Block time and frequency domain modified covariance algorithms forspectral analysis

Block modified covariance algorithms are proposed for autoregressive parametric spectral estimation. First, the authors develop the block modified covariance algorithm (BMCA) which can be implemented either in the time or in the frequency domain-with the latter being more efficient in high-order cases. A block algorithm is also developed for the energy weighted combined forward and backward prediction. This algorithm is called energy weighted BMCA (EWBMCA) and its performance is analogous to that of the weighted covariance method proposed by Nikias and Scott (1983). Time-varying convergence factors, designed to minimize the error energy from one iteration to the next, are given for both algorithms. In addition, three updating schemes are presented, namely block-by-block, sample-by-sample, and sample-by-sample with time-scale separation. The performance of the proposed algorithms is examined with stationary and nonstationary narrowband and broadband processes, and also with sinusoids in noise. Lastly, the authors discuss the computational complexity of the proposed algorithms and give performance comparisons to existing modified covariance algorithms     

Efficient lattice realizations of adaptive IIR algorithms

Computationally efficient adaptive IIR-filter algorithms are presented based on lattice realizations allowing the adaptive filter stability to be easily monitored. New simplified recursive-in-order equations relating the parameters of the direct-form realization with the ones of two lattice realizations are presented. These equations lead to a simplified technique to compute the regressor vector and to a general method to implement any adaptive IIR algorithm using lattice realization. Results indicate that the proposed lattice-based algorithms converge to a set of parameters that realize the same transfer function as the corresponding direct-form algorithms     

Convergence analysis of adaptive filtering algorithms with singulardata covariance matrix

The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algorithms. Both the signal and weight behavior of the algorithms are considered. The signal behavior is evaluated in terms of the moments of the excess output error of the filter. The weight behavior is evaluated in terms of the moments of the filter weight misalignment vector. It is found that the RLS and SRA diverge when the input covariance matrix is singular. The steady-state signal behavior of the LMS and SA can be made arbitrarily fine by using sufficiently small step sizes of the algorithms. Indeed, the long-term average of the mean square excess error of the LMS is proportional to the algorithm step size. The long-term average of the mean absolute excess error of the SA is proportional to the square root of the algorithm step size. On the other hand, the steady-state weight behavior of both the LMS and SA have biases that depend on the weight initialization. The analytical results of the paper are supported by simulations     

Givens rotation based least squares lattice and related algorithms

The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed     

Stable and efficient lattice algorithms for adaptive IIR filtering

Previous attempts at applying lattice structures to adaptive infinite-impulse-response (IIR) filtering have met with gradient computations of O(N²) complexity. To overcome this computational burden, two new lattice-based algorithms are proposed for adaptive IIR filtering and system identification, with both algorithms of O(N) complexity. The first algorithm is a reinterpretation of the Steiglitz-McBride method (1965), while the second is a variation on the output error method. State space models are employed to make the derivations transparent, and the methods can be extended to other parameterizations if desired. The set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct-form versions of the Steiglitz-McBride and output error methods, whose properties are well studied. The derived algorithms are as computationally efficient as existing direct-form based algorithms, while overcoming the stability problems associated with time-varying direct-form filters     

The Leech lattice, the octacode, and decoding algorithms

New multilevel constructions of the Golay code and the Leech lattice are presented. These are derived from the Turyn construction and the “holy construction” with the octacode as the glue code. Further, we show that the “holy construction” of the Leech lattice with the octacode as the glue code is essentially different from the permuted Turyn construction, although both constructions rely on the octacode. The Turyn construction is based on an “odd” type of the octacode, whereas any type of the octacode can be used in the “holy construction.” Moreover, the multilevel representation of the “holy construction” leads to a novel lattice partition chain. Based on these structures, we derive new bounded-distance decoders for the Golay code and the Leech lattice whose effective error coefficient is smaller than that of any previously known bounded-distance decoder. We provide a general theorem for computing the effective error coefficient of coset decoding with bounded distance decoding for the subcode     

Complexity-performance trade-off of algorithms for combined lattice reduction and QR decomposition

Over the last years, numerous equalization schemes for multiple-input/multiple-output channels have been studied in the literature. New low-complexity approaches based on lattice basis reduction are of special interest, since they achieve the optimum diversity behavior. Although the per-symbol equalization complexity of these schemes is very low, the initial calculation of the required matrices may impose an enormous burden in arithmetic complexity. In this paper, we give a tutorial overview and assess algorithms, which, given the channel matrix, result in the feedforward, feedback, and unimodular matrix required in lattice-reduction-aided decision-feedback equalization or precoding. To this end, via a unified exposition of the Lenstra–Lenstra–Lovász (LLL) algorithm, the LLL with deep insertions, and the reversed Siegel approach similarities and differences of these approaches are enlightened. A modification of the LLL swapping criterion, better matched to the equalization setting, is discussed. It is shown that using lattice-reduction-aided equalization/precoding better performance can be achieved at lower complexity compared to classical equalization or precoding approaches.     

QRD-BASED MULTICHANNEL ADAPTIVE LATTICEALGORITHMS FOR THE PARAMETERIDENTIFICATION PROBLEM

A pair of multichannel recursive least squares (RLS) adaptive lattice algorithms based on the order recursive of lattice filters and the superior numerical properties of Givens algorithms is derived in this paper. The derivation of the first algorithm is based on QR decomposition of the input data matrix directly, and the Givens rotations approach is used to compute the QR decomposition. Using first a prerotation of the input data matrix and then a repetition of the single channel Givens lattice algorithm, the second algorithm can be obtained. Both algorithms have superior numerical properties, particularly the robustness to wordlength limitations. The parameter vector to be estimated can be extracted directly from internal variables in the present algorithms without a backsolve operation with an extra triangular array. The results of computer simulation of the parameter identification of a two-channel system are presented to confirm efficiently the derivation.     

RLS-Laguerre lattice adaptive filtering: error-feedback,normalized, and array-based algorithms

This paper develops several lattice structures for RLS-Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattice filters, and normalized lattice filters. All structures are efficient in that their computational cost is proportional to the number of taps, albeit some structures require more multiplications or divisions than others. The performance of all filters, however, can differ under practical considerations, such as finite-precision effects and regularization. Simulations are included to illustrate these facts     

The Burg algorithm for segments

In many applications, the duration of an uninterrupted measurement of a time series is limited. However, it is often possible to obtain several separate segments of data. The estimation of an autoregressive model from this type of data is discussed. A straightforward approach is to take the average of models estimated from each segment separately. In this way, the variance of the estimated parameters is reduced. However, averaging does not reduce the bias in the estimate. With the Burg algorithm for segments, both the variance and the bias in the estimated parameters are reduced by fitting a single model to all segments simultaneously. As a result, the model estimated with the Burg algorithm for segments is more accurate than models obtained with averaging. The new weighted Burg algorithm for segments allows combining segments of different amplitudes     

Burg算法在雷达测速中的应用

为将Burg算法应用在汽车测速中,在多普勒效应原理的基础上,推导出移动物体发射波频率与接收波频率之间的关系,并分别用直接法和Burg算法估计测速模型中发射波频率82 Hz与接收波频率81 Hz。经Matlab仿真表明：直接法估计的发射波与接收波主频率分别接近于82 Hz和81 Hz,但频率主峰旁边存在大量噪声频率的假峰;Burg算法估计出的发射波与接收波主频率更准确,同时主峰清晰且较其他噪声频率突出明显。故Burg算法对间隔不大的发射波与接收波的频率分辨力远远优于直接法,可应用于测速环境中。     

Burg算法与自相关在科氏流量计中的应用

传统科氏流量计信号处理采用DFT谱分析方法,对数据进行加窗处理,导致谱分辨率降低。为提高谱分辨率,将Burg算法引入科氏流量计频率解算,无需对窗口之外数据进行假设。为解决信号初相以及噪声干扰对谱分辨率的影响,对Burg算法进行了分析并改进,引入了自相关算法。在此建立了科氏流量计的信号模型,采用Matlab对本算法进行仿真验证,结果表明该算法的解算精度优于一般流量计的要求,算法可以用于科氏流量计频率解算。     

Adaptive lattice IIR filtering revisited: convergence issues andnew algorithms with improved stability properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability     

Cross Burg entropy maximization and its application to ringingsuppression in image reconstruction

We present a multiplicative algorithm for image reconstruction, together with a partial convergence proof. The iterative scheme aims to maximize cross Burg entropy between modeled and measured data. Its application to infrared astronomical satellite (IRAS) data shows reduced ringing around point sources, compared to the EM (Richardson-Lucy) algorithm.     

一种基于Burg谱估计和FFT的频偏估计方法

针对星间链路通信中常用的BPSK、QPSK、UQPSK和64QAM等调制信号的载波频偏估计问题,提出了一种基于Burg谱估计和FFT的通用频偏估计方法。采用Burg谱估计方法对信号进行粗频偏估计,补偿该频偏后得到含有较小残留频偏的信号;并进行改进的四次方非线性变换,去除调制信息;再利用FFT估计出较高精度的残留频偏值。仿真结果表明,该方法估计精度高、范围大。     

基于MSE和Burg的两步目标识别分类器研究

SAR目标分类识别是现代战场侦察的重要组成部分,SAR目标分类问题是目标识别的关键步骤之一,对目标识别等很多后续的应用有较大的影响,因此研究SAR图像目标分类技术具有非常重要的意义。针对这一研究热点,结合MSE匹配方法和超分辨Burg算法,提出一种两步分类器,采用该两步分类器对实测SAR图像进行了目标分类识别实验,取得较好的识别效果。     

基于 Burg 算法功率谱估计的参数选择

介绍了现代功率谱估计中常用的基于自回归（AR）模型的Burg算法,分析了Burg算法中参数选择对功率谱估计的影响,并给出综合最优的Burg算法参数选择方法,最后将本文参数选择方法应用于列车测速系统进行实验验证,准确地估计出了列车的多普勒频率。     

拆分型Bloom Filter

Bloom Filter对数据集合采用一个位串表示并能有效支持集合元素的哈希查找操作.在对Bloom Filter及其改进型进行综述性分析研究并探讨它们的实用性之后,本文提出了使用位矩阵表示数据集合的拆分型Bloom Filter并对其作了分析比较研究,以允许集合元素不断增加的分布式系统应用模型为例,证明它能缓解增长问题并能有效节省全局的集合表示空间需求量.