关 键 词：

基于 MATLAB 宽带 脉冲 位置 调制 仿真 说明书 开题 报告

资源描述：

基于MATLAB的超宽带脉冲位置调制仿真说明书及开题报告,基于,MATLAB,宽带,脉冲,位置,调制,仿真,说明书,开题,报告

内容简介：

XXXXXX设计任务书（工科及部分理科专业使用）题 目： 基于MATLAB的超宽带脉冲位置调制仿真 学 科 部： 专 业： 班 级： 学 号： 学生姓名： 起讫日期： 指导教师： 职称： 学科部主任： 审核日期： 一、毕业设计的要求和内容（包括原始数据、技术要求、工作要求）超带宽（UWB）脉冲通信是一种与其它技术有很大不同的无线通信技术，它具有通信容量大、辐射功率密度低，抗多径干扰，结构简单和密度性好等优点。超带宽信号及其调制解调是研究超带宽通信系统时需要考虑的重要因素。针对超宽带信号的超短脉冲和极低发射功率造成接收机同步十分困难的问题,本课题提出用脉冲位置调制（PPM）的方法对其进行研究，先根据UWB信号的定义和调制解调理论分析而建立的UWB信号仿真模型，对UWB信号在不同噪声干扰、不同调制方式、不同解调方式下进行Matlab仿真，然后利用脉冲位置调制的方法进行研究并仿真，最后对仿真的结果进行分析比较，得出具有一定实践指导意义的结论。二、毕业设计图纸内容、张数及要求要求有系统仿真图并对其进行详细分析。三、毕业设计计算书、实物内容及要求无 四、毕业设计进度计划序号各阶段工作内容起讫日期备 注1理解课题内容，查阅相关资料，形成初步设计方案，写出开题报告。2011.11.20-2011.11.302完成部分毕业设计任务（程序设计与系统仿真）2011.12.1-2011.12.253完成外文资料翻译，基本完成毕业设计论文初稿。2011.12.26-2012.1.84继续修改完善毕业设计，进一步修改论文。2012.1.9-2012.5.136补充资料，完成毕业论文，准备毕业答辩。2011.5.14-2011.6.2五、主要参考资料1 蔡成林，卢晓春，李孝辉，吴海涛.高斯脉冲三因子组合的UWB测距脉冲设计J,微计算机信息，2009.7，25(7):67-71. 2 王瑞军，谢京稳，王鹏毅. 基于UWB的多目标测控通信技术J. 飞行器测控学报，2010.4，(4):7-10. 3 Dashti Marzieh，Ghoraishi Mir，Haneda Katsuyuki. Optimum Threshold for Indoor UWB ToA-Based RangingJ. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES，2011.8，E94A(10) : 2002-2012.4 Shirazi G，Lampe L. UWB many event detect the NetworkJ. IEEE Transactions on Signal Processing，2011.9，59(9) : 18-23.5 刘鹏，张国鹏，杨小冬，赵小虎，丁恩杰.基于UWB的井下无线传感网信道模型研究J，武汉理工大学学报，2011.6，33(6) : 63-67.六、毕业设计进度表（本表每两周由学生填写一次，交指导教师签署审查意见）第一、二周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第三、四周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第五、六周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日 第七、八周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第九、十周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第十一、十二周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第十三、十四周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第十五、十六周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日第十七、十八周（ 月 日至 月 日）学生主要工作：指导教师审查意见：年 月 日七、其他（学生提交）1开题报告1份 2外文资料译文1份（1200字以上，并附资料原文） 3毕业设计说明书1份（4000字以上） 4毕业设计计算书及图纸1份。 指 导 教 师： 朱启标 系 负 责 人： 黄仁如 学生开始执行任务书日期： 2011.11.20 学 生 姓 名： 葛剑鹏 送交毕业设计日期： 2012.5.21 XXXXXXXXX设计（XX）开题报告题 目： 基于MATLAB的超宽带脉冲位置调制仿真 学 科 部： 专 业： 班 级： 学 号： 姓 名： 指导教师： 填表日期： 20XX 年 11 月 23 日一、 选题的依据及意义超带宽（UWB）脉冲通信是一种与其它技术有很大不同的无线通信技术，它具有通信容量大、辐射功率密度低，抗多径干扰，结构简单和密度性好等优点。利用UWB脉冲通信是对无线频谱资源的利用进行新的探索，它解决了困扰传统无线技术多年的有关传播方面的重大问题。这项新兴技术对方兴未艾的无线接入技术是一个有力的支持，因此需要深入研究并掌握这项技术。超带宽信号及其调制解调是研究超带宽通信系统时需要考虑的重要因素。本课题提出用脉冲位置调制（PPM）的方法对其进行研究，先根据UWB信号的定义和调制解调理论分析而建立的UWB信号仿真模型，对UWB信号在不同噪声干扰、不同调制方式、不同解调方式下进行MATLAB仿真，然后利用脉冲位置调制的方法进行研究并仿真，最后对仿真的结果进行分析比较，得出具有一定实践指导意义的结论。二、 国内外研究现状及发展趋势UWB(UltraWideband)超宽带，一开始是使用脉冲无线电技术，此技术可追溯至19世纪。后来由Intel等大公司提出了应用了UWB的MBOFDM技术方案，由于两种方案的截然不同，而且各自都有强大的阵营支持，制定UWB标准的802.15.3a工作组没能在两者中决出最终的标准方案，于是将其交由市场解决。2009年1月，何海莲等利用Rssler超混沌系统构造了一种新的超混沌序列,分析了序列的相关特性,并将其应用于直接序列超宽带(DS-UWB)系统中,提高了它的误码性能1。2009年3月，赵羽等采用被动谐波锁模环形光纤激光器作为超宽带(UWB)光脉冲源,进行了UWB over Fiber室内无线传输的实验研究，将光纤激光器的光脉冲转换为满足FCC规定的UWB微波脉冲序列进行传输2。2009年7月，蔡成林等从提高发射功率和降低系统误码率的统一角度出发,研究了一种利用高斯脉冲三因子优化组合的超宽带(UWB)测距脉冲快速设计方法。这种方法适用于发射频谱任意规定的UWB波形设计，对UWB测距脉冲优化设计具有一定的参考价值3。2010年4月，王瑞军等针对较高码率的多目标测控通信需求，提出了一种基于超宽带和扩频技术的解决方案，给出了其多用户的调制解调方法，分析了其在多用户情况下的误码率性能。该解决方案可以利用超宽带纳秒级的窄脉冲，实现1m以内的测距定位精度4。2011年8月，Dashti Marzieh等根据UWB信号在室内到达不同位置的变化多径干扰不同，得到了最优阈值。提出了阈值标准信道模型5。2011年9月, Shirazi G.等提出了一个最大化的框架UWB多事件检测网络，解决了超宽频传感器网络中最大化事件检测的冲突问题6。2011年11月，Hirsch Ole等针对频率选择性衰弱信道下协作通信系统信道估计复杂的问题,提出了一种模拟合并放大转发超宽带(UWB)协作通信方案。仿真结果证明，相对于无协作通信系统，模拟合并转发协作系统无需信道估计就可获得传输性能的有效提升7。2011年1月，徐艳云等利用转台旋转目标，基于超宽带脉冲源和超宽带收发天线以及高性能取样示波器，配以同步触发脉冲和自行研发的数据采集软件，搭建了该时域雷达实验系统，实现了分辨率为8mm的近距离目标的成像，准确地反映了目标的位置、形状和大小等信息8。2011年6月，刘鹏等根据地形、人员和设备环境的不同对井下信道进行分类，并根据Frensel定理给出节点间存在信号可视(LOS)通路的必要条件，很好地刻画UWB信号在不同井下环境中的传播特性，为进一步设计井下高效的UWB信号Rake接收机，降低误码率提供了重要的依据9。三、 本课题研究内容本课题是研究在不同噪声干扰下的超带宽脉冲位置的调制和解调。其中涉及到不同的调制方式和不同的解调方式对模型的影响，并且从中找出规律，得出最佳方案。系统模型如图3.1所示。脉冲产生编码数据/用户接口噪声数据/用户接口脉冲检测LPF低噪声放大器解码图3.1系统模型通过不同的算法可以得到不同的UWB波形，可以在MATLAB中仿真比较出来。用UWB波形作为调制信号，对各个频段的信号进行调制，然后再对信号进行解调。观测信号前后的变化程度，由于这个过程在现实传播过程中会存在一些干扰的噪声信号，理想的模拟环境是无法表现出来，所以也模拟了几种常见的噪声信号，将不同噪声信号加入到信道中，使其对调制信号进行干扰，再进行解调。这样就更加真实的反映了整个系统的调制解调过程。这整个过程的仿真都是通过在MATLAB中以图形的方式表现出来。四、 本课题研究方案在充分检索文献资料的基础上，研究不同的算法产生超带宽脉冲并通过MATLAB进行仿真，比较各种算法的优劣，选择一种适合的算法。熟悉掌握调制（图4.1）和解调（图4.2）的基本原理，通过Matlab仿真比较不同的调制载波信号解调信号解调得出的结果。由于仿真是在理想情况下进行的，所以必须模拟出不理想的环境，在这样的情况下研究不同的噪声对系统的影响，比较他们对有用信号的影响程度，对特殊噪声进行特殊处理，研究怎样处理不同的噪声。调制信号图4.1调制原理LPF载波信号解调信号图4.2解调原理结合上面做的工作，进行系统设计并整体联调，再对MATLAB仿真的结果进行深入研究，逐步修改，从而得出理想结果。五、 研究目标、主要特色及工作进度1、研究目标能够在MATLAB中仿真出来信号在调制之前和调制之后的变化情况，还可以分析在不同程度的噪声进行干扰下系统的变化情况，而且将这些微妙的变化情况都在MATLB软件上用图表的形式直观的反映出来。2、主要特色研究的课题的本身就是当今很前沿的一个领域，当在实际电子通信系统中进行试验研究比较困难或者根本无法实现时，采用仿真技术对其进行性能分析和系统设计时缩短了研究的时间，提高了科研效率。3、工作进度时间计划需完成任务2011.11.152011.11.25进行方案设计，完成开题报告2011.11.262011.11.30完成一篇课题相关外文的翻译2011.12.12011.12.7 学习MTLAB并进行程序仿真2011.12.82011.12.20进一步修改程序并仿真，实现设计功能 2011.12.202011.12.30完成论文初稿2012.1.12012.2.15修改和完善论文2012.2.152012.6.2整理资料，准备答辩6、 参考文献1 何海莲，王光义. 超混沌序列对DS-UWB多址性能的改善J.通信技术，2009.1，46(1):36-38. 2 赵羽，刘永智，赵德双.UWB over Fiber室内无线传输的实验研究J. 光电子.激光，2009.3，(3):12-15. 3 蔡成林，卢晓春，李孝辉，吴海涛.高斯脉冲三因子组合的UWB测距脉冲设计J,微计算机信息，2009.7，25(7):67-71. 4 王瑞军，谢京稳，王鹏毅. 基于UWB的多目标测控通信技术J. 飞行器测控学报，2010.4，(4):7-10. 5 Dashti Marzieh，Ghoraishi Mir，Haneda Katsuyuki. Optimum Threshold for Indoor UWB ToA-Based RangingJ. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES，2011.8，E94A(10) : 2002-2012.6 Shirazi G，Lampe L. UWB many event detect the NetworkJ. IEEE Transactions on Signal Processing，2011.9，59(9) : 18-23.7 Hirsch Ole，Janson Malgorzata，Wiesbeck Werner. A Low-power UWB Transceiver by Use of Trigger Receiving MethodJ. Journal of Circuits, Systems and Computers，2010.11，11(15) : 44-50.8 徐艳云，张群英，方广有.超带宽时域近距离高分辨ISAR成像J. 电子与信息学报，2011.1，33(1) : 43-48.9 刘鹏，张国鹏，杨小冬，赵小虎，丁恩杰.基于UWB的井下无线传感网信道模型研究J，武汉理工大学学报，2011.6，33(6) : 63-67.4 Direction of Arrival Estimation of Multiple UWB Signals V. V. Mani R. Bose Abstract :This paper deals with the problem of estimation of direction of arrivals (DOA) of a multiple ultra-wideband (UWB) pulse postion modulation signals incident on a smart antenna in the presence of white Gaussian noise. We transform the received signal into frequency domain in order to split the array output into multiple frequency channels. Corre- sponding frequency channels data of the array is arranged into a model similar to narrowband DOA estimation. Iterative quadratic maximum likelihood algorithm is applied to yield DOA estimates. These separate estimates at different frequencies are combined into a single estimate of DOA for each source in an appropriate manner. The performance of the proposed method is studied via extensive computer simulations. It is seen that the technique can successfully resolve the DOA of the closely-spaced UWB signals. Keywords :Ultra-wideband PPM Smart antenna Direction-of arrival IQML 1 IntroductionUltra-wideband (UWB) technology has increasingly been used in personal area wireless networks and Radio Frequency Identication (RFID). This technology is characterized bythe transmission of extremely short duration pulses, has become a candidate technology for ranging and positioning applications 1,2. Ultra-wideband signals have ne time and angle resolution capability. By adding multi-antenna techniques to UWB, additional spatial parameters e.g direction of arrival (DOA), time of arrival(TOA) can be extracted, leading to enhanced precision in positioning applications 3. Unlike narrowband, UWB signalcovers awide range of spectrumthat causesmany narrowband array processingmethods to be ineffective. Moreover, the approach of broadband array processing faces difculties in such a wide spectrum.The problem of maximum likelihood (ML) estimation of the DOAs of multiple UWB sources has been rarely addressed in the literature. Until recently, the papers of Najar et al.,Lee et al., Keshavaraz are a few who dealt this problem 46. However, these authors are mainly concerned with single source DOA & TOA estimation. Kesavaraz 6 proposed the use of weighted signal-subspace method of DOA estimation for UWB pulse postion modulation (PPM) sources impinging on ULA (Uniform linear array). There have been other approaches that consider the estimation of the angle of arrival based on temporal delays as in Pierucci and Roig 7, where authors propose DOA estimation by evaluating the propagation delays impinging from each element array. This approach suffers from constraints associated with high sampling rate requirements. The authors proposed in Navarro and Najar 4 the use of low-complexity frequency domain approach for joint estimation of TOA and DOA for a single UWB source.This paper, is an attempt to proceed further with the solution of UWB multiple sources DOA estimation problem based on maximum likelihood principles. However, DOA estimators proposed for narrowband signals does not exploit the advantage of large signal bandwidth of UWB. Our objective here is to explore the possibility of computationally efcient algorithm for maximum likelihood UWB DOA estimation. Time shift property of Fourier transforms used to develop a frequency domain model for the data that is similar to models used in DOA estimation in narrowband case. In this respect, we have been motivated by theapproach proposed by Bresler and Macovski 8 for the parameter estimation of exponential signals in narrow band case with ULA. In this approach, an iterative method, called iterative quadratic maximum likelihood (IQML) has been formulated for obtaining the ML solution.This involves the creation of toeplitz matrix which spans the subspace orthogonal to signal space, and can be parameterized by the coefcients of a prediction polynomial, whose roots yield the DOA estimates. UWB data model is transformed into frequency domain and on each bin, IQML is applied to generate DOA estimates.This solution, however, falls short of providing single ML estimate for the DOA of each UWB source. This is because the IQML search is conducted over an expanded signal spacewhich in turn leads to generation of separate DOA estimates for different frequencies. For applications where we would require a separate DOA estimate for each source. So, separate estimates at different frequencies are combined into a single estimate of DOA for each source in an appropriately average sense. It is seen that procedure leads to very good estimates, as evidenced by simulation results.This paper has been organized as follows. In Sect. 2 UWB data model is given and in Sect. 3 problem formulation and its mathematical description for direction nding are presented. In Sect. 4 we develop the ML criterion for DOAs estimation and in Sect. 5 UWB ML estimation algorithm presented. Results and simulation studies are presented in Sect. 6. Finally the paper is concluded in Sect. 7.2 UWB Data ModelIn theUWB communication systemthe transmitted signals of each user consists of sub-nano-second pulses. Each user transmits one pulse per frame. Each frame of Tf seconds contains Nh hopping chips with duration Tc seconds per chip. In each Tf , one pulse will be placed in one of the Nh slots according to the corresponding user time hopping sequence. The location of the transmitting pulse within the allocated hopping slot is determined by the information bit. A typical transmitted time-hopping PPM signal for qth user is modeled as 9 (1)tr (t) represents the transmittedmonocyclewaveformand the receiving antennamodies the shape of tr (t) to (t) which is modeled as second derivative Gaussian waveform 10,11. Tf is the frame interval and is typically hundred or thousand times wider than the monocycle width, resulting in a signal with very low duty cycle. The data sequence ofthe qth user is a binary symbol stream that conveys some form of information. When data symbol is 0, no additional time shift is added whereas when the data symbol is 1, a time shift of is added to the monocycle. In the next section we formulate the signal model for nding the DOA estimates of UWB sources impinging on smart antenna.3 UWB Direction FindingTime Domain: Let Q M UWB-PPM sources sq (t), q = 1,., Q impinge upon an M element smart antenna array (Fig. 1). The signal received by the mth antenna at time t equals (2)Fig. 1 Smart antenna for DOA estimation of UWB signalswhere vm(t) denotes the mth antenna additive Gaussian noise, sq (t) represents the qth UWB transmitted signal, and m(q ) refers to the qth signal sources propagation delay at the mth antenna. For a ULA the propagation delay associated to the mth antenna for the qth source is given by (3)with d being the distance between antenna elements in the array, c the speed of light and q direction of arrival of the qth source. The received signal consists of the attenuated and delayed version of the transmitted pulse train caused by multipath during propagation in the medium. The derivation below assumes that multipath proles for each array element are the same due to small inter element spacing. The problem of interest is to estimate the direction of arrivals of UWB impinging signals i.e q s. Also, we make the assumption that the total number of sources Q impinging on the array are known.Frequency Domain: Since the frequency range of UWB signal is wide in nature and also to generalize the narrow band DOA estimation techniques to UWB, we are transforming the signal into frequency domain. The received signal xm(t) time- sampled at fs ,then apply a K-point discrete Fourier transform (DFT). (4)where k , k = 0,., K 1L ,H and Vm(k ) denote the mth antenna noise at frequency k and Sq (k ) refers to the Fourier transform of sq (t). DOAs are embedded inexponential component i.e , q = 1,., Q which are to be estimated. so, we arrange the corresponding k DFT components of the array in the following vector notation. (5)The above formulated data model is compactly described by the following vector notation.For notational simplicity we use k in place of k : (6)where X(k) and V(k) are the M 1 vectors, S(k) is a Q 1 vector (7) (8) (9)and A(, k) is a M Q matrix with a block representation (10)where=1,.,Q Twith a(q , k) is a M 1 column matrix (11)A(, k) is a vendermonde matrix 8 whose columns are the steering vectors of the impinging UWB wave fronts. We use the notation ()T to denote transpose operation, ()H for Hermitian-transpose operation and ()* to denote complex conjugate.The receiver expects signal from the source within a short window of time Tr and both transmitter and receiver are working synchronously. In this formulation the unknown param- eters are (q )s and Sq (k)s. Hence our estimation problem can be formulated as follows. For the given window of data, estimate (q )s and Sq (k)s where (q )s are embedded in the steering matrix A and S(k) are the components of the vector s(t).However, this estimation would require the solution of a nonlinear optimization problem in terms of the Q parameters q , q = 1,., Q.We consider the problem as estimating the spatial vector , whose components q contain the required DOA information.4 The Maximum Likelihood CriterionAs discussed in the previous section, the rst step of the problemis concernedwith estimation of the parameter vector . The solution of this problem is discussed in this section. It has been shown that under white Gaussian noise, ML estimators and least square estimators are equivalent 12. Hence ML estimate of the signal parameters can be obtained by solving the non-linear least square problem （12）whereis the Euclidean norm. This expression may be further simplied by rst substituting the least square estimate of S(k) in terms of A as （13）where is the pseudoinverse of A(, k).Bysubstituting (13)into(12), the S(k)s are eliminated and it is reduced to the equivalent formulation 12 （14）where and are the projection matrices onto the column space of A(, k) and onto itsorthogonal complement, respectively, and are given by （15）Once the ML estimate ML is determined by solving (14), S(k)s are found by the linear relationship of (13). Computationally expensive global search is required to minimize (14). Therefore the approach proposed by Bresler and Macovski 8 is adapted here to nd the DOA estimates.As mentioned in 8 output vector of the ULA obeys a special Auto Regressive Moving Average (ARMA) model, and the ML estimates of its parameters are directly related to its coefcients. Use of this model converts the problem of estimating the DOAs to that of estimating special ARMA parameters, fromwhich the DOAs can be easily derived. Thismethod consists of the following steps:(i) Establish a relation to represent the null space of the array steering matrix associated with the model of the space-time staked vector X(k) as dened in (6) in terms of coefcients bi of the special ARMA model.(ii) Formulate theminimization problemin terms of a constrained quadraticminimization procedure for obtaining the ARMA coefcients bi .(iii) Once the coefcients bi of the polynomial are estimated, the unknown DOAs can be obtained by nding the roots of b(z) for each spatial frequency (k).We next present the procedure for the calculation of polynomial coefcients.As A(, k) is in Vendermondematrix form, there exists a Toeplitzmatrix B of dimension M M Q such that 8 （16）The matrix B is given by （17）and its elements are taken from the coefcients of the polynomial （18）This polynomial regarded as linear predictor polynomial for the noiseless signal of (4). Columns of B are orthogonal to those of A 8, and B has full rank equal to M Q, its columns span the orthogonal complement to the range space of the Q columns of A, and the projection PB onto the subspace is equal to , . The generating polynomial b(z) and generating vector b are uniquely associated with as denoted by b(z). Then , can be written as （19）(14) can now be rewritten as （20）Using the commutative property of the convolution operation we get （21）where the data matrix (k) is dened as （22）Using this result (20) becomes （23）As mentioned in 8, the ML solution for the b is sought over appropriate constraint set, which guarantee non-triviality aswell as optimality. Typically, such a non-triviality constraint is imposed by either to be monic polynomial in z, i (referred as linear constraint) or setting, i (called norm constraint). Furthermore, since z is a pure complex sinusoid, it follows that bi(z) should have its roots on unit circle in the z-plane, i .Thisisachieved by imposing conjugate symmetry on the bi(z) polynomial i ,i.e （24）Where （25）5 UWB ML Estimation AlgorithmTheML estimate of the polynomials bi(z) can be obtained byminimizing (23) over an appropriate constraint set as discussed earlier. This constrained nonlinear minimization problem can be solved by the IQML algorithm of Bresler and Macovski 8, which requires the solution of a quadratic minimization problem at each step, and generally converges in a small number of steps. This IQML algorithm adopted to the UWB case can be summarized as follows:(a) Initialization: Set d = 0; choose an initial vector b and denote it by b(0)(b) Compute （26）where B(d) is computed from b(d) in the same manner as B in (17)(c) Solve the quadratic minimization problem （27）over an appropriate constraint set (c.s).(d) d = d + 1(e) Check convergence:( is chosen according to the desired precision)ifyesgotostep(f)if not got to step (b)(f) Find roots of b(d)(z). These are the estimated DOAs (q , q = 1,., Q).5.1 Some Remarks on the Implementation of the Constraint SetAs per the previous discussion, we need to impose the constraints of conjugate symmetry and non-triviality on the polynomials b(i ) (z). It is possible to incorporate these constraints in the iterative process by modifying the data matrix (k). We rst describe the procedure for the conjugate symmetry constraint.Let P be an odd number such that P = 2q +1 (for the even case similar expressions can be developed). Partition b and (k) such that （28）and （29）For conjugate symmetry of , dening the reverse matrix （30）the symmetry relation for b represented by or .Let c and (k) be dened as （31）And （32）This reduces the minimization problem in (27)to （33）Dene （34）It is shown in Bresler and Macovski 8 that solving the above minimization problem is equivalent to: （35）In as far as the norm constraint is considered, minimization is easily implemented by searching for the eigenvector corresponding to theminimumeigenvalue of thematrix C . Obtained eigen vector is related to b via (31). Form the polynomial b(z) from the coefcients of b,DOAs are obtained by rooting the b(z) polynomial. This procedure is carried out for each frequency bin independently and average the DOA estimates over the all the bins. Since each decomposed signal is approximated as a narrowband signal, the narrowband estimation method is applicable for each bin.6 Simulation ResultsThe validity of the proposed method has been studied via simulation experiments. Simulation experiments have been carried out with a ULA of 24 elements with antenna separation equal to one half of the wavelength corresponding to the highest frequency is considered(10.6 GHz). We have considered a scene with 3 correlated UWB PPM pulses each of duration 1ns (Q = 3) shown in Fig. 2 in the eld at 60, 0, 30 relative to the broadside of the array are received by the smart antenna. These closely spaced pulses (shown in Fig. 2) spectrum are shown in Fig. 3. Spatially and temporally white Gaussian noise is added to each antenna output according to SNR level. All sources assumed to have the same power. On each antenna data over the observation time of one frame period, DFT of length 256 applied.For nding DOA estimation of the sources corresponding frequency bins of data on each antenna are stacked, and applied IQML algorithm using norm constraint on b.TheIQML algorithm was initialized with BH(0) B(0) = I i.e b =1, 0,., 0 which satises the norm constraint.Fig. 2 UWB signals incident on the ULAFig. 3 Spectrum of incident signals on ULASince the received pulse shapes was assumed to be known, most of the signal energy was known to be concentrated in only half of the DFT frequency bins, and only data from these bins were used to estimate the DOAs. The mean square error (MSE) in estimating the DOAs for each sources for various SNRs (in dB) is computed by averaging the squared error over 100 independent trials. The results are shown in Fig. 4. The performance is better for the sources close to the broadside, at high SNRs. It is clearly evident in Fig. 4 for the 0 angle of arrival source MSE is better than other sources at high SNR. It attained approximately 20 dB improvement in MSE.Figure 5ad illustrates the MSE vs. SNR for the various angles of arrivals of 3 closely spaced UWB sources. We observe a significant performance improvement when the signals are arriving from the broadside. Here we note the difference from Fig. 5dwhenthethree signals arrive from 15, 30, 75 respectively. Nearer to the broadside signal i.e. 15 gives better performance at high SNR compared to the rest of two signals. Moreover, when all the signals are located nearer to broadside estimation error in DOA is increasing further. In Fig. 5b, c, we can closely observe the difference in MSE. The signals at 20, 10, 20angles are attaining 30 dB improvement in MSE compared to the signals of 10, 0, 10angles at 35 dB of SNR level.Fig. 4 MSE vs. SNR for three closely spaced UWB signalsFig. 5 MSE comparison for different angle of arrivals of closely spaced signalsBy increasing the number of antenna elements, the number of unknown parameters to be estimated (DOAs) remain the same. It may be expected, therefore, the estimation of these direction parameters will improve with the increase in the number of antenna elements. Inorder to study the behavior of ML estimator with IQML algorithm simulations have also been carried out for antenna elements of M = 8, 12, 16, 20, 24. Similarly Fig. 6 shows the MSE in DOA estimation of single source true direction 0 as a function of SNR for different antenna elements. IQML estimates are seen to improve consistently with the element number index.Fig. 6 Effect of DOA estimation error on number of antenna elements for true signal direction 07 ConclusionsA novel approach for DOA of coherent UWB signals received by smart antenna is presented. Time shift property of Fourier transform was used to develop a frequency domain model for the data that is similar to models used in narrowband DOAs. The frequency domain structured data of the array was formulated into a form of ML expression for estimating the DOA parameters of superimposed UWB signals. An iterative algorithm (IQML) for the minimization of the ML criterion is then presented.It is evident fromthe simulation results that smart antenna can accurately resolve the DOA of closely spaced UWB signals. When the closely spaced signals are shifted away from the broad side by 100, the smart antenna provides a 30 dB improvement in angle estimation error at high SNR values. It is also observed that when the angle separation of signals are wide enough, the broad side signal gives better accuracy in DOA estimates compared to far away signals from broad side. The results show that the technique succe