改进的差分进化算法及其在通信信号处理中的应用研究
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摘要
受计算机技术发展的推动,智能优化技术日臻成熟,已经发展成为一门重要的应用学科,在认识世界和改造世界中的作用也日益显现出来。工程应用实践业已表明,经过优化处理的系统,其性能可以得到显著提升。在通信信号处理领域,许多应用问题本质上也可以归结为优化问题,如通信信号的波形优化成型设计、调制信号的特征提取、多输入多输出通信系统的符号检测等等。对于诸如此类的问题,传统的方法往往难以直接得到满意解,采用优化计算的方法可求得近似最优的处理结果。作为一种新型的优化计算方法,差分进化以简单实用、收敛快、鲁棒性好等特点得到了人们的广泛研究和应用,对进化优化计算的思想创新和技术发展做出了特有的贡献。
但是,类似于其它基于种群的演化算法,差分进化也存在某种缺陷,主要表现为搜索停滞和早熟收敛,尤其对于高维复杂工程应用问题,标准差分进化算法不能有效解决。针对此问题,论文提出了相应的改进方法,并通过经典测试函数进行了实验验证,同时研究了改进的差分进化算法在通信信号处理中的两种具体应用。论文的主要研究成果如下:
(1)提出了基于参数自适应和混沌局部优化的Memetic差分进化算法(DECLS)。该算法利用参数的自适应调整提高差分进化的全局寻优性能,并利用嵌入的混沌局部优化在最优值附近详细开发,以补偿标准差分进化算法在精细搜索方面的不足,提高最终优化精度。同时,混沌搜索的随机性还可在一定程度上弥补标准差分进化早熟收敛的缺陷。实验证明,混沌搜索和自适应差分进化的组合是十分合理的。DECLS算法在一系列测试中均明显优于标准差分进化算法,也优于其它差分进化变种。并且,DECLS算法在高维函数优化中也表现出一定的优越性。
(2)由于标准差分进化是为解决连续问题优化而设计的,不能直接用于二进制空间优化。针对此问题,论文提出了基于参数自适应策略的二进制离散差分进化算法(ABDE)。该算法对标准差分进化算法的变异方法进行了改进,同时令交叉因子和收缩因子根据优化环境自适应调整,以达到最好的优化效果。在13个标准测试函数和经典的二进制规划0-1背包问题上的测试表明,与其它两种二进制DE算法和常用的遗传算法相比,该算法具有更强的搜索能力、更快的收敛速度和更稳定的优化性能。
(3)对甚小线性调频(VMCK)调制信号进行了分析,并基于数值拟合原理,提出了基于正弦基拟合分解和差分进化的甚小线性调频信号优化方案,以达到改善VMCK频谱结构的目的,理论分析和仿真表明该方案可成功的去除VMCK谐波线谱,得到带宽更窄,边带抑制更强,且能量更为集中的VMCK波形,同时信号的解调性能有了进一步提高。
(4)通过将多输入多输出(MIMO)通信系统的最小误码率(MBER)问题转化为一种最优化问题,研究了差分进化在MIMO通信系统符号检测中应用的可行性,并提出了利用Memetic连续差分进化算法优化MBER解码矩阵W系数的MIMO线性检测方法。实验表明,该方法优于基于MMSE和ZF的MIMO线性检测算子。进一步的,论文又给出了一种以二进制离散差分进化算法寻优代替最大似然检测穷搜索技术的非线性MIMO符号检测方案,以期在可接受的误码率范围内,尽最大可能的降低最大似然检测的计算消耗。
With the promotion of computer technology, the intelligent optimization technique becomes mature gradually. It has been developed as an important application subject and increasingly revealed effects in understanding and transforming the world. Proved by engineering applications, the performance of a system can be enhanced significantly with an optimizing procedure. In communication and signal processing area, many problems can boil down to a kind of optimization issue in nature. For instance, communication waveforms shaping and optimizing design, features extraction of modulation signals, and symbol detection in MIMO (multi-input multi-output) communication system, etc.. These problems usually can not be solved ideally by traditional methods. However, we can obtain their approximate optimal solutions through an optimization process. As a new search technique, differential evolution has been profoundly researched and widely used for its advantages of simple and particle uses, fast convergence, and robust. It has made special contributions to the theoretical innovation and technological development of evolutionary computation.
However, similar to other population based optimizers, differential evolution has certain drawbacks such as stagnation and premature convergence. Particularly for high-dimensional complex problems, the standard differential evolution can not solve them effectively. To overcome the defects of standard differential evolution algorithm, improving ways have been proposed and further tested over benchmark functions in this dissertation. Finally, two specific applications in communication area have been studied based on the improved differential evolution algorithm. The main contributions of the work are as follows:
(1) The dissertation proposes an effective memetic differential evolution algorithm, or DECLS, that utilizes parameter adaptation to enhance the global optimizing performance, and chaotic local search to improve the final solution accuracy by carefully exploiting around the best individual. Moreover, the randomness of chaotic search can compensate for the premature convergence of standard DE to some extent. Simulations proved that the combination of a chaotic local search and a parameter adaptation mechanism is very reasonable. Results show that DECLS is superior to the standard DE and other DE variants. What is more, the DECLS has also shown certain advantages in solving high dimensional problems.
(2) To overcome the problem that standard DE can not be directly used in a binary search space, the dissertation proposed an adaptive binary Differential Evolution algorithm, or ABDE, that improves the mutation strategy and adaptively controls the scaling and crossover factors to obtain a better optimization result. Experiments have been carried out by comparing ABDE with two binary DE variants and the most used Genetic Algorithm on a set of 13 selected benchmark functions and the classical 0-1 knapsack problem. Results show that the ABDE performs better than, or at least comparable to, the other algorithms in terms of search ability, convergence speed, and solution accuracy.
(3) By analyzing the Very Minimum Chirp Keying (VMCK) modulation signal, the dissertation proposed an optimization scheme that utilizes the sinusoidal basis fitting and differential evolution to modify the spectrum shapes. The theoretical analysis and simulation show that the proposed scheme can remove the harmonic spectral lines successfully and obtain an optimized VMCK waveform with narrower bandwidth, lower spectrum sidebands, and better demodulation performance.
(4) By transforming the minimization of bit error rate of a Multi-input Multi-output (MIMO) communication system into an optimization problem, the dissertation proposed a new linear MIMO symbol detector that utilizes the memetic differential evolution to optimize the MBER detector’s coefficients. Simulation shows that the proposed detector is superior to MMSE and ZF linear detectors. Further, to save the computation consumption of ML detector under the allowed bit error rate, the dissertation presents a new non-linear MIMO symbol detection method which uses a binary differential evolution optimization to replace the exhaustive search technique.
但是,类似于其它基于种群的演化算法,差分进化也存在某种缺陷,主要表现为搜索停滞和早熟收敛,尤其对于高维复杂工程应用问题,标准差分进化算法不能有效解决。针对此问题,论文提出了相应的改进方法,并通过经典测试函数进行了实验验证,同时研究了改进的差分进化算法在通信信号处理中的两种具体应用。论文的主要研究成果如下:
(1)提出了基于参数自适应和混沌局部优化的Memetic差分进化算法(DECLS)。该算法利用参数的自适应调整提高差分进化的全局寻优性能,并利用嵌入的混沌局部优化在最优值附近详细开发,以补偿标准差分进化算法在精细搜索方面的不足,提高最终优化精度。同时,混沌搜索的随机性还可在一定程度上弥补标准差分进化早熟收敛的缺陷。实验证明,混沌搜索和自适应差分进化的组合是十分合理的。DECLS算法在一系列测试中均明显优于标准差分进化算法,也优于其它差分进化变种。并且,DECLS算法在高维函数优化中也表现出一定的优越性。
(2)由于标准差分进化是为解决连续问题优化而设计的,不能直接用于二进制空间优化。针对此问题,论文提出了基于参数自适应策略的二进制离散差分进化算法(ABDE)。该算法对标准差分进化算法的变异方法进行了改进,同时令交叉因子和收缩因子根据优化环境自适应调整,以达到最好的优化效果。在13个标准测试函数和经典的二进制规划0-1背包问题上的测试表明,与其它两种二进制DE算法和常用的遗传算法相比,该算法具有更强的搜索能力、更快的收敛速度和更稳定的优化性能。
(3)对甚小线性调频(VMCK)调制信号进行了分析,并基于数值拟合原理,提出了基于正弦基拟合分解和差分进化的甚小线性调频信号优化方案,以达到改善VMCK频谱结构的目的,理论分析和仿真表明该方案可成功的去除VMCK谐波线谱,得到带宽更窄,边带抑制更强,且能量更为集中的VMCK波形,同时信号的解调性能有了进一步提高。
(4)通过将多输入多输出(MIMO)通信系统的最小误码率(MBER)问题转化为一种最优化问题,研究了差分进化在MIMO通信系统符号检测中应用的可行性,并提出了利用Memetic连续差分进化算法优化MBER解码矩阵W系数的MIMO线性检测方法。实验表明,该方法优于基于MMSE和ZF的MIMO线性检测算子。进一步的,论文又给出了一种以二进制离散差分进化算法寻优代替最大似然检测穷搜索技术的非线性MIMO符号检测方案,以期在可接受的误码率范围内,尽最大可能的降低最大似然检测的计算消耗。
With the promotion of computer technology, the intelligent optimization technique becomes mature gradually. It has been developed as an important application subject and increasingly revealed effects in understanding and transforming the world. Proved by engineering applications, the performance of a system can be enhanced significantly with an optimizing procedure. In communication and signal processing area, many problems can boil down to a kind of optimization issue in nature. For instance, communication waveforms shaping and optimizing design, features extraction of modulation signals, and symbol detection in MIMO (multi-input multi-output) communication system, etc.. These problems usually can not be solved ideally by traditional methods. However, we can obtain their approximate optimal solutions through an optimization process. As a new search technique, differential evolution has been profoundly researched and widely used for its advantages of simple and particle uses, fast convergence, and robust. It has made special contributions to the theoretical innovation and technological development of evolutionary computation.
However, similar to other population based optimizers, differential evolution has certain drawbacks such as stagnation and premature convergence. Particularly for high-dimensional complex problems, the standard differential evolution can not solve them effectively. To overcome the defects of standard differential evolution algorithm, improving ways have been proposed and further tested over benchmark functions in this dissertation. Finally, two specific applications in communication area have been studied based on the improved differential evolution algorithm. The main contributions of the work are as follows:
(1) The dissertation proposes an effective memetic differential evolution algorithm, or DECLS, that utilizes parameter adaptation to enhance the global optimizing performance, and chaotic local search to improve the final solution accuracy by carefully exploiting around the best individual. Moreover, the randomness of chaotic search can compensate for the premature convergence of standard DE to some extent. Simulations proved that the combination of a chaotic local search and a parameter adaptation mechanism is very reasonable. Results show that DECLS is superior to the standard DE and other DE variants. What is more, the DECLS has also shown certain advantages in solving high dimensional problems.
(2) To overcome the problem that standard DE can not be directly used in a binary search space, the dissertation proposed an adaptive binary Differential Evolution algorithm, or ABDE, that improves the mutation strategy and adaptively controls the scaling and crossover factors to obtain a better optimization result. Experiments have been carried out by comparing ABDE with two binary DE variants and the most used Genetic Algorithm on a set of 13 selected benchmark functions and the classical 0-1 knapsack problem. Results show that the ABDE performs better than, or at least comparable to, the other algorithms in terms of search ability, convergence speed, and solution accuracy.
(3) By analyzing the Very Minimum Chirp Keying (VMCK) modulation signal, the dissertation proposed an optimization scheme that utilizes the sinusoidal basis fitting and differential evolution to modify the spectrum shapes. The theoretical analysis and simulation show that the proposed scheme can remove the harmonic spectral lines successfully and obtain an optimized VMCK waveform with narrower bandwidth, lower spectrum sidebands, and better demodulation performance.
(4) By transforming the minimization of bit error rate of a Multi-input Multi-output (MIMO) communication system into an optimization problem, the dissertation proposed a new linear MIMO symbol detector that utilizes the memetic differential evolution to optimize the MBER detector’s coefficients. Simulation shows that the proposed detector is superior to MMSE and ZF linear detectors. Further, to save the computation consumption of ML detector under the allowed bit error rate, the dissertation presents a new non-linear MIMO symbol detection method which uses a binary differential evolution optimization to replace the exhaustive search technique.
引文
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