基于量子Grover算法的MIMO-OFDM系统信号检测技术的研究
摘 要
以量子态并行计算为基础的Grover量子搜索算法，对于长度为 的无序数据库，计算复杂度仅为 ，而常规搜索算法的复杂度为 。
通信系统的低误码率和低计算复杂度是所有检测技术所追求的目标，特别是近年来，基于量子并行计算的量子智能算法有效地降低了一些经典难解算法的计算复杂度。本文正是基于这一目标，针对量子Grover算法在MIMO-OFDM系统信号检测中的应用展开了较为深入的研究，以期达到性能和计算复杂度的良好折衷。
首先，介绍了量子Grover搜索算法的主要思想，在经典计算机上模拟实现了Grover算法搜索单解时的迭代次数情况，接着分析了Grover算法搜索多目标解时存在的问题，并针对Grover算法存在的不足，提出了一种改进算法，当目标解 时，仅用一次搜索就能以不低于98.01%的成功概率搜索到目标解。
其次，介绍了MIMO-OFDM系统和几种经典的信号检测算法，并对其检测性能和时间复杂度进行了仿真和分析比较。
最后，设计了一种基于Grover算法的MIMO-OFDM系统信号检测方案，通过MATLAB仿真，将Grover算法及其改进算法与传统检测算法在性能和复杂度方面做了全面的分析比较，以期达到在有效降低经典最佳检测算法复杂度的同时，与经典最佳检测算法保持基本相同的性能。
关键词：量子并行计算；Grover算法；改进算法；MIMO-OFDM；信号检测
ABSTRACT
Grover’s algorithm, which is based on the quantum parallel computation, can find the desired value precisely with iterations in a large unsorted database which contains elements. However, to find the desired value in the database, any classical algorithm would need at least steps.
Low error rate and reduced complexity of communications system are two pursuing targets of all detection techniques.Particularly in recent years, quantum algorithms, based on the parallel quantum computation, simplify some classic information systems which are not easy to solve on the background of classic system. In order to achieve the goal, a much deeper investigation of the signal detection applications with Grover’s algorithm in the MIMO-OFDM system has been developed. At last,we expect to acquire a good compromise between the performance and the computational complexity.
Firstly, the basic principle of Grover’s algorithm is introduced in the thesis and the number of iterations is simulated in classic computer when searching the single solution with Grover’s algorithm.Then the problems of searching multi-objective solution with the Grover’s algorithm are analyzed.And an improved algorithm which can find the object with the successful probability at least 98.01% with one step when the fraction of marked items is greater than 1/4 is proposed for its shortcomings.
Secondly, the MIMO-OFDM systems and several classic signal detection algorithms are introduced, then their detection performances and time complexities are simulated, analyzed and compared.
Finally, a signal detection program based on Grover algorithm of MIMO-OFDM system is designed.Through the MATLAB simulation,the Grover algorithm,its improved algorithm and the traditional detection algorithm are made a comprehensive analysis and comparison in the detection performance and the time complexity.We expect that the improved algorithm can reduce the complexity of the traditional optimum detection algorithm efficiently ,while achieving the same performance.
Keywords:Quantum Computation;Grover Algorithm;The Improved Algorithm;
MIMO-OFDM; Signal Detection
目 录
摘 要 I
ABSTRACT II
目 录 IV
第一章 绪 论 1
1.1 课题研究背景及意义 1
1.2 论文的主要内容 3
第二章 量子Grover算法及其改进算法 4
2.1 量子信息论基础 4
2.1.1 量子态及表示 4
2.1.2 量子逻辑门 6
2.1.3 量子并行计算 8
2.2 Grover搜索算法 9
2.2.1 Grover算法描述及几何可视化 9
2.2.2 Grover算法的迭代次数及模拟实现 12
2.2.3 Grover算法存在的问题分析 13
2.3 Grover算法的改进 15
2.3.1 算法的改进思路 15
2.3.2 改进算法描述 16
2.3.3 改进算法的实现 18
2.4本章小结 20
第三章 MIMO-OFDM系统及其信号检测技术 21
3.1 MIMO-OFDM系统 21
3.1.1 MIMO技术 21
3.1.2 OFDM原理 22
3.1.3 MIMO-OFDM技术 23
3.2 经典MIMO-OFDM信号检测算法仿真分析与比较 26
3.2.1 最大似然检测算法 27
3.2.2 迫零算法 28
3.2.3 最小均方误差算法 28
3.2.4 三种经典算法仿真及性能分析 29
3.2.5 VBLAST算法仿真及性能分析 33
3.3 各种算法的运算复杂度比较 37
3.4本章小结 38
第四章 基于量子Grover算法的MIMO-OFDM系统信号检测技术 39
4.1 基于量子Grover算法的MIMO-OFDM检测方案设计 39
4.1.1 方案设计的思路 39
4.1.2 方案设计的算法描述 40
4.2 基于Grover算法的仿真与性能分析 41
4.2.1基于原始Grover算法的仿真与性能分析 41
4.2.2基于Grover改进算法的仿真与性能分析 44
4.3 经典算法与量子算法复杂度的比较与分析 47
4.4 本章小结 47
第五章 总结与展望 48
5.1 课题研究总结 48
5.2 研究展望 48
致 谢 50
参考文献 51
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