scholarly journals Computational complexity of determining which statements about causality hold in different space–time models

2008 ◽  
Vol 405 (1-2) ◽  
pp. 50-63 ◽  
Author(s):  
Vladik Kreinovich ◽  
Olga Kosheleva
Keyword(s):  
Computational Complexity ◽  
Space Time

Новый критерий оптимальности пространственно-временных матриц

2020 ◽  
Author(s):  
A.A. Reznev ◽  
V.B. Kreyndelin
Keyword(s):  
Computational Complexity ◽  
Large Scale ◽  
Noise Immunity ◽  
Optimality Criterion ◽  
Mimo Systems ◽  
Optimality Criteria ◽  
Space Time ◽  
Space Time Codes ◽  
Golden Code ◽  
New Criterion

The application of optimality criteria for the study of space-time codes is considered. Known rank and determinant criteria are described. The computational complexity of determinant criteria is presented taking into account some estimation of the real CPUs specifications. An algorithm for calculating a new optimality criterion is described. The computational complexity of the new optimality criterion is evaluated. The new criterion is applied to the study of the space-time Golden matrix. The obtained criterion value is used to modify the Golden code. The modeling for Golden code demonstrates that criterion works and gives us better levels for noise immunity. The proposed optimality criterion is acceptable in terms of computational complexity even for a large number of antennas, which is typical for large-scale MIMO systems. Рассматривается применение критериев оптимальности для исследования пространственно-временных кодов.Описаны известные ранговый и детерминантный критерии. Для детерминантного критерия оценена вычислительная сложность с учетом определения специальных высокопроизводительных процессоров. Описан алгоритм расчета нового критерия оптимальности. Проведена оценка вычислительной сложности нового критерия оптимальности. Новый критерий применен для исследования пространственно-временной матрицы Голден. Полученное значение критерия использовано для модификациикода Голден. Продемонстрированы кривые помехоустойчивости для кода Голден и кода Голден с модифицированным параметром, получен энергетический выигрыш. Предложенный критерий оптимальности приемлем с точки зрения вычислительнойсложности даже при большом числе антенн, характерном для систем широкомасштабного MIMO.

scholarly journals Computational Complexity of Decoding Orthogonal Space-Time Block Codes

2011 ◽  
Vol 59 (4) ◽  
pp. 936-941 ◽  
Author(s):  
Ender Ayanoglu ◽  
Erik G. Larsson ◽  
Eleftherios Karipidis
Keyword(s):  
Computational Complexity ◽  
Block Codes ◽  
Space Time ◽  
Time Block ◽  
Space Time Block Codes ◽  
Orthogonal Space

scholarly journals An Efficient Broadband Adaptive Beamformer without Presteering Delays

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1100
Author(s):  
Ming Zhang ◽  
Xiaojian Wang ◽  
Anxue Zhang
Keyword(s):  
Computational Complexity ◽  
Computational Cost ◽  
Weight Vector ◽  
Space Time ◽  
Constraint Matrix ◽  
Matrix Operations ◽  
Frequency Constraint ◽  
Simpler Algorithm ◽  
Specific Direction ◽  
Constraint Method

Broadband adaptive beamformers have been widely used in many areas due to their ability of filtering signals in space domain as well as in frequency domain. However, the space-time array employed in broadband beamformers requires presteering delays to align the signals coming from a specific direction. Because the presteering delays are direction dependent, it is difficult to make precise delays in practice. A common way to eliminate the presteering delays is imposing constraints on the weight vector of the space-time array. However, the structure of the constraint matrix is not taken into account in the existing methods, leading to a computational complexity of O(N2) when updating the weight vector. In this paper, we describe a new kind of constraint method in time domain that preserves the block diagonal structure of the constraint matrix. Based on this structure, we design an efficient weight vector update algorithm that has a computational complexity of O(N). In addition, the proposed algorithm does not contain matrix operations (only scalar and vector operations are involved), making it easy to be implemented in chips such as FPGA. Moreover, the constraint accuracy of the proposed method is as high as the frequency constraint method when the fractional bandwidth of the signal is smaller than 10%. Numerical experiments show that our method achieves the same performance of the state-of-the-art methods while keeping a simpler algorithm structure and a lower computational cost.

Space-Time Adaptive Processing and Jamming

2018 ◽  
pp. 38-62
Keyword(s):  
Signal Processing ◽  
Computational Complexity ◽  
Covariance Matrix ◽  
Basic Concept ◽  
Processing Technique ◽  
Space Time ◽  
Adaptive Processing ◽  
Signal Processing Technique ◽  
Space Time Adaptive Processing ◽  
Established Technique

Space-time adaptive processing (STAP) has been a well-established technique, whose basic concept and theory are first put forward by Brennan and Reed. However, it is difficult to implement in the practical system because of the computational complexity and the sample limitation for estimating the clutter covariance matrix. STAP is a modern signal processing technique that can improve target detectability in the presence of a strong clutter Klemm.

SS-BMUSIC Algorithm for Space-Time 2D Signal Model

2014 ◽  
Vol 654 ◽  
pp. 346-351 ◽  
Author(s):  
Yang Jun ◽  
Qi Feng
Keyword(s):  
Computational Complexity ◽  
Space Time ◽  
Smoothing Effect ◽  
Spatial Smoothing ◽  
Music Algorithm ◽  
Signal Model ◽  
Simulation Results

This paper presents a beamforming matrix with spatial smoothing effect, and extends it to the space-time 2D signal model, which not only reduces the computational complexity of the space-time 2D MUSIC algorithm and improves the coherence resolution capacity, simulation results show that this algorithm has better performance and effectiveness than MUSIC itself.

scholarly journals A Novel Beamforming Algorithm for GNSS Receivers with Dual-Polarized Sensitive Arrays in the Joint Space–Time-Polarization Domain

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4506 ◽  
Author(s):  
Haiyang Wang ◽  
Zhicheng Yao ◽  
Jian Yang ◽  
Zhiliang Fan
Keyword(s):  
Computational Complexity ◽  
Adaptive Filter ◽  
Density Ratio ◽  
Joint Space ◽  
Space Time ◽  
Least Mean Square ◽  
Minimum Variance Distortionless Response ◽  
Gnss Receivers ◽  
Dual Polarized ◽  
Beamforming Algorithm

Dual-polarized sensitive arrays (DPSAs) with the space–time-polarization adaptive processing (STPAP) technique, which employs the polarization domain as well as the space domain and time domain to filter out interferences, can cancel a larger number of wideband interferences for GNSS receivers. However, the traditional STPAP beamforming algorithm, which requires a separate adaptive filter for each GNSS satellite, will make the process computationally intensive as there are multiple GNSS satellites in the field of view (FOV). In order to overcome the shortcoming, a novel STPAP beamforming algorithm based on the minimum variance distortionless response (MVDR) criterion is proposed. Compared with the traditional STPAP beamforming algorithm, the proposed STPAP beamforming algorithm can process multiple GNSS satellites at once using only one adaptive filter, which will greatly reduce the computational complexity. Moreover, the proposed algorithm will not lead to a sharp deterioration in the output carrier-to-noise density ratio (C/N0) performance if the number of GNSS satellites processed in the same adaptive filter is proper. Furthermore, to calculate weight vector iteratively, an adaptive algorithm based on the constrained least mean square (CLMS) method is derived for the proposed STPAP beamforming algorithm. Simulation results validate that the proposed algorithm is effective in mitigating interferences for GNSS receivers in the joint space–time-polarization domain and meanwhile has lower computational complexity when maintaining the output C/N0 performance close to that of the traditional STPAP algorithm.

scholarly journals Random Nyström Approach to Clutter Subspace Estimation for Polarimetric Space-Time Adaptive Processing

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1488
Author(s):  
Kang Zhao ◽  
Zhiwen Liu ◽  
Shuli Shi ◽  
Yulin Huang ◽  
Yougen Xu
Keyword(s):  
Computational Complexity ◽  
Covariance Matrix ◽  
Selection Procedure ◽  
Space Time ◽  
Adaptive Processing ◽  
Noise Covariance Matrix ◽  
Noise Covariance ◽  
Subspace Estimation ◽  
Simulation Results ◽  
Space Time Adaptive Processing

A random Nyström (R-Nyström) scheme for clutter subspace estimation is proposed in the context of polarimetric space-time adaptive processing (pSTAP). Unlike the standard Nyström scheme making use of only partial columns of the clutter plus noise covariance matrix (CNCM), R-Nyström exploits full CNCM information with a properly designed selection procedure under the newly developed random ridge cross leverage score (RRCLS) criterion. With R-Nyström, sup-ported by the complete CNCM columns, upgraded clutter subspace estimation can be achieved at the expense of an insignificant increase in computational complexity, in contrast to the standard Nyström. The R-Nyström-based pSTAP, termed pR-Nyström, is shown to be superior over the current eigendecomposition-free subspace pSTAP in the signal to clutter plus noise loss and computational complexity. The efficacy of R-Nyström/pR-Nyström is validated by the simulation results.

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