A fast learning algorithm for Gabor transformation

An adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2-D Gabor (1946) transform representation is introduced. The algorithm uses a recursive least squares (RLS) type algorithm. The aim is to achieve minimum mean squared error for the reconstructed image from the set of the Gabor coefficients. The proposed RLS learning offers better accuracy and faster convergence behavior when compared with the least mean squares (LMS)-based algorithms. Applications of this scheme in image data reduction are also demonstrated.     

OFDM系统自适应数字预失真研究

研究了正交频分复用（OFDM）传输系统中高功率放大器（HPA）的自适应预失真方法。针对OFDM信号的高峰平比特性及HPA带来的非线性失真,提出一种基于训练序列的最小均方误差（LMS）算法和递归最小二乘（RLS）算法的组合算法,将其应用到基于记忆多项式模型的数字预失真系统中。用MATLAB构建一个基于该自适应算法的预失真系统。仿真结果表明：该算法能有效的改善放大器的非线性特性。     

Adaptive minimum-BER linear multiuser detection for DS-CDMA signalsin multipath channels

The problem of constructing adaptive minimum bit error rate (MBER) linear multiuser detectors is considered for direct-sequence code division multiple access (DS-CDMA) signals transmitted through multipath channels. Based on the approach of kernel density estimation for approximating the bit error rate (BER) from training data, a least mean squares (LMS) style stochastic gradient adaptive algorithm is developed for training linear multiuser detectors. Computer simulation is used to study the convergence speed and steady-state BER misadjustment of this adaptive MBER linear multiuser detector, and the results show that it outperforms an existing LMS-style adaptive MBER algorithm presented by Yeh et al. (see Proc. Globecom, Sydney, Australia, p.3590-95, 1998)     

An adaptive algorithm for differentially coherent detection in the presence of intersymbol interference

An adaptive equalization method is proposed for use with differentially coherent detection of M-ary differential phase-shift keying (DPSK) signals in the presence of unknown carrier frequency offset. A decision-feedback or a linear equalizer is employed, followed by the differentially coherent detector. The equalizer coefficients are adjusted to minimize the post-detection mean squared error. The error, which is a quadratic function of the equalizer vector, is used to design an adaptive algorithm of stochastic gradient type. The approach differs from those proposed previously, which linearize the post-detection error to enable the use of least mean squares (LMS) or recursive least squares (RLS) adaptive equalizers. The proposed quadratic-error (Q) algorithm has complexity comparable to that of LMS, and equal convergence speed. Simulation results demonstrate performance improvement over methods based on linearized-error (L) algorithm. The main advantages of the technique proposed are its simplicity of implementation and robustness to carrier frequency offset, which is maintained for varying modulation level.     

一种新的变步长LMS自适应算法

研究了自适应最小均方误差滤波算法的步长选取问题。在分析现有变步长LMS算法的基础上,给出一种以双曲正切函数的改进形式为变步长的LMS算法。在相同收敛速度的前提下,该算法具有更小的超量均方误差;而在相同超量均方误差的前提下,该算法具有更快的收敛速度。经实验,仿真结果与理论分析相一致,证实了该算法的优越性。     

DFT/LMS算法在DSSS中的应用及性能分析

本文分析了直接序列扩频(DSSS)系统中最小错误概率(MPE)意义下的最优滤波器,并依据矩阵求逆引理证明最小均方误差(MMSE)意义下的最优滤波——维纳滤波也是MPE意义下的最优滤波。在DSSS中应用自适应滤波,无须先验已知扩频码的码型和干扰的统计特性,就能一并完成解扩以及有效抑制干扰。离散傅立叶变换/最小均方(DFT/LMS)算法的收敛速度远快于LMS算法,而运算量、稳健性与LMS算法基本相同。基于DFT/LMS算法的自适应滤波大大简化DSSS系统接收机的设计,显著增强系统抗干扰能力,具有很强的实用性。     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

MBER Space-Time Decision Feedback Equalization Assisted Multiuser Detection for Multiple Antenna Aided SDMA Systems

This paper proposes a space-time decision feedback equalization (ST-DFE) assisted multiuser detection (MUD) scheme for multiple receiver antenna aided space division multiple access systems. A minimum bit error rate (MBER) design is invoked for the MUD, which is shown to be capable of improving the achievable bit error rate performance and enhancing the attainable system capacity over that of the standard minimum mean square error (MMSE) design. An adaptive implementation of the MBER ST-DFE assisted MUD is proposed using a stochastic gradient-based least bit error rate algorithm, which is demonstrated to consistently outperform the classical least mean square (LMS) algorithm, while achieving a lower computational complexity than the LMS algorithm for the binary signalling scheme. Our simulation results demonstrate that the MBER ST-DFE assisted MUD is more robust to channel estimation errors as well as to potential error propagation imposed by decision feedback errors, compared to the MMSE ST-DFE assisted MUD.     

Optimal tracking of time-varying channels: a frequency domainapproach for known and new algorithms

In this paper, we developed a systematic frequency domain approach to analyze adaptive tracking algorithms for fast time-varying channels. The analysis is performed with the help of two new concepts, a tracking filter and a tracking error filter, which are used to calculate the mean square identification error (MSIE). First, we analyze existing algorithms, the least mean squares (LMS) algorithm, the exponential windowed recursive least squares (EW-RLS) algorithm and the rectangular windowed recursive least squares (RW-RLS) algorithm. The equivalence of the three algorithms is demonstrated by employing the frequency domain method. A unified expression for the MSIE of all three algorithms is derived. Secondly, we use the frequency domain analysis method to develop an optimal windowed recursive least squares (OW-RLS) algorithm. We derive the expression for the MSIE of an arbitrary windowed RLS algorithm and optimize the window shape to minimize the MSIE. Compared with an exponential window having an optimized forgetting factor, an optimal window results in a significant improvement in the h MSIE. Thirdly, we propose two types of robust windows, the average robust window and the minimax robust window. The RLS algorithms designed with these windows have near-optimal performance, but do not require detailed statistics of the channel     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

Modified LMS algorithm for unbiased impulse response estimation innonstationary noise

In the presence of input interference, the Wiener solution for impulse response estimation is biased. It is proved that bias removal can be achieved by proper scaling of the optimal filter coefficients and a modified least mean squares (LMS) algorithm is then developed for accurate system identification in noise. Simulation results show that the proposed method outperforms two total least squares (TLS) based adaptive algorithms under nonstationary interference conditions     

Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.     

Averaged stochastic gradient algorithms for adaptive blindmultiuser detection in DS/CDMA systems

In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging. This ingenious concept of averaging was invented by Polyak and Juditsky (1992)-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems. We prove that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS. Simulations are used to compare our averaged gradient algorithm with the blind LMS and LMS schemes     

A class of order statistic LMS algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types     

Fast Converging Semi-Blind Space-Time Equalisation for Dispersive QAM MIMO Systems

A novel semi-blind space-time equaliser (STE) is proposed for dispersive multiple-input multiple-output systems that employ high-throughput quadrature amplitude modulation signalling. A minimum number of training symbols, approximately equal to the dimension of the STE, are first utilised to provide a rough initial least squares estimate of the STE?s weight vector. A concurrent gradient-Newton constant modulus algorithm and soft decision-directed scheme is then applied to adapt the STE. The proposed semi-blind adaptive STE is capable of converging fast to the minimum mean square error STE solution. Simulation results confirms that the convergence speed of this semi-blind adaptive algorithm is very close to that of the training-based recursive least squares algorithm.     

一种基于自适应阵列天线的波束赋形算法

自适应阵列天线中的数字波束赋形(DBF)技术是智能天线数字信号处理部分的核心.提出了一种可用于自适应阵列波束赋形的SMI-LMS算法--由SMI(采样协方差矩阵求逆)算法决定LMS(最小均方)算法的初始权向量.该算法充分结合了SMI算法收敛速度快和LMS算法稳态误差小的优点,能在较强干扰环境下,确保权向量的快速收敛和跟踪速度.与传统的LMS算法相比,SMI-LMS算法具有良好的收敛性能、较快的跟踪速度和较小的输出误差,并可以有效改善自适应方向图的副瓣性能.仿真结果验证了该结论.     

Consistent normalized least mean square filtering with noisy data matrix

When the ordinary least squares method is applied to the parameter estimation problem with noisy data matrix, it is well-known that the estimates turn out to be biased. While this bias term can be somewhat reduced by the use of models of higher order, or by requiring a high signal-to-noise ratio (SNR), it can never be completely removed. Consistent estimates can be obtained by means of the instrumental variable method (IVM),or the total/data least squares method (TLS/DLS). In the adaptive setting for the such problem, a variety of least-mean-squares (LMS)-type algorithms have been researched rather than their recursive versions of IVM or TLS/DLS that cost considerable computations. Motivated by these observations, we propose a consistent LMS-type algorithm for the data least square estimation problem. This novel approach is based on the geometry of the mean squared error (MSE) function, rendering the step-size normalization and the heuristic filtered estimation of the noise variance, respectively, for fast convergence and robustness to stochastic noise. Monte Carlo simulations of a zero-forcing adaptive finite-impulse-response (FIR) channel equalizer demonstrate the efficacy of our algorithm.     

Equivalent transfer functions of minimum output variancemean-square estimators

An analysis of the behavior of adaptive filters designed around practically useful, minimum effort cost functions is presented. It is shown that equivalent transfer functions can be derived for both a conventional minimum variance system and for an estimator whose controlling algorithm attempts to minimize the norm square of the filter's weight vector, this latter system being exactly equivalent to the leaky LMS (least mean squares) algorithm. Although the equivalent transfer functions are generally time variant, they assume time invariant form for several important classes of reference signal. In such cases the equivalent transfer function can be used to predict both transient and steady state aspects of the adaptive estimator's performance, as demonstrated for the particularly important case of synchronous periodic estimation     

应用于流水线ADC的LMS自适应校准算法与FPGA实现

研究了应用于流水线模数转换器(ADC)的LMS自适应数字校准算法及其FPGA实现。该校准算法可用于校准大多数已知的误差,包括非线性运算放大器的有限增益、电容失配,以及比较器的失调等。通过Simulink软件,对一个12位160 MS/s的流水线ADC进行建模。采用LMS自适应校准算法对该流水线ADC进行校准,并将算法在Virtex-5上实现了硬件设计。实验结果表明, 输入信号频率为58.63 MHz时,流水线ADC的无杂散动态范围(SFDR)和有效位(ENOB)分别由校准前的46.31 dB和7.32位提高到校准后的82.03 dB和11.12位。     

Improvement in adaptive noise canceling using a nonlinear filter based on the pontryagin minimum principle

This paper introduces a new nonlinear filter that is used for adaptive noise canceling. The derivation and convergence properties of the filter are presented. The performance, as measured by the root mean square error between the signal and its estimate, is compared with that of the commonly used least mean square (LMS) algorithm. It is shown, through simulation, that the proposed nonlinear noise canceler has, on the average, better performance than the LMS canceler. The proposed adaptive noise canceler is based on the Pontryagin minimum principle and the method of invariant imbedding. The computational time for the proposed method is about 10% of that of the LMS, in the studied cases, which is a substantial improvement.