scholarly journals Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme with Barzilai-Borwein Method

2020 ◽  
Author(s):  
Tongtong Xu ◽  
Zheng Xiang
Keyword(s):  
Theoretical Analysis ◽  
Gradient Method ◽  
Optimization Problems ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Step Size ◽  
Unconstrained Optimization Problems ◽  
Communications Systems ◽  
Simulation Results ◽  
Wireless Communications Systems

Abstract In this work, concurrent modified constant modulus algorithm and decision-directed scheme with the Barzilai-Borwein method is proposed for blind equalization of wireless communications systems. The Barzilai-Borwein method, the two-step gradient method, is usually used to solve multidimensional unconstrained optimization problems. The proposed algorithm concurrently operates a modified constant modulus algorithm equalizer and a decision directed equalizer, it then adaptively adjusts the step size of the decision directed equalizer using Barzilai-Borwein method. Theoretical analysis is provided to illustrate that the proposed algorithm has a faster convergence speed, and better equalization performance than the original one. Simulation results support the new proposed technique.

scholarly journals Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

2021 ◽  
Vol 15 ◽  
Author(s):  
Tongtong Xu ◽  
Zheng Xiang ◽  
Hua Yang ◽  
Yun Chen ◽  
Jun Luo ◽  
...  
Keyword(s):  
Wireless Communication ◽  
Optimization Problems ◽  
Blind Equalization ◽  
Wireless Channel ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Step Size ◽  
Pilot Signal ◽  
Unconstrained Optimization Problems ◽  
Wireless Communications Systems

At present, in robot technology, remote control of robot is realized by wireless communication technology, and data anti-interference in wireless channel becomes a very important part. Any wireless communication system has an inherent multi-path propagation problem, which leads to the expansion of generated symbols on a time scale, resulting in symbol overlap and Inter-symbol Interference (ISI). ISI in the signal must be removed and the signal restores to its original state at the time of transmission or becomes as close to it as possible. Blind equalization is a popular equalization method for recovering transmitted symbols of superimposed noise without any pilot signal. In this work, we propose a concurrent modified constant modulus algorithm (MCMA) and the decision-directed scheme (DDS) with the Barzilai-Borwein (BB) method for the purpose of blind equalization of wireless communications systems (WCS). The BB method, which is two-step gradient method, has been widely employed to solve multidimensional unconstrained optimization problems. Considering the similarity of equalization process and optimization process, the proposed algorithm combines existing blind equalization algorithm and Barzilai-Borwein method, and concurrently operates a MCMA equalizer and a DD equalizer. After that, it modifies the DD equalizer's step size (SS) by the BB method. Theoretical investigation was involved and it demonstrated rapid convergence and improved equalization performance of the proposed algorithm compared with the original one. Additionally, the simulation results were consistent with the proposed technique.

New Hybrid Blind Equalization Algorithms

2012 ◽  
Vol 182-183 ◽  
pp. 1810-1815
Author(s):  
Shun Lan Liu ◽  
Lin Wang
Keyword(s):  
Blind Equalization ◽  
Convergence Speed ◽  
Variable Step Size ◽  
Constant Modulus ◽  
Computation Complexity ◽  
Constant Modulus Algorithm ◽  
Step Size ◽  
Variable Step ◽  
Simulation Results ◽  
The Cost

A novel decision-directed Modified Constant Modulus Algorithm (DD-MCMA) was proposed firstly. Then a constellation matched error (CME) function was added to the cost function of DD-MCMA and CME-DD-MCMA algorithm was presented. Furthermore, we improve the CME-DD-MCMA by replacing the fixed step with variable step size, that is VSS-CME-DD-MCMA algorithm. The simulation results show that the proposed new blind equalization algorithms can tremendously accelerate the convergence speed and achieve lower residual inter-symbol interference (ISI) than MCMA, and among the three proposed algorithms, VSS-CME-DD-MCMA has the fastest convergence speed and the lowest residual ISI, but it has the largest computation complexity.

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950017 ◽  
Author(s):  
Wen-Li Dong ◽  
Xing Li ◽  
Zheng Peng
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Gradient Method ◽  
Line Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Search Technique ◽  
Unconstrained Optimization Problems ◽  
Armijo Line Search ◽  
Line Search Technique

In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

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