新的四元序列族及其在压缩传感中的应用

发布时间：2018-07-25 12:30

【摘要】：伪随机序列族因为其良好的自相关性、互相关性、长周期、大线性复杂度、平衡性、易于实现等特点被广泛应用于雷达、声呐、通信系统、密码系统等领域。从便于硬件实现的角度,二元序列和四元序列成为应用于实际中的首选序列。二元序列研究比较早,其中最著名的是m序列和Gold序列。m序列在通信领域有着广泛的应用。Gold序列是1967年R.Gold在m序列的基础上提出的一种特性较好的伪随机序列。基于伽罗华环的四元序列的研究比较晚,但是人们发现对于给定的序列族大小M和序列族周期L,根据Welch和Sidelnikov界,设计出最大互相关值比最优二元序列族的最大互相关值更小的四元序列族是可以的,其最大互相关函数值是最优二元序列的1/2。目前已构造出的具有良好特性的四元序列族不是很多,因此构造出具有良好特性的四元伪随机序列族具有重要意义。为了不失真地恢复模拟信号,奈奎斯特采样定理要求采样频率应该不小于模拟信号频谱中最高频率的2倍,这极大地限制了信息的处理能力。压缩传感理论的出现打破了这一传统定理使得高分辨率信号的采集成为可能,在很多领域表现了显著优势。测量矩阵的设计是压缩传感理论的一个热点问题,它关系着信号能否实现压缩和信号能否精确重构。目前使用最广泛的测量矩阵是随机投影矩阵或者服从独立同分布的矩阵,例如高斯随机矩阵、贝努利矩阵。因为这两种矩阵与其他所有的稀疏变换基不相干,它使我们在没有先验知识的条件下无损伤的感知来自原始域的信号,除此之外,我们可以在满足一定测量值的要求下实现原始信号的精确重构。但是在实际应用中构造出硬件容易实现的测量矩阵才是压缩传感理论应用于实际的关键。本文研究的主要成果:1、构造出具有良好特性的四元序列。Tang提出了一种将周期为奇数的序列族周期扩展2倍的方法,但这种方法不适用于周期为偶数的序列族。新方法是将周期为偶数的序列族周期扩展2倍。将新方法应用于序列族B和序列族U1得到两类新的周期为4(2n-1)(n为整数)的四元序列族。分析表明,新的序列族有良好的低相关性和较大的线性复杂度。2、构造出硬件容易实现的测量矩阵。新的序列族有良好的平衡性与低相关性。文中首先通过理论分析说明了由新序列族构造的矩阵与某些稀疏变换基不相干,可用于压缩传感中的测量矩阵;其次通过MATLAB仿真实验验证了新矩阵用于测量矩阵时,能够实现信号的完美重构,同时给出了新测量矩阵和高斯随机矩阵的对比结果。
[Abstract]:Pseudorandom sequences are widely used in radar, sonar, communication systems, cryptographic systems and other fields because of their good autocorrelation, cross-correlation, long period, large linear complexity, balance, easy to implement and so on. Binary sequences and quaternions are the preferred sequences for practical applications from the point of view of easy hardware implementation. Binary sequences were studied earlier, in which m sequence and Gold sequence. M sequence is widely used in communication field. Gold sequence is a pseudorandom sequence proposed by R.Gold on the basis of m sequence in 1967. The study of quaternion sequences based on Galois ring is relatively late, but it is found that for a given sequence family size M and sequence family period L, according to Welch and Sidelnikov bounds, It is possible to design a quaternion sequence family with a maximum cross-correlation value smaller than that of the optimal binary sequence family. The maximum cross-correlation function value of the quaternion sequence is 1 / 2 of the optimal binary sequence. At present, there are not many quaternion sequences with good properties, so it is important to construct quaternion pseudorandom sequences with good properties. In order to recover the analog signal without distortion, Nyquist sampling theorem requires that the sampling frequency should not be less than 2 times of the highest frequency in the analog signal spectrum, which greatly limits the processing ability of the information. The emergence of compression sensing theory breaks this traditional theorem and makes the acquisition of high resolution signals possible. It shows remarkable advantages in many fields. The design of measurement matrix is a hot issue in the theory of compression sensing. It relates to whether the signal can be compressed and whether the signal can be reconstructed accurately. The most widely used measurement matrices are random projection matrices or matrices with independent distribution such as Gao Si random matrices and Bernoulli matrices. Because these two matrices are irrelevant to all the other sparse transform bases, it allows us to perceive signals from the original domain without prior knowledge without damage, except that, We can realize the accurate reconstruction of the original signal under the requirement of certain measurement value. But the key to the application of compression sensing theory is to construct the measurement matrix which is easy to be realized by hardware in practical application. In this paper, we construct quaternion sequences with good properties and construct quaternion sequences with good properties. Tang has proposed a method to extend the period of sequence families with odd periods by 2 times, but this method is not suitable for families of sequences with even periodic numbers. The new method is to extend the period of even sequence families by 2 times. The new method is applied to sequence family B and sequence family U1 to obtain two new classes of quaternion sequences with a period of 4 (2n-1) (n as an integer). The analysis shows that the new sequence family has good low correlation and large linear complexity. The measurement matrix which is easy to be realized by hardware is constructed. The new sequence family has good balance and low correlation. In this paper, the theoretical analysis shows that the matrix constructed by the new sequence family is incoherent with some sparse transformation bases, and it can be used to compress the measurement matrix in the sensor. Secondly, the new matrix is proved to be used in the measurement matrix by MATLAB simulation. The signal can be reconstructed perfectly and the comparison between the new measurement matrix and the Gao Si random matrix is given.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

【共引文献】