基于ADSP-TS201的复数QR分解算法的递归实现

复矩阵的QR分解在很多领域都有重要的应用,但是现有算法没有给出Householder变换矩阵的递归表达式,从而限制了它的使用,对此进行了修正,并在此基础上介绍了该算法在ADSP-TS201上的具体实现。     

基于脉动阵的自适应波束形成算法仿真

为了满足自适应波束形成技术对实时性的要求,将脉动阵应用于波束形成算法中,以实现自适应权向量的实时获取.通过对QR分解采样矩阵求逆算法、混合型QR分解采样矩阵求逆算法和逆QR分解采样矩阵求逆算法的理论分析,利用脉动阵,对输入数据矩阵进行QR分解,得到旋转因子,实现自适应权向量的实时更新.针对三种算法各自的脉动阵进行仿真,结果表明,基于脉动阵的自适应波束形成算法实现了权向量的高速获取,并为后续的工程实践提供了理论依据.     

基于QR分解的LS优化算法研究

本文对基于 QR 分解的 LS 优化算法进行研究，通过构造矩阵的方法，优化 Q 矩阵和 R 矩阵的计算算法，实现了对 LS 算法的优化，减少了算法对时间和空间资源的需求，并对算法进行了时间复杂度和空间复杂度分析，证明了该优化算法的有效性。     

空时自适应处理的滑窗递推QR算法

在局部平稳的杂波环境下,滑窗样本选取方法可以比较准确地估计检测单元的杂波统计特性。该文提出基于滑窗选取样本的递推QR算法,它采用双曲Householder变换实现QR分解的递推,能有效地抑制局部平稳杂波,且具有数值稳定性好,计算量小的优点。仿真数据处理和实测数据处理验证了该方法的有效性。     

CORDIC算法及其应用

五十年代末期,Volder提出了强有力的坐标旋转数字计算算法即CORDIC算法该算法以其运算及硬件结构简单和多功能性而倍受人们的注意。它不但能作一般的旋转运算,而且能实现诸如三角函数、双曲函数及指数等基本函数,其运算过程只有移位和加减,它已被广泛用作现代信号处理各种算法实现中的运算单元,诸如离散傅里叶变换、矩阵的QR分解、矩阵特征值的求解、奇异值分解、Cholesky分解、线性预测参数的求解等.近二十年来人们对它的研究和运用从未间断过,至今仍方兴未艾。随着VLSI技术的高速发展,该算法将得到越来越广泛的应用.本文旨在向读者介绍该算法及其在数字信号处理方面的应用,同时介绍其发展情况及其前景.     

基于SVD的波束形成算法研究

本文通过对采样数据矩阵进行QR分解,将求解加权矢量问题转换为求解三角线性方程组,通过避免对自相关矩阵的估计和求逆来提高数值鲁棒性;接着提出一种改进方案:对采样数据矩阵进行SVD分解完成波束形成,此方案利用奇异值和奇异值矢量计算加权矢量,并且通过改变对较小的奇异值赋零的多少,在复杂度与性能之间进行折衷。仿真结果显示,提出的改进方案和QR分解算法的性能接近,都能正确实现波束形成。     

基于QR分解的MIMO-OFDM系统信道估计降噪方法

MIMO-OFDM传输系统的信道估计降噪算法多是基于DFT,如果系统中含有虚载波,该方法将严重影响系统的性能。为使信道估计性能不受系统虚载波影响,提出了基于QR分解的系统信道估计降噪方法,该方法将部分频域变换矩阵经过QR分解,得到酉矩阵,将其与LS频域信道估计矢量相乘后得出信道估计噪声。用Matlab对提出的算法进行了仿真,通过对仿真结果进行分析比较并得出结论,验证了改进算法的优越性。     

适于参数识别的多信道QRD自适应格型算法

本文基于格型滤波器的阶递归特性和Givens旋转算法的优越数值性能,推导了两种多信道递归最小二乘格型算法。第一种算法的推导是直接基于对输入数据矩阵进行正交-三角分解,并利用Givens旋转方法来计算其正交-三角分解。首先对输入数据矩阵进行预旋转,然后重复利用单信道Givens格型算法,便可得到第二种算法。两种算法都具有优越的数值性能,尤其是对有限字长的稳健性。待估计的滤波器参数矢量可根据算法的内部变量直接提取,而无需额外的三角阵进行后向代入求解运算。两信道参数识别的计算机模拟结果验证了本文的推导。     

DFT(2~m)通用递归分解算法

本文从DFT的变换矩阵分解成矩阵Kronecker积形式出发,提出一种通用递归分解算法(GRFA)。采用不同的分解基,可导出常规FFT、MD-FFT、SR-FFT和RCFA等各种递归分解算法的矩阵Kronecker积表示式。从GRFA出发,论证了DFT(2~m)递归分解算法的最小实数乘法次数是(m-3)2~m+4。SR-FFT或RCFA算法是OFT(2~m)递归分解算法实数乘法次数最少的最佳算法。     

基于非下采样剪切波变换和QR分解的鲁棒零水印算法

针对数字图像的版权保护问题,提出了一种基于非下采样剪切波变换(NSST,non-subsam-pled shearlet transform)和QR分解的零水印算法。首先,采用NSST对宿主图像进行分解;然后利用Logistic混沌系统从分解后的低频逼近分量中随机抽取出一幅子图,并将其分割成互不重叠的子块;最后对每一个子块进行QR分解,通过判断各个子块R矩阵中第1行元素向量的l1范数和所有子块R矩阵第1行元素向量l1范数的均值之间的大小关系构造零水印。实验结果表明,本文算法对添加噪声、滤波、JPEG压缩和剪切具有很强的鲁棒性,同时还能抵抗一定程度的旋转、缩放和平移(RST)几何攻击。     

New fast QR decomposition least squares adaptive algorithms

This paper presents two new, closely related adaptive algorithms for LS system identification. The starting point for the derivation of the algorithms is the inverse Cholesky factor of the data correlation matrix, obtained via a QR decomposition (QRD). Both algorithms are of O(p) computational complexity, with p being the order of the system. The first algorithm is a fixed order QRD scheme with enhanced parallelism. The second is an order recursive lattice type algorithm based exclusively on orthogonal Givens rotations, with lower complexity compared to previously derived ones. Both algorithms are derived following a new approach, which exploits efficient the and order updates of a specific state vector quantity     

VLSI algorithms and architectures for complex householder transformation with applications to array processing

The Householder transformation is considered to be desirable among various unitary transformations due to its superior computational efficiency and robust numerical stability. Specifically, the Householder transformation outperforms the Givens rotation and the modified Gram-Schmidt methods in numerical stability under finite-precision implementations, as well as requiring fewer arithmetical operations. Consequently, the QR decomposition based on the Householder transformation is promising for VLSI implementation and real-time high throughput modern signal processing. In this paper, a recursive complex Householder transformation (CHT) with a fast initialization algorithm is proposed and its associated parallel/pipelined architecture is also considered. Then, a CHT based recursive least-squares algorithm with a fast initialization is presented. Its associated systolic array processing architecture is also considered.This work was supported in part of the National Science Council of the R.O.C. under grant NSC80-E-SP-009-01A.This work was supported in part by a UC Micro grant and NSF grant NCR-8814407.     

Novel semi-blind channel estimation schemes for Rician fading MIMO channel

In this paper, we propose two novel semi-blind channel estimation techniques based on QR decomposition for Rician fading Multiple Input Multiple Output (MIMO) channel. In the first technique, the MIMO channel matrix H can be decomposed as an upper triangular matrix R and unitary rotation matrix Q as H = RQ. The matrix R is estimated blindly from only received data by using the orthogonal matrix triangularization based Householder QR decomposition, while the optimum rotation matrix Q is estimated exclusively from the algorithm of Orthogonal Pilot Maximum Likelihood Estimator (OPML) based on pilot information. In the second technique, the joint semi-blind channel and data estimation is performed by using the Least Square (LS) algorithm based on QR decomposition. The simulation results obtained for 4-PSK data modulation scheme using two transmitters and six receiver antennas for different Rice factor (K) have shown that the BER performance increases with an increase in the Rice factor. Finally, we compare these two new techniques with the conventional semi-blind channel estimation technique based on Whitening Rotation (WR), and the results show that the first proposed technique outperforms and the second technique achieves a very nearby performance as compared to the technique based on whitening rotation.     

Multichannel fast QRD-LS adaptive filtering: new technique andalgorithms

A direct, unified approach for deriving fast multichannel QR decomposition (QRD) least squares (LS) adaptive algorithms is introduced. The starting point of the new methodology is the efficient update of the Cholesky factor of the input data correlation matrix. Using the new technique, two novel fast multichannel algorithms are developed. Both algorithms comprise scalar operations only and are based exclusively oh numerically robust orthogonal Givens rotations. The first algorithm assumes channels of equal orders and processes them all simultaneously. It is highly modular and provides enhanced pipelinability, with no increase in computational complexity, when compared with other algorithms of the same category. The second multichannel algorithm deals with the general case of channels with different number of delay elements and processes each channel separately. A modification of the algorithm leads to a scheme that can be implemented on a very regular systolic architecture. Moreover, both schemes offer substantially reduced computational complexity compared not only with the first algorithm but also with previously derived multichannel fast QRD schemes. Experimental results in two specific application setups as well as simulations in a finite precision environment are also included     

Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

QR decomposition techniques are well known for their good numerical behavior and low complexity. Fast QRD recursive least squares adaptive algorithms benefit from these characteristics to offer robust and fast adaptive filters. This paper examines two different versions of the fast QR algorithm based on a priori backward prediction errors as well as two other corresponding versions of the fast QR algorithm based on a posteriori backward prediction errors. The main matrix equations are presented with different versions derived from two distinct deployments of a particular matrix equation. From this study, a new algorithm is derived. The discussed algorithms are compared, and differences in computational complexity and in finite-precision behavior are shown.     

一种用于MIMO检测中的QR快速分解算法

针对多输入多输出系统中常用的非线性检测算法,如排序QR分解(Sorted QR Decomposition,SQRD)、球型译码（Sphere Decoding,SD）、K-Best或QRM（QR Decomposition and M algorithm）等,提出了一种具有最优检测顺序的QR快速分解方法,作为检测前的预处理操作。该算法首先对信道矩阵进行第一次QR分解,根据所得上三角矩阵R可确定最优的检测顺序,并按该顺序对R进行列重排。然后对R进行第二次QR分解,即得具有最优检测顺序的QR分解结果。与现有的基于R对角元素的模值排序的QR分解算法相比,本算法可保证检测顺序最优从而性能最优。仿真结果表明天线配置为4*4和6*6时,在误码率10^-3处可节约信噪比分别为:1dB和2dB;与现有的基于信干噪比排序的QR分解算法相比,本算法与其性能一致的基础上可节约25%的复乘法次数和33%的复加法次数。      

空间相关环境下一种稳健的V-BLAST迭代检测算法

利用Householder变换,并结合WY表示形式,该文首先提出一种修正的Householder QR分解(M-H-QRD)算法,与排序QRD(S-QRD)检测算法相比:M-H-QRD检测算法在空间相关信道环境下具有稳健的数值特性;然后以此为基础,提出了一种基于M-H-QRD的V-BLAST迭代检测算法。仿真结果表明:在空间相关信道环境下,该算法比S-QRD检测算法、M-H-QRD检测算法在性能上具有明显的改善;与标准的V-BLAST算法相比,在高信噪比范围,迭代检测算法取得了与标准的V-BLAST算法几乎同等的性能,在中低信噪比范围,迭代检测算法优于标准的V-BLAST检测算法,同时数值特性比标准的V-BLAST检测算法更为稳健。     

一种基于无平方根QR分解的流水RLS算法

传统ＱＲ分解（ＧＩＶＥＮＳ旋转）中存在着平方根运算,在用数字电路实现时,会在时间和面积上花费较大的代价,因此,已有无平方根的ＱＲ分解算法出现,这些算法避免了平方根运算,但遇射为Ｓｙｓｔｏｌｉｃ阵列以实现ＲＬＳ算法时,却不能实现单元内部的流水,本文提出了一种新的无平方要ＱＲ分解,能够实现单元内部的流水,进一步提高了速度。