外文翻译基于lms自适应滤波器在直达波消除中的运用using-lms-adaptive-filter-in-direct-wave-cancellation.doc

外文翻译 学生姓名 顾洛怡 学 号 20071305129 院 系 电子与信息工程专 业 电子信息工程指导教师 陈金立 二一一 年 六 月 二 日基于LMS自适应滤波器在直达波消除中的运用徐元军，陶源，王越，单涛电子工程系，信息科学与技术学院，北京理工大学，北京100081，中国摘要：本文介绍了使用最小均方(LMS)算法消除无源雷达收到的直达波。并由此推导出直达波的模型。通过使用基于LMS算法的FIR自适应滤波器，从而开发出来调频无源雷达的软件解决方案，从而代替了利用硬件对无源雷达的调试。由此我们获得的一些无源雷达的仿真结果。这些仿真结果预示着利用LMS算法消除直达波是十分有效的。关键字：LMS算法；自适应滤波器；直达波消除；在以往的雷达系统的研究中，大多数的雷达专家都曾经专注于无源雷达系统，但是只是把它当做只用作为商业电台的广播电台发射器，比如电视和GSM发射机等。而这种无源雷达系统的其他的一些潜在运用仅仅只是在一些实验1中被介绍.无源雷达系统通常包括一个参考接收器和一个回波接收器。在实际中，无源雷达的回波接收器通常不仅收到目标的回波，而且也接收到由于多径传播效应而产生的回波。由于在实际中的雷达的横截面(RCS)的目标通常是非常小的，与多径传播效应而产生的回波相比，目标的回波是非常微弱的，这使得检测信号变得十分困难。这就是为什么在这种情况下，实现目标的检测成为一项极其艰巨的任务。在实际中，无源雷达设备使用了各种各样的不同方案来解决这个问题23。但是这些方法都需要添加特殊的硬件才能够实现直达波的消除。为了解决这个问题，现在我们可以采用软件的方法来实现直达波的消除。在过去几十年的滤波器理论研究中，自适应信号处理经过不断的发展已经成为了现在研究的热门领域之一。越来越多的自适应理论被广泛地运用于实际生活和生产中。实际中的一些重要的运用主要包括自适应线性预测，回波消除，自适应通道均衡等。自适应理论的这些运用使我们意识到也可以采用自适应滤波器来实现直达波消除。通过分析了直达波的特性后,发现基于LMS 自适应滤波器可以被用来解决这个问题。1直达波的模式为了详细的分析这个问题，我们必须先建立一个准确的直达波的模型。经过分析对比，我们发现直达波的特性与无线电信道中的多径传播十分相似。两者都是由与第一个到达的波信号相比，经过不同的延时的分布振幅所构成的。所以无线电信道系统中的多径传播模型可以用于直达波的表示。因此我们可以得到直达波的脉冲响应可表示为4： (1) 其中表示信号的振幅，是信号的时间延迟，是相移，N是信号多径传播的总共路数。因为我们有： (2)等式(1)可以看做一个连续时间FIR滤波器的脉冲响应。在无源雷达系统中，无源雷达的接收器的输出是与雷达的数字信号处理器相连。我们引入一个新的复杂参数来替换等式(2)，并把等式(1)进行Z变换后，得到表达式如下： (3)这就是直达波的在Z域的模型的表达式。如果我们把等式(3)看作一个FIR滤波器的传递函数，并且其脉冲响应是已知的，由此我们对直达波是可以进行估计的。从而直达波消除的问题转变为如何获得等式(3)中的系数，即如何准确的定义直达波的模型，实际中，这有很多不同的方式完成这个问题。由于FIR滤波器的结构，基于LMS自适应滤波器理论能够被用于解决这个问题。2 基于LMS自适应滤波器的直达波消除的实现自从Widrow和Hoff在1960年提出了LMS算法5，LMS算法被广泛地用于各种各样的自适应滤波器。LMS算法的一个显著特点是运算的简单方便。它不需要经过复杂的计算，并且它可以保持系统良好的稳定性，并且可以轻而易举地在DSP系统上实现。通常LMS算法包括两个基本的过程：一个是滤波器过程，另一个是自适应过程6。在滤波器进行滤波过程中，第一步是根据滤波器的输入值计算滤波器输出值，第二步是由自适应滤波器的实际输出值和期望输出值相比较，从而通过计算可以得到估计误差。在自适应过程中，滤波器抽头输出值的加权系数会根据估计误差自动地进行调整。因此抽头输出值的加权系数会被不断地重新确定。在实际滤波器过程中，通常这两步是一起进行的，并且构成一个闭环的反馈回路。其作用主要是使得估计误差逐渐地趋近于零。当信号中有噪声存在时，在这两个过程不断地重复若干次后，基于LMS滤波器的估计误差输出值将收敛于可以接受的水平。因此，我们可以给出下面的三个重要的表达式：滤波器的输出： . (4)估计误差：. (5)滤波器的抽头加权系数的跟新：, (6)其中表示来自滤波器的抽头系数所组成的向量，表示滤波器的输入向量，表示步长因子，它决定了基于LMS的自适应滤波器的收敛速度。在下一步中，我们将提出把基于LMS自适应滤波用于直达波消除的方法。根据上面一节介绍基于LMS的自适应滤波器理论知识可知，这项工作的关键是如何从直达波的模型中获得基于LMS自适应滤波器的参数。 图1是包含有参考输入信号和回波信号的自适应直达波消除的原理框图，其输出是滤波器的抽头系数。与标准的基于LMS的自适应滤波器相比较，在直达波消除中，滤波器的输入向量是由参考信号的一些延迟波所组成的。抽头系数向量与等式(3)中参量是相对应的。图1自适应直达波的消除当自适应算法达到收敛点时，滤波器的估计误差就是回波信号，而此时直达波已经被成功地滤除了。通常在一个无源雷达系统中，当在所选择的区域内没有所希望的目标时，抽头系数的设置可以通过基于LMS算法的自适应滤波器获得，因此我们通过这种方法可以建立起直达波的模型，并且我们可以把抽头系数的值存储在DPS系统的内部存储器中。当无源雷达工作时，存储在DSP系统内部存储器中的抽头系数被调用，从而可以把直达波从信号中滤除。这种消除的方式可以用下面的等滤波器哦式表示： (7)式中表示回波信号。表示自适应滤波器的输入向量，它是由参考信号的一些延时信号波组成的。表示LMS自适应滤波器的抽头系数值组成的向量。3 仿真结果为了评估基于LMS自适应滤波器直达波消除的性能，在把这种滤波器被运用于实际之中前，我们必须先进行一些仿真。在MATLAB的软件环境下，由于MATALB包括许多子模块，比如调频信号器，加性信道噪声，直达波的形成和基于LMS自适应滤波器等模块。由此模拟系统能够被顺利地建立起来。在FM广播信号发射器的分路中，首先调频参数是根据调频广播标准初始化的，且调制信号是来自声波文件的。而信道的噪声是被假定添加的是高斯白噪声(AWGN)。在直达波的形成过程中，多径传播的总的路数为16，所以自适应滤波器的抽头数也是16，并且每个传播路径的幅度是单独给出的。基于LMS的自适应滤波器的程序开发是按照第二部分的三个关系式设计的。由于当抽头系数输出值获得后，消除操作变得十分的简单，所以如何准确的获得抽头系数将变得极其重要。我们知道基于LMS的自适应滤波器只有当估计误差收敛时才能正常工作。为了掌握LMS算法的动态，估计误差必须能够被显示出来。所以仿真的输出包括两个部分：一个是滤波器的抽头系数值，另外一个是估计误差。图2展示了滤波器抽头系数的实际值与采用LMS算法的获得抽头系数值之间的对比。从图上我们可以清楚地看出，利用基于LMS算法的自适应滤波器获得输出值是十分接近于真实值的。并且由此我们可以推导出滤波器的抽头系数的输出值的估计误差十分小的。并且直达波的模型参数可以直接从两个无源雷达接收机中获得。图(2) 实际抽头系数的值与采用LMS算法的获得抽头系数值之间的对比基于LMS的自适应滤波器的收敛过程可以从图(3)获得图(3) 基于LMS的自适应滤波器的输出误差这表明大约在计算了两百次之后，自适应滤波器能够达到了稳定状态，并且估计误差不断地趋近于零，从而准确的抽头系数的估计值可以获得了。4结论我们描述了一个自适应方式，它可以消除FM发射信号的无源雷达回波中的直达波。直达波的特性被完整准确地分析了，并且研究的结果已经被展现出来了，从仿真结果来看，自适应滤波器的优势已经被完全的验证了。Using LMS Adaptive Filter in Direct Wave CancellationXU Yuan-jun,TAO Ran,WANG Yue,SHAN Tao(Department of Electronic Engineering, School of Information Science and Technology, Beijing Institute of Technology, Beijing 100081, China）Abstract:the way to use the least-mean-square (LMS) arithmetic to cancel the direct wave for a passive radar system is introduced. The model of the direct wave is deduced. By using the LMS adaptive FIR filter, the soft-ware solution for FM passive radar system is developed instead of the hardware consumption of the existent exper-iment system of passive radar. Further more some simulative results are given. The simulative results indicate thatusing LMS arithmetic to cancel the direct wave is effective.Key words: LMS arithmetic; adaptive filtering; direct wave cancellationOver the past years, most radar experts focused on the passive radar system, which only uses commercial radio broadcast station as a source of the radar transmitter, such as TV and GSM transmitter. The potential usefulness of this radar system is presented by some experiments1. A passive radar system includes a reference receiver and an echo wave receiver. Mostly the echo receiver received the targets echo as well as the wave from the broadcast station through multipath propagation effect. As the radar cross-section(RCS) of the target is uaually very small, the echo wave of the target is very weak compared with the multipath propagation wave. This is the reason why the target detection becomes a challenging task under this circumstance. The existent experiments of passive radar used some different ways2,3, all of which need to use special hardware to perform direct entering wave cancellation, to solve this problem. However, it is possible to make this task by software. Over the last several years, the adaptive signal processing has been an active area of research, more and more theories were introduced into practical applications. Examples of some important area include linear prediction, echo wave cancellation, channel equalization, etc. Those examples remind us how to use the adaptive signal processing into direct wave cancellation. After analyzing the behavior of the direct wave, the least-mean-square (LMS) adaptive filter is applied to solve this problem.1 The Mode of Direct WaveTo analyze this problem in detail, it is necessary to set up a correct model of direct wave. The behavior of the direct wave is very like the multipath propagation of radio channel, both of them are composed of distributed amplitude at different time delays in comparison of the first arriving ray, so the model of mutipath propagation of the radio channel can be introduced, thus the impulse response of the direct wave can be expressed as4 (1)Where is the amplitude,nis the time delay,isthe phase shift, andN is the total number of multipath propagation components.Because we have (2)Equation (1) can be considered as a continuous time FIR filters impulse response. In the passiveradar system, the output of the receiver is digitalized at the digital radar signal processor. By introducing a new complex parameteraito substitute the value of Eq.(2), Eq.(1) is changed toz-transform representation given as (3)This is the model of the direct wave inZdomain, if Eq.(3) is taken as the transfer function ofan FIR filter. The impulse response is known, and the direct wave could be estimated. Thus the problem of adaptive direct wave cancellation becomes a problem of how to get the factoranin Eq.(3), i.e. how to identify the model of direct wave. There are several different ways to complete this task. Because of its FIR structure, the LMS adaptive filter method can be introduced to solve the problem.2 Implementing LMS Adaptive Filter In Direct Wave CancellationSince Widrow and Hoff developed the LMS arithmetic5in 1960, LMS arithmetic has been widely used in adaptive filters. A significant feature of the LMS is its simplicity, it does not need complicated computations, it could keep its excellent stability and it can be easily implemented in DSP system. Usually the LMS arithmetic consists of two basic processes: one is the filtering process, the other is the adaptive process6. In the filtering process, the first step is to compute the filter output with a set of input taps; the second step is to calculate the estimation error by comparing the filter output with a desired output. During the adaptive process the tap weights ofthe filter will be adjusted in accordance with the estimation error, so a new set of taps will be determined. Those two steps work together, and constitute a feedback loop, the result of which is to make the estimation error approach zero. When there exists noise, after repeating the two processes several times, the output estimation error of LMS filter will be converged to the acceptable level. Thus the three relations can be given as below: Filter output:. . (4)Estimation error:. . (5)Tap-weight adjustment:, (6)whered(n)denotes the tap of the filter,x(n) denotes the input vector of filter,is called the stepfactor, which determines the convergence speed of the LMS filter.In the next step, we propose the way to apply the LMS adaptive filter to the direct wave cancellation. Based on the knowledge of LMS filter in the previous section, the key task is how to load the right LMS filter parameter from the model of direct wave.Figure 1 is the block diagram of the adaptive direct wave cancellation with the input reference wave and echo wave, whose output is the tap-weight.Compared with the standard relations of LMS adaptive relations, the input vector x(n) is composed of some delays of the reference wave, and the taps of the filter d(n) correspond to the factors in Eq.(3).When the adaptive arithmetic reaches the convergence point, the estimation error of the filter is the echo wave signal whose direct wave is largely removed. In a practical radar system, when there is no interested object in the detected space, a set of tap-weights can be got by using the LMS adaptive filter, so the model of the direct wave is established, and the tap-weights are stored in the memory of the DSP system. When the passive radar system works, the stored tap-weights are recalled to fulfil the direct wave cancellation. The cancellation operation can be expressed by: (7)wherer(n)denotes the echo wave signal,x(n)denotes the input vector, that consists of the delays ofreference wave, andd(n)denotes the tap-weight of the LMS adaptive filter.3 Some Simulative ResultTo evaluate the performance of LMS adaptive direct wave cancellation, some simulations should be done before putting it into practical applications. Under the Matlab environment, which includes some sub-routings such as the FM broadcast signal generator, the channel noise adder, the direct wave forming and the LMS adaptive filter program, the simulation routings are developed. In the FM broadcast signal generator sub-routing, first the FM parameters areinitialized according to the FM broadcast standard, and the modulating signal comes from the sound wave file. The channel noise is assumed to be the additive white Gaussian noise (AWGN). During the direct wave forming, the number of the multipath propagation components is 16, so the number of LMS adaptive taps is 16, and the amplitude for each mutipath propagation is given individually. The LMS adaptive filter program is developed in accordance with the three relations stated in section 2. Because the cancellation operation is performed easily after the tap-weight is got, the process of how to get the right tap-weight is very important. We know that the LMS adaptive filter can work normally only if the estimation error is convergent. To monitor the state of the LMS arithmetic, the estimation error should become visible. So the output of the simulation includes two parts, one is the output tap-weights, the other is the estimation error.Figure 2 shows the comparison of the true value and the adaptive result of the tap-weights, fromwhich it is found that the LMS adaptive result is close to the true value, which implies that the estimation error of the tap-weights is very small, and the model parameters of the direct wave are available from the two receivers of the passive radar.The convergent process of the LMS adaptive filter could be obtained from Fig.3, which shows that after calculating about 200 times, the filter reaches the stable state, the estimation error tends to zero, and the right estimating tap-weight is got. 4 ConclusionsWe have described an adaptive means to eliminate the direct wave from the echo wave in the passive radar system based on the FM broadcast signal. The behavior of the direct wave is analyzed fully, and the results of research have been presented. From the simulation results, the advantage of this adaptive filter is demonstrated.References:1David A. Passive system hints at stealth detectionJ. Aviation Week & Space Technology, 1998(12): 70-71.2Howland P E. A passive metric radar using a transmitter of opportunityZ. International Conference on Radar,Paris, 1994.3Sahr J D, Lind F D. The manastash ridge radar: A passive bistatic radar for upper atmospheric radio scienceJ.Radio Science, 1997, 32:2345-2358.4Baniak J, Baker Dr G, Marie A. Silent sentryTMpassive surveillance J. Lockheed Martin Mission Systems,1999,1(6):1-10.5Haykin S. Adaptive filter theoryM. Engle Wood Cliffs,Prentice-Hall, 1986.6Smith S W. Digital signal processingM. San Diego: California Technical Publishing, 1996.