li ◽  
Renjie Ju
Keyword(s):  
Channel Estimation ◽  
Rotation Angle ◽  
Mimo Systems ◽  
Estimation Algorithm ◽  
Low Complexity ◽  
Three Dimension ◽  
Optimal Rotation ◽  
3D Mimo ◽  
Training Resources ◽  
Optimal Rotation Angle

Abstract This paper proposes a low complexity channel estimation algorithm for unmanned aerial vehicle (UAV) three dimension multi-user multiple-input-multiple-output (3D MIMO) systems with the uniform planar array (UPA) at base station (BS) using paired spatial signatures. With the aid of antenna array theory and array signal processing, 3D channel is firstly modeled based on the angles between the direction of arrival (DOA) along x- and y-axis of the UPA. And 3D MIMO channels can be projected onto the x- and y-directions, respectively. Then, channel estimation for multi-user uplinks using small amount of training resources is divided into two phases. At the first uplink preamble phase, each user is assigned the orthogonal pilot, and the paired spatial signatures and optimal rotation angle of each user through the same pilot sequence are obtained. We also propose a user grouping strategy based on three-dimension angle-division multiple access (3D-ADMA) to ensure that the user's spatial signatures do not overlap. At the second phase during several coherence times, the same pilot sequence within a group and orthogonal pilot sequences between groups are assigned, then, the channel state information of the user's x- and y-directions are recovered by the paired space signatures and optimal rotation angle of each user obtained in the preamble phase, respectively. And dynamically updating the user's paired spatial signatures and optimal rotation angle utilizes the obtained channel parameter of x- and y-directions. Finally, the channel parameter of the x- and y-directions are reconstructed by the updated user's space signatures and the optimal rotation angle, and the 3D MIMO channel estimation is obtained through the Kronecker product. Compared with the conventional channel estimation method of the 3D MIMO system under UPA using a low-rank model, the proposed methods reduce the computational complexity without degrading the estimated performance to a large extent. Furthermore, it is carried out with limited training resources, and the pilot resource overhead of the system is greatly reduced by the 3D-ADMA packet and the two-stage pilot allocation. Simulation results verified that the proposed algorithm is effective and feasible. Keywords 3D MIMO, 3D Channel Modeling, Unmanned Aerial Vehicle, Channel Estimation, Computational Complexity

scholarly journals Modulation Set Optimization for the Improved Complex Quadrature SM

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Asif Iqbal ◽  
Manar Mohaisen ◽  
Kyung Sup Kwak
Keyword(s):  
Euclidean Distance ◽  
Rotation Angle ◽  
Computational Cost ◽  
Low Complexity ◽  
Spatial Modulation ◽  
Optimal Rotation ◽  
Wide Range ◽  
Channel Realization ◽  
System Configurations ◽  
Optimal Rotation Angle

At each channel use, the complex quadrature spatial modulation (CQSM) transmits two signal symbols drawn from two disjoint modulation sets. The indices of the antennas from which symbols are transmitted also carry information. In the improved CQSM (ICQSM), an additional antenna is used to transmit the second signal symbol only when the indices of the antennas to be used for transmission are equal. Conventionally, the second modulation set is a rotated version of the first, where the rotation angle is optimized such that the average unconditional error probability (AUP) is reduced. In this paper, we propose a low-complexity method to design the PSK modulation sets based on reducing the AUP. After introducing min-BER and max-dmin, two exhaustive search methods, we analytically show that the AUP depends on Euclidean distance between transmitted vectors, which in turn depends on the power of signal symbols, the Euclidean distance between the symbols of each modulation set, and the Euclidean distance between the symbols of the two sets. The optimal rotation angle is analytically derived for any modulation order and the radii of the modulation sets are optimized such that AUP is reduced for a wide range of system configurations. The simulation results show that more than 3 dB of power gain is achieved in the case of 16PSK, where higher gains are achieved for higher modulation orders. These gains are achieved at no computational cost because the optimization does not depend on the channel realization.

A Novel Method of Parameter Estimation in Wideband Bistatic MIMO Radar System

2014 ◽  
Vol 556-562 ◽  
pp. 5038-5041
Author(s):  
Li Li
Keyword(s):  
Rotation Angle ◽  
Mimo Radar ◽  
Radar System ◽  
Music Algorithm ◽  
Signal Model ◽  
Bistatic Mimo Radar ◽  
Optimal Rotation ◽  
Novel Method ◽  
Esprit Algorithm ◽  
Optimal Rotation Angle

This paper proposes a new wideband signal model and a novel method in wideband bistatic MIMO radar system. Firstly, a new signal array model is proposed. Secondly, Doppler stretch and time delay are jointly estimated by searching the optimal rotation angle to meet concentrated-energy of the fractional correlation function. Furthermore, two algorithms are presented for the estimation of DODs and DOAs, including based on MUSIC algorithm and ESPRIT algorithm. Simulation results are presented to verity the effectiveness of the proposed method.

scholarly journals Low complexity channel estimation algorithm using paired spatial signatures for UAV 3D MIMO systems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Peizhong Xie ◽  
Yingqing Wan ◽  
Ting Li ◽  
Renjie Ju
Keyword(s):  
Channel Estimation ◽  
Rotation Angle ◽  
Mimo Systems ◽  
Estimation Algorithm ◽  
Low Complexity ◽  
Three Dimension ◽  
Optimal Rotation ◽  
3D Mimo ◽  
Training Resources ◽  
Optimal Rotation Angle

AbstractThis paper proposes a low complexity channel estimation algorithm for unmanned aerial vehicle three dimension multi-user multiple-input-multiple-output (3D MIMO) systems with the uniform planar array (UPA) at base station using paired spatial signatures. With the aid of antenna array theory and array signal processing, 3D channel is firstly modeled based on the angles between the direction of arrival along x- and y-axis of the UPA. And 3D MIMO channels can be projected onto the x- and y-directions, respectively. Then, channel estimation for multi-user uplinks using small amount of training resources is divided into two phases. At the first uplink preamble phase, each user is assigned the orthogonal pilot, and the paired spatial signatures and optimal rotation angle of each user through the same pilot sequence are obtained. We also propose a user grouping strategy based on three-dimension angle-division multiple access (3D-ADMA) to ensure that the user's spatial signatures do not overlap. At the second phase during several coherence times, the same pilot sequence within a group and orthogonal pilot sequences between groups are assigned, then, the channel state information of the user's x- and y-directions are recovered by the paired space signatures and optimal rotation angle of each user obtained in the preamble phase, respectively. And dynamically updating the user's paired spatial signatures and optimal rotation angle utilizes the obtained channel parameter of x- and y-directions. Finally, the channel parameter of the x- and y-directions are reconstructed by the updated user's space signatures and the optimal rotation angle, and the 3D MIMO channel estimation is obtained through the Kronecker product. Compared with the conventional channel estimation method of the 3D MIMO system under UPA using a low-rank model, the proposed methods reduce the computational complexity without degrading the estimated performance to a large extent. Furthermore, it is carried out with limited training resources, and the pilot resource overhead of the system is greatly reduced by the 3D-ADMA packet and the two-stage pilot allocation. Simulation results verified that the proposed algorithm is effective and feasible.

Computation for polarizer's optimal rotation angle on airborne optical platform

2011 ◽  
Author(s):  
Bin Feng ◽  
Ze-lin Shi ◽  
Qing-hai Ding ◽  
Xin-rong Yu
Keyword(s):  
Rotation Angle ◽  
Optimal Rotation ◽  
Optimal Rotation Angle

Optimal rotation angle for finite constellation over additive white Gaussian noise multiple access wiretap channel

2020 ◽  
Vol 14 (21) ◽  
pp. 3845-3852
Author(s):  
Shahid Mehraj Shah ◽  
Rufaidah Riyaz ◽  
Taiba Majid Wani ◽  
Arieb Ashraf ◽  
Syed Farah Naz
Keyword(s):  
Gaussian Noise ◽  
Multiple Access ◽  
Rotation Angle ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Wiretap Channel ◽  
Optimal Rotation ◽  
Optimal Rotation Angle
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