Narrow-band interference rejection in DS/CDMA systems using adaptive (QRD-LSL)-based nonlinear ACM interpolators

An Mth order adaptive lattice filter automatically generates all M of the outputs that would be provided by M separate transversal filters. This feature may effectively suppress narrow-band interference (NBI) of either unknown or time-varying bandwidth (or number of frequency bands) in direct-sequence code-division multiple access systems for which the order of the interference rejection filter that achieves the optimal performance is unknown or constantly changing. Moreover, a lattice filter may significantly outperform its transversal counterpart in complex jamming environments in which the adaptive lattice filter must suppress multiple jammers, since each stage of a lattice filter adapts to suppress an orthogonal component of the NBI. The paper develops a computationally efficient and numerically stable adaptive QR-decomposition-based least squares lattice (QRD-LSL)-based nonlinear approximate conditional mean interpolator to suppress NBI effectively. Simulation results demonstrate that both the signal-to-noise ratio improvement and the convergence rate achieved by the proposed interpolators outperform those of other existing prediction-based techniques.     

直扩系统中IIR格型滤波器抑制窄带干扰新方法与性能分析

该文提出一种直扩系统中基于IIR格型陷波器时域频域相结合的窄带干扰抑制新方法,该方法采用时域频域并行处理的结构,通过最优加窗和频谱校正技术在频域精确估计出干扰信号的频率,根据频率估计误差和干信比求出最优陷波带宽,由此自适应地调整时域IIR格型陷波器的参数。分析和实验表明,该方法较传统的自适应IIR窄带干扰抑制方法不仅具有更高的稳定性和实时性,而且在干扰得到有效抑制的情况下使有用信号的损失达到最小。     

Further improved 2-D lattice filter structure employing missing reflection coefficients

A new lattice filter structure to model two-dimensional (2-D) autoregressive (AR) fields is proposed. The proposed structure utilizes and extracts the information contained in the backward prediction error fields and their delayed versions. The main idea is to use two sets of reflection coefficients corresponding to two quadrant filters and to increase the number of reflection coefficients with the order of the lattice filter. Increasing the number of reflection coefficients at each stage produces a sufficient number of independent parameters to model AR fields up to order three, which is an improvement over the existing 2-D lattice filter structures. The improvement is confirmed by computer simulations. In addition, a relationship between the reflection coefficients and the AR coefficients is derived. It is also shown that the entropy contained in the backward prediction error field vector of the proposed structure is closer to the input entropy when compared to those contained in existing 2-D lattice filters.     

An efficient algorithm to design weighted minimax perfectreconstruction quadrature mirror filter banks

An efficient algorithm is presented to design lattice structure two-channel perfect reconstruction quadrature mirror filter (PR-QMF) banks. We formulate the filter bank design problem as an unconstrained weighted least squares problem with respect to the coefficients of the lattice structure. The proposed iterative algorithm optimizes the lattice coefficients and provides flexible control of the filters' stopband ripple profiles. Typically, only a few iterations of the algorithm are needed to obtain an optimal solution in the weighted minimax sense. We include a set of practical design rules for use with our algorithm. These rules allow very good estimation of important filter bank characteristics, such as the filter length and the number of signed digits for quantization of the lattice coefficients into canonic signed digit representation, to meet a given set of PR-QMF bank specifications     

Blind Multiple Access Interference Suppression Algorithm Based on Relaxed Subgradient Projection for DS/CDMA Systems

A novel blind multiple access interference suppression algorithm based on relaxed parallel subgradient projection is proposed for DS/CDMA systems. The qualification “relaxed” is manifest in two aspects: first, the new expression for updating the interference suppression filter coefficients vector relaxes paralleled projection fields and reduces computation complexity. In addition, the relaxation parameter in the updated process is adaptively determined to guarantee the interference suppression filter coefficients vector falling into fields containing the optimal filter coefficients vector after several iterations. Theoretical analysis and simulation results conclude that this algorithm has a fast convergence speed, steady interference suppression performance, low computation and low bit error rate.     

Behavior of the partial correlation coefficients of a least squareslattice filter in the presence of a nonstationary chirp input

This paper studies the performance of the a posteriori recursive least squares lattice filter in the presence of a nonstationary chirp signal. The forward and backward partial correlation (PARCOR) coefficients for a Wiener-Hopf optimal filter are shown to be complex conjugates for the general case of a nonstationary input with constant power. Such an optimal filter is compared to a minimum mean square error based least squares lattice adaptive filter. Expressions are found for the behavior of the first stage of the adaptive filter based on the least squares algorithm. For the general nth stage, the PARCOR coefficients of the previous stages are assumed to have attained Wiener-Hopf optimal steady state. The PARCOR coefficients of such a least squares adaptive filter are compared with the optimal coefficients for such a nonstationary input. The optimal lattice fitter is seen to track a chirp input without any error, and the tracking lag in such an adaptive filter is due to the least squares update procedure. The expression for the least squares based PARCOR coefficients are found to contain two terms: a decaying convergence term due to the weighted estimation procedure and a tracking component that asymptotically approaches the optimal coefficient value. The rate of convergence is seen to depend inversely on the forgetting factor. The tracking lag of the filter is derived as a function of the rate of nonstationarity and the forgetting factor. It is shown that for a given chirp rate there is a threshold adaptation constant below which the total tracking error is negligible. For forgetting factors above this threshold, the error increases nonlinearly. Further, this threshold forgetting factor decreases with increasing chirp rate. Simulations are presented to validate the analysis     

无乘法的线性相位滤波器组的优化设计

提出了一种新的优化方法来设计系数为2的幂和(SOPOT)形式的线性相位完全重构(LPPR)滤波器组。其基本思想是将LPPR格型结构滤波器组中的格型系数直接表示成SOPOT形式，并将这些系数编码成个二进制码串，然后在一定的目标函数下利用遗传算法对这二进制码串进行优化。利用这种方法可以省去传统方法中首先设计无限精度系数的步骤，简化SOPOT型系数的LPPR滤波器组的设计过程。实验结果表明，该方法可以得到较好设计结果。     

Frequency shift keyed narrowband interference rejection: optimal exponential weighting factor for the RLS algorithm

Cochannel narrowband interference can limit the performance of direct sequence spread spectrum (DSSS) and high frequency (HF) systems. Narrowband interference (NBI) can be single tone, chirped or frequency shift keyed (FSK) in nature and numerous techniques for its removal have been proposed. Linear adaptive prediction filters based on autoregressive modelling have been suggested owing to their ability to perform in a non-stationary environment. In the FSK narrowband interference case, adaptive filters are susceptible to excess residual errors owing to instantaneous frequency step changes and the finite convergence time required for the filter to adapt to a new interference frequency. The signal degradation owing to this type of interference becomes greater in high SNR regimes and has been found to be a function of the frequency parameters of the FSK interference signal. The paper discusses the convergence and frequency tracking properties of the recursive least squares (RLS) adaptive lattice filter using a posteriori estimation errors in the presence of FSK narrowband interference. An optimal exponential weighting factor that balances convergence time and steady state error is derived for this case of NBI. Results are compared to those of a previously proposed fast converging minimum frequency error (FCMFE) RLS lattice filter.     

Fast-converging minimum frequency error RLS lattice filter for narrowband interference with discrete frequency steps

This paper discusses the fundamental convergence and frequency tracking properties of the recursive-least-squares (RLS) lattice filter in the presence of narrowband interference (NBI) whose frequency varies in discrete steps. It is shown for filters of this type, that the residual forward energy (RFE) after a frequency transition is a function of the input signal-to-noise ratio (SNR), separation of the sequential frequencies and the filter time constant and is exponentially decaying in nature. Reducing the RFE is important in removing unwanted transient artefacts from the desired signal. The convergence behaviour of the RLS algorithm based on a posteriori estimation errors is analysed under a number of conditions by varying the SNR and frequency step size. In order to limit the impact of the RFE while maintaining a minimum frequency tracking error in steady conditions, a fast-converging minimum frequency error (FCMFE) RLS lattice filter is suggested. For comparison, a least-mean-square (LMS) based gradient-adaptive lattice (GAL) filter is also analysed for this class of narrowband interference.     

A new normalized relatively stable lattice structure

This paper proposes a new lattice filter structure that has the following properties. When the filter is linear time invariant (LTI), it is equivalent to the celebrated Gray-Markel lattice. When the lattice parameters vary with time, it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability, provided that the lattice coefficients are magnitude bounded in a region where all LTI lattices have the same degree of stability. We also show that the resulting LTV lattice obeys an energy contraction condition. This structure thus generalizes the normalized Gray-Markel lattice, which has similar properties but only with respect to stability as opposed to relative stability     

Comparing LS FIR filtering and l-step ahead linearprediction

This comparative study of the l-step-ahead linear prediction and least-squares finite impulse response (LS FIR) filtering problems emphasizes the numerical behavior of the resulting Toeplitz systems. It is shown that, although these systems are similar, the restraints on the autocorrelation coefficients fundamentally differentiate them. In the process of doing so, a new algorithmic scheme for the computation of the lagged lattice coefficients is developed, which exhibits fundamentally improved numerical behavior. Moreover, explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm. Finally, the bounds of the LS FIR filter coefficients are treated in comparison with the supremums of the lagged quantities     

Lattice filter parameterization and modeling of nonstationary processes

A general theory of constant-parameter modular lattice models for discrete-time nonstationary second-order processes is presented. A complete parametrization of such processes in terms of Schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and Schur's test for positive-definiteness of matrices. Schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances, and they coincide with the well-known reflection (or PARCOR) coefficients when the covariance is stationary. The congruence coefficients provide the time-varying gains of a tapped-delay-line realization of the whitening filter for the process. A constant-parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line, both with time-invariant gains. This configuration also provides a recursive relation for the congruence coefficients (namely, a generalized Levinson-Szego recursion). The tapped-delay-line part of the realization can be eliminated by introducing the concept of admissibility. Admissibility also reduces the parametrization of a nonstationary process to Schur coefficients alone, in analogy to stationary processes, which are completely characterized by their PARCOR coefficients.     

基于频域块LMS算法的实时虚拟暗室测试方法

针对电磁辐射现场测试被测设备信号和干扰未知的情况,提出了一种基于频域块最小均方算法的实时虚拟暗室测试方法。该方法采用双通道接收机,根据测试通道和背景通道中干扰信号的相关性设计自适应滤波器,在频域对背景通道信号滤波以趋近测试通道中的干扰分量,采用瞬时双通道信号迭代更新滤波器系数,滤波器系数收敛后系统输出中只有被测设备信号。仿真与分析表明,该方法在背景通道有无被测设备信号泄露的情况下都能有效抑制干扰,与基于时域最小均方算法的方法相比,在滤波器长度相同的情况下其计算复杂度更低,适用于实时现场测试。     

The generalized lapped pseudo-biorthogonal transform: oversampled linear-phase perfect reconstruction filterbanks with lattice structures

We investigate a lattice structure for a special class of N-channel oversampled linear-phase perfect reconstruction filterbanks with a decimation factor M smaller than N. We deal with systems in which all analysis and synthesis filters have the same finite impulse response (FIR) length and share the same center of symmetry. We provide the minimal lattice factorization of a polyphase matrix of a particular class of these oversampled filterbanks (FBs). All filter coefficients are parameterized by rotation angles and positive values. The resulting lattice structure is able to provide fast implementation and allows us to determine the filter coefficients by solving an unconstrained optimization problem. We consider next the case where we are given the generalized lapped pseudo-biorthogonal transform (GLPBT) lattice structure with specific parameters, and we a priori know the correlation matrix of noise that is added in the transform domain. In this case, we provide an alternative lattice structure that suppress the noise. We show that the proposed systems with the lattice structure cover a wide range of linear-phase perfect reconstruction FBs. We also introduce a new cost function for oversampled FB design that can be obtained by generalizing the conventional coding gain. Finally, we exhibit several design examples and their properties.     

Interference rejection in FFH systems using least squaresestimation techniques

A fast frequency-hopped (FFH) receiver which uses a prewhitening filter to reject narrowband interference is described. By using an appropriate fractional tap spacing, it is shown that interference can be estimated independently of the desired signal. Bit error rate results are presented for the receiver for linear square-law combining. The results compare favorably to those obtained by a near-optimal automatic gain-control (AGC) combining technique. The performance of the prewhitening filter interference rejection method is shown to be superior to that of a nonparametric self-normalizing receiver. Finally, simulation results for an FFH receiver using the complex least mean-square (LMS) algorithm to update the prewhitening filter coefficients are presented     

Design of optimal symmetric FIR receive filters

A method for designing optimal symmetric odd-length finite impulse response digital receive filters is proposed. The filter jointly minimises the mean power of intersymbol interference and additive noise or interference under the constraint that the filter coefficients are symmetric. The method yields exactly symmetric filters with the same performance as the earlier unconstrained design but with a lower computational complexity     

一种有限脉冲响应滤波器格型结构优化方法及灵敏度分析

有限脉冲响应(FIR)滤波器是无线通信研究中多载波调制系统的主要组成单元.针对有限字长效应导致FIR滤波器性能下降问题,该文提出一种FIR滤波器格型结构改善因量化导致的滤波器系数误差,即降低系数灵敏度,利用状态空间结构表示相应改进格型结构系数,并推导分析其系数灵敏度表达式.仿真实例验证理论推导结果,即改进格型结构系数灵...     

Design of three-dimensional adaptive IIR notch filters

This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter. The procedures are mainly divided into two parts: frequency-detecting and sinusoidal interference removal. The detections are based on adaptive line enhancer on infinite impulse response (IIR) lattice structure. In the interference removal part, a non-separable version of a 3-D notch filter is effectively applied. The magnitude response of a 3-D adaptive IIR notch filter is illustrated. At the end of the paper, the implementation of an IIR notch filter on a 3-D image is also conducted in order to show how to remove a sinusoidal interference superimposed on a 3-D image.     

自适应格型滤波器新算法及其在语音线性预测合成中的应用

本文从自适应格型滤波器导出自适应线谱对(LSP)滤波,提出了使用最小均方(LMS)型自适应算法逐级更新计算线谱对系数的方法。实验表明,该算法与其它算法比较,具有更高的收敛率和较低的失调。用该算法计算得到的LSP系数进行语音线性预测合成,获得比使用PARCOR系数更好的结果。     

Tracking model of an adaptive lattice filter for a linear chirp FMsignal in noise

The paper studies the behavior of the partial correlation (PARCOR) coefficients and the output misadjustment of the stochastic gradient adaptive lattice filter in response to a complex linear chirp FM signal in white Gaussian noise. Analytic expressions for the optimal PARCOR coefficients of the filter are derived. Analytic as well as iterative models for a three-stage filter are also derived. The analytic expressions show that the tracking and convergence properties of the filter are separate phenomena. Simulation results also show that the spectral contents of the PARCOR coefficients for the stochastic gradient update algorithm consist of a stationary and a linearly swept component. A single-stage model is developed to explain this behavior. Finally, output misadjustment plots for the filter show that an optimum value for the forgetting factor can be obtained to minimize the misadjustment, but the value required to achieve local minimum misadjustment varies with each stage of the filter. It is shown that in applications where the input has a high signal-to-noise ratio (SNR), the misadjustment decreases rapidly at each successive stage, thus implying that relatively short filter lengths are sufficient to provide effective tracking