Ambiguity Functions for Quadratic Phase-Coded Pulse Trains

The matched filter ambiguity function is presented for a burst waveform composed of repeated subbursts, each one of which consists of N pulses in which the phase is varied quadratically from pulse to pulse. The resulting ambiguity function exhibits small residual ambiguities along the delay axis separated by the reciprocal of the pulse repetition frequency (PRF). A cross-ambiguity function is derived which reduces these ambiguities to zero amplitude. A third cross-ambiguity function is presented for a receiver matched to a generalized Hamming weighted repeated quadratic burst. The location in the delay/Doppler plane of the waveform ambiguities for these waveforms is compared with that of an uncoded pulse burst.     

Variable Format Radar Receiver Using a SAW Convolver

A technique for receiving radar pulse trains is presented [which can be of a variable format in the sense that they vary from pulse to pulse]. The heart of the receiver is a sufrace ascoustic wave (SAW) convolver. In addition to prsenting experimental results for variable format waveform reception, it is shown that the convolver can easily generate ambiguity functions for virtually any waveform, and specific results for signals such as Barker codes and linear FM (chirp) waveforms are presented.     

一种步进频率信号认知雷达波形优化设计方法

认知雷达常用于完成探测、跟踪、成像及识别等多重任务,为提高其综合性能,需兼顾多方面因素研究其波形优化设计问题。基于此,提出一种基于压缩感知（CS）RIPless准则的步进频率信号认知雷达波形优化设计方法。首先,建立了目标回波信号稀疏模型,分析了其与发射信号模糊函数之间的关系。其次,根据模型中观测矩阵的构造,基于RIPless准则,将波形设计问题转化为概率分布的互相干参数及其协方差矩阵的条件数的优化问题,从而通过自适应寻优算法,获得优化的步进频率信号脉冲重复时间间隔序列和子脉冲频率序列。相较于传统方法,所提方法在信号发射与接收之间形成了信息实时反馈和信号优化重构的闭环,在高概率准确重构目标径向一维距离像的同时,也实现了发射信号模糊函数的优化。最后,仿真计算验证了所提方法的有效性。     

Range, radial velocity, and acceleration MLE using radar LFM pulsetrain

An efficient implementation of the maximum likelihood estimator (MLE) is presented for the estimation of target range, radial velocity, and acceleration when the radar waveform consists of a wideband linear frequency modulated (LFM) pulse train. Analytic properties of the associated wideband ambiguity function are derived; in particular the ambiguity function, with acceleration set to zero, is derived in closed form. Convexity and symmetry properties of the ambiguity function over range, velocity, and acceleration are presented; these are useful for determining region and speed of convergence for recursive algorithms used to compute the MLE. In addition, the Cramer-Rao bound (CRB) is computed in closed form which shows that the velocity bound is decoupled from the corresponding bounds in range and acceleration. A fast MLE is then proposed which uses the Hough transform (HT) to initialize the MLE algorithm. Monte Carlo simulations show that the MLE attains the CRB for low to moderate signal-to-noise depending on the a priori estimates of range, velocity, and acceleration     

Ambiguity Removal When Using Burst Waveforms. Part II: Nonlinear Processing

An effective technique for removing range ambiguities (detections at ranges other than the true range of the object) arising when using a burst waveform is to transmit two bursts with different pulse repetition frequencies nearly simultaneously and then to process their outputs nonlinearly. This correspondence introduces two nonlinear processors which combine coincidence detection with either noncoherent multiplication or integration. It is shown that the combined false alarm and ambiguity removal performance of these nonlinear processors is superior to the performance of coincidence detection, noncoherent multiplication, or noncoherent integration when used separately.     

Doppler ambiguity resolution using multiple PRF

An algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF) is presented. It relies on the choice of particular values for the PRFs. The folded frequency of the target signal is obtained by averaging the folded frequency estimates for each PRF, and a quasi maximum likelihood criterion is maximized for ambiguity order estimation. The fast implementation of this nonambiguous estimation procedure is based on the fast Fourier transform (FFT), The proposed waveform allows full exploitation of any (even) number of PRFs, which appears to be important for estimation improvement. The effects of the waveform parameters and the folded frequency estimation variance on the performance of the ambiguity order estimation procedure are evaluated theoretically and through computer simulations. Mean square error (MSE) curves are given to assess the Doppler frequency estimation accuracy. Finally, the new method is compared with a classical technique and the implementation of the algorithm in a clutter environment is addressed.     

脉冲超宽带信号测量性能分析

超宽带技术是一项新兴的无线通信技术,具有极其广阔的发展前景,但目前仅用于室内短距离通信,少见用于航天测控系统。为了将超宽带技术应用于测控系统中,以模糊函数为工具,对脉冲超宽带信号的测量性能进行分析。首先推导矩形脉冲串信号和载波调制矩形脉冲串信号的模糊函数,并对其模糊特性进行仿真分析。在此基础上,主要针对用于测控系统的伪码调制脉冲超宽带信号,利用其模糊函数分析其测距测速性能。结果表明:该超宽带信号具有良好的测距测速性能,其最大无模糊距离为1个伪码周期,最大无模糊多普勒频率为脉冲重复频率的倒数;单脉冲宽度越窄,其测距性能越好而测速性能越差。     

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.     

相控阵主动雷达导引头波形策略

针对高脉冲重复频率脉冲多普勒(HPRF-PD)体制的相控阵主动雷达导引头中存在的距离遮挡问题,设计了一种新的波形选择策略。首先,利用提出的脉冲重复频率(PRF)波形选择策略,离线计算得到距离对应PRF的波形查找表。然后,通过叉积自动频率控制环路滤波(CPAFCLF)算法预估下个相参处理间隔(CPI)导引头与目标间的径向相对速度,并联合提出的基于Sage-Husa带有速度预测的自适应"当前"统计模型(SH-ACSMVP)算法得到的距离跟踪值,获得下个CPI的距离预测值。在跟踪机动目标场景中,相比于"当前"统计(CS)模型跟踪算法及基于"当前"统计模型的自适应无迹卡尔曼滤波(CAUKF)算法,本文算法得到的距离预测误差更小,误差收敛速度更快。根据此距离预测值从波形查找表中选择波形发射,作为下个CPI的发射波形,实现后续跟踪阶段的抗距离遮挡,提高目标跟踪性能。仿真结果表明了本文所设计波形选择策略的正确性及有效性。     

弹载合成孔径雷达自适应重频分析与设计

弹载合成孔径雷达(Synthetic Aperture Radar,SAR)的目标距离、视线角由于高速逼近目标而快速变化,这导致传统的固定脉冲重复频率(Pulse Repetition Frequency,PRF)(简称重频)波形难以兼顾弹载SAR雷达在成像各方面的约束条件,故需要根据当前弹体运动和弹目关系变化情况实时计算重频。详细分析了影响重频选择的各项因素,包括避免距离模糊、方位模糊、高度杂波、发射遮挡影响及SAR成像分辨率、系统相参性要求等影响因素,并设计了自适应重频计算的工作流程。某SAR雷达系统实验表明,该设计能够在实际飞行弹道条件下根据实际弹目关系自适应调整脉冲重复频率,从而更好地实现SAR雷达系统的工作性能,有效解决了固定重频波形不能适应弹载SAR工作条件的难题。     

Some High-Velocity Clutter Effects in Matched and Mismatched Receivers

A generalized ambiguity function including the effects of Doppler dispersion is defined as the time cross correlation of the complex envelopes of two signals, both derived from the same basic waveform but with different delays and Doppler effects. The Doppler effects include the frequency shift and expansion or contraction of the modulation time scale. This expansion or contraction is the Doppler dispersion. While the general ambiguity function cannot be expressed directly in terms of the Woodward or undispersed ambiguity function, its squared magnitude can be expressed in terms of the Woodward ambiguity function. The relation is not simple, being an integral form. Nevertheless, since the Woodward ambiguity function is known for many signals, the relation may simplify the determination of the squared magnitude of the general ambiguity function. We consider the clutter output of a matched filter or correlation receiver where the receiver is matched to a waveform having a specific delay and specific time compression. The variance of the clutter output is the two-dimensional convolution of the clutter ``scattering function' with the squared magnitude of the general ambiguity function. This is a generalization of an earlier result which is formally the same but using the Woodward ambiguity function. This last result is generalized for a mismatched receiver. In such a case, the variance of the clutter output is the double convolution of the clutter scattering function with the cross ambiguity function of the transmitted waveform, modified by the average velocity of the clutter, and the receiver reference waveform.     

Radar Waveform Synthesis by Mean Square Optimization Techniques

The synthesis of the phase-modulated waveform whose ambiguity function is the optimum estimate of some desired ambiguity function is accomplished by expanding the phase modulation in an orthogonal series. The ambiguity function x (?, ?d)|2 and the value of an arbitrary cost function defined on the (?, ?d) plane are then expressed in terms of the coefficients of the orthogonal series. The optimum waveform can then be determined by solving the variational equations for the coefficients. Numerical examples are presented for the case where it is desired to synthesize a desired ambiguity function x(?, ?d) for some rectangular region of the (?, ?d) plane.     

Radar/Sonar Signal Design for Bounded Doppler Shifts

In many detection and estimation problems, Doppler frequency shifts are bounded. For clutter or multipath that is uniformly distributed in range and symmetrically distributed in Doppler shift relative to the signal, detectability of a point target or a communication signal is improved by minimizing the weighted volume of the magnitude-squared autoambiguity function. When clutter Doppler shifts are bounded, this volume is in a strip containing the range axis on the range-Doppler plane. For scattering function estimation, e.g., for weather radar, Doppler flow meters, and distributed target classifiers, it is again relevant to minimize ambiguity volume in a strip. Strip volume is minimized by using a pulse train, but such a signal has unacceptably large range sidelobes for most applications. Other waveforms that have relatively small sidelobe level within a strip on the range-Doppler plane, as well as small ambiguity volume in the strip, are obtained. The waveforms are composed of pulse pairs that are phase modulated with Golay complementary codes.     

高空低气压下电晕放电电磁脉冲辐射特性模拟实验

为研究高空低气压下飞行器表面电晕放电电磁脉冲辐射特性,以尖端导体电晕放电为研究对象,进行了低气压下电晕放电电磁脉冲辐射特性模拟实验,给出了辐射电场幅值与气压的关系表达式,并基于气体放电和电磁场理论总结了电晕放电电磁脉冲辐射特性随电压极性、气压以及测试距离的变化规律。结果表明:电晕放电电磁脉冲辐射电场时域波形呈衰减振荡形式,持续时间约为600 ns,首脉冲方向随电压极性的不同而不同,且辐射电场分量主要集中在与放电针相同的极化方向;辐射电场频谱主要分布在500 MHz以内,在35 MHz和170 MHz处出现稳定的波峰;在气压为4~30 kPa范围内,随着气压的降低,放电电磁脉冲辐射电场增强;随着测试距离的增加,电晕放电电磁脉冲辐射电场逐渐衰减。该研究结论可为低气压下飞行器电晕放电电磁脉冲辐射特性研究提供有益参考。     

Ultra-wideband impulse radar-an overview of the principles

Over the past decade, extensive research work has been carried out to develop the ultra-wideband (UWB) technology for radar applications, and to resolve the practical challenges in implementing an efficient UWB radar system. In this paper, we present an overview of the basic principles of UWB impulse radar. The focus is on the principles of UWB signal generation, impulse radiation, waveform design, pulse compression, range-velocity resolution (ambiguity function), array beamforming, and radar-target signature     

Synthesis of Ambiguity Functions for Prescribed Responses

The synthesis of radar ambiguity functions is approached using burst-pulse time-frequency waveform coding. Noting that the parameters that define the central response of the ambiguity function for these code classes also define the waveform code, a statistical decision procedure based upon the central response is employed to obtain Bayes-type codes. The selection of the code parameters is subject to restrictions imposed by the noncentral response of the ambiguity function. Three classes of random time-frequency codes are treated: 1) uniform amplitude, uniform pulsewidth matched codes; 2) uniform amplitude, nonuniform pulsewidth matched codes; and 3) uniform amplitude, uniform pulsewidth with receiver amplitude mismatch.     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.     

Dwelltime Minimization for Radar Target Detection in the Clear

Consider the design of a minimum dwelltime set of coherent, range-unambiguous pulse bursts that will provide a specified target detection performance in a clutter-free ("clear") range interval [Rmin,Rmax]. Practical procedures are presented here for finding these optimal waveform sets versus Rmax/Rmin, subject to a peak transmit power constraint. It is always possible to design a multiple-PRF clear mode that achieves the same effective use of energy as a single-PRF waveform with a 33 percent duty ratio. Slightly higher effective duty ratios can be achieved if the radar is capable of transmitting and processing two interleaved pulse bursts at the same PRF.     

Nullifying ACF grating lobes in stepped-frequency train of LFM pulses

An effective way to increase the bandwidth of a coherent pulse-train is to add a frequency step /spl Delta/f between consecutive pulses. A large /spl Delta/f implies a large total bandwidth, hence improved range resolution. However, when the product of the frequency step times the pulse-duration t/sub p/, is larger than one (t/sub p/ /spl Delta/f > 1), the autocorrelation function (ACF) of the stepped-frequency pulse-train suffers from ambiguous peaks, known as "grating lobes." It is well known that replacing the fixed-frequency pulses with linear FM (LFM) pulses of bandwidth B can reduce those grating lobes. We present a simple analytic expression for the ambiguity function (AF) and ACF of such a signal and derive from it very simple relationships between /spl Delta/f, B, and t/sub p/ that will place s exactly where the grating lobes are located, and thus remove them completely.     

Sparse frequency transmit-and-receive waveform design

A computationally efficient algorithm derives complex digital transmit and receive ultra-wideband radar and communication waveforms with excellent arbitrary frequency band suppression and range sidelobe minimization. The transmit waveform minimizes a scalar function penalizing weighted spectral energy in arbitrary frequency bands. Near constant power results from another penalty function for deviations from constant power, or constant power is enforced by a phase-only formulation. Next, a least squares solution for the receive waveform minimizes a weighted sum of suppressed band spectral energy and range sidelobes (for pulse and continuous wave operation), with a mainlobe response constraint. Both waveforms are calculated by iterative algorithms whose updates require only linear order in memory and computation, permitting quick calculation of long pulses with thousands of samples.