Medium PRF radar PRF selection using evolutionary algorithms

Evolutionary algorithms are applied to the optimization of pulse repetition frequency (PRF), for both eight-and nine PRFs, in medium PRF radar while considering the detailed effects of sidelobe clutter and many other technical factors. The algorithm presented also ensures that all the solutions produced are fully decodable and have no blind velocities. The evolutionary algorithm was able to identify near-optimum PRF sets for a realistic radar system with only a modest computational effort.     

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.     

Medium PRF set selection using evolutionary algorithms

This paper presents a new and novel method of selecting multiple pulse repetition frequency (PRF) sets for use in medium PRF pulsed-Doppler radars. Evolutionary algorithms are used to minimise the blind areas in the range/Doppler space. The evolutionary algorithm allows optimal solutions to be generated quickly, far faster than with exhaustive searches, and is fully automatic, unlike existing techniques. The evolved solutions compare very favorably against the results of both an exhaustive search and existing published PRF set selection methods. This evolutionary approach to generation of PRF sets is a major advance in medium PRF radar design.     

Medium PRF Performance Analysis

A discussion of various types of x-band airborne radars is presented together with their systematic development through the years to the present time. Starting with simple, low pulse-repetition frequency (PRF) radars for measuring radar-target range, airborne radar development proceeded with more sophisticated high PRF Doppler radars where radar-target range and range rate were measured simultaneously. The use of Doppler (frequency) in signal processing allowed the separation of moving from nonmoving targets (ground), enabling the detection of moving targets in the presence of ground clutter. More recent developments in waveform generation and selection has resulted in the development of medium PRF radars, whereby a greater degree of tactical flexibility in target detection is achieved by combining the desirable features of both low and high PRF radars. Part of the available literature gives an overview, together with a specific example of the design and performance of an airborne medium PRF radar. Here, however, the systematic evolution of these radars is emphasized and the necessary theoretical background is developed for their performance calculations. Modern day airborne radars may be equipped with all three modes of operation, low, medium, and high PRF, allowing the operator to utilize the mode best suited for the tactical encounter. Low PRF and high PRF radars have been described elsewhere and are given here primarily for the sake of completeness and for the necessary background for developing medium PRF radar equations. They are also needed for developing the reasons why medium PRF radars came into being.     

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。     

STAP with medium PRF mode for non-side-looking airborne radar

Space-time adaptive processing (STAP) has been widely discussed for airborne radar systems to improve the system performance of detecting targets. This is especially true for airborne early warning (AEW) radar, which should find long-range and small radar cross section (RCS) targets such as the stealth aircraft and missiles. However, in existing airborne radar literature, STAP is mainly considered for clutter and jamming rejection in side-looking airborne radar (SLAR) applications. There have been fewer discussions on airborne radar with non-side-ways looking array radar (non-SLAR). The STAP of non-SLAR such as forward looking array radar is also very important and can not be avoided for airborne radar to detect targets in all directions. The STAP of the non-SLAR is studied here. A scheme has been proposed, which is processed by the way of STAP combined with multiple staggered medium pulse repetition frequencies (PRFs). We further study the selection of PRFs in order to make the scheme more available for non-SLAR radar. We analyze two typical non-SLAR cases, i.e., inclined-sideways looking array and forward looking array. We examine this scheme by comparing the performances of three processing systems under the criteria of range-velocity blind zone minimization. Computer simulation results show the multiple-PRFs STAP scheme is feasible for non-SLAR and can be applied to phased-array AEW radar systems     

Properties of Staggered PRF Radar Spectral Components

Expressions for moving target indicator (MTI) improvement factor limitation due to pulse repetition frequency (PRF) staggering and loss of target detectability for various values of Doppler frequency in the passband are presented. It is also shown that the product of variance of stagger periods and clutter variance is an important parameter determining the performance of a staggered PRF MTI radar.     

中等PRF机载PD雷达频域恒虚警处理性能计算

 一、引言 在中等脉冲重复频率（PRF）工作时,MTI-FFT-CFAR是PD或MTD雷达信号处理器的一种典型结构。Lawrence和Moore对MTD雷达在地杂波和气象杂波背景中的检测性能的计算中,假设了邻近距离单元中的杂波样本是独立同分布的（iid）。而在MTI-FFT-频域单元平均CFAR处理器中,频域单元的杂波样本明显偏离iid假设。门     

Mitigating Range Ambiguity in High PRF Radar using Inter-Pulse Binary Coding

The paper proposes a way to increase the energy within a coherent processing interval (CPI) using more pulses instead of longer pulses. Long coded pulses result in masking targets at close range and poor Doppler tolerance. Increasing the number of pulses implies high pulse repetition frequency (PRF), which suffers from range ambiguity and target folding. These drawbacks of a high PRF can be mitigated by inter-pulse coding. The approach suggested here should be attractive for close and mid range applications of radar, ground penetrating radar, ultrasound imaging, and more.     

Probability of Pulse Coincidence in a Multiple Radar Environment

Elementary probability theory is used to develop three formulas for the probability of two or more pulses being coincident at an observer's aircraft position in a multiple radar environment. The first formula is for nonscanning tracking type radars with different pulsewidths (PWs) and pulse repetition frequencies (PRFs), the second is for generically identical nonscanning radars with similar PWs and PRFs, and the third is for scanning type radars such as air search radars with similar PWs and PRFs. The probability of coincidence is related to the mean-time-between-coincidences (MTBC) and to the average coincidence rate. Two sample problems are given.     

Clutter Spectra of Low PRF AMTI Pulse-Doppler Radar

Approximate expressions are derived for the video clutter spectra in the receiver of a low pulse repetition frequency (PRF), airborne moving target indicator (AMTI), pulse-Doppler radar for both step-scanning and continuous-scanning antennas. The receiver is assumed to process the received waveform with a clutter-tracking oscillator and a window function is employed to obtain short-term spectra. Except for the broadening effects of the window function, it is shown that the clutter spectrum can be simply related to the antenna voltage-gain pattern. It is further shown, in the scanning antenna case, that the combined spectral broadening due to platform motion and antenna scanning cannot be assumed to be the result of the convolution of the separate effects unless the antenna gain pattern has a Gaussian shape. The approximate clutter expressions are illustrated by examples and are shown to agree well with the results of computer calculations.     

On the Optimization of MTI Clutter Rejection

In this paper is formulated the problem of optimization of the improvement factor of a nonrecursive MTI by minimization of a quadratic form. The minimum normalized clutter output (a reciprocal of the average improvement factor) is the minimum eigenvalue of this quadratic form, and the corresponding eigenvector is the optimal weight to be used in this filter. By use of classic matrix theory, some properties of this MTI improvement factor are shown, namely, that it is bounded and is a monotonic function of the clutter spectrum variance. Also discussed is the limit of an MTI system having a large number of cancellers. Finally, the problem of a staggered-PRF MTI filter is examined, for which it is shown that its improvement factor is bounded by two equivalent constant-PRF MTI systems. One of these systems has a PRF equal to the lowest PRF of the staggered-PRF system, while the other has a PRF equal to the highest PRF of the staggered system.     

结合视线方向运动补偿的滑动聚束SAR子孔径成像算法

滑动聚束合成孔径雷达(SAR)是一种新兴的成像模式,既可以提高方位向分辨率又能够扩展成像范围。其数据处理时需要考虑两个关键问题:一是系统脉冲重复频率(PRF)不足,方位向信号发生混叠;二是合成孔径长度的增加使运动误差的影响更为突出,运动补偿(MOCO)精度要求提高。基于子孔径技术,提出了一种改进的高分辨率成像算法。划分子孔径克服了PRF不足的问题;子孔径数据处理采用结合视线(LOS)方向运动补偿的Omega-K算法,实现更高精度的运动补偿,提高了聚焦质量。最终的方位向分辨率达到0.1 m,具有实际工程应用价值。点目标仿真和实测数据处理验证了算法的有效性。     

Velocity estimation of fast moving targets using a single SAR sensor

A new methodology is presented to retrieve slant-range velocity estimates of moving targets inducing Doppler-shifts beyond the Nyquist limit determined by the pulse repetition frequency (PRF). The proposed approach exploits the linear dependence (not subject to PRF limitations) of the Doppler-shift with respect to the slant-range velocity, at each wavelength. Basically, we propose an algorithm to compute the skew of the two-dimensional spectral signature of a moving target. Distinctive features of this algorithm are its ability to cope with strong range migration and its efficiency from the computational point of view. By combining the developed scheme to retrieve the slant-range velocity with a methodology proposed earlier to estimate the velocity vector magnitude, the full velocity vector is unambiguously retrieved without increasing the mission PRF. The method gives effective results even when the returned echoes of the moving targets and the static ground overlap completely, provided that the moving targets signatures are digitally spotlighted and the signal-to-clutter ratio (SCR) is, roughly, greater than 14 dB. The effectiveness of the method is illustrated with simulated and real data. As an example, slant-range velocities of moving objects with velocities between 6 and 12 times the Nyquist velocity are estimated with accuracy better than 3%.     

Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

Reduced-rank STAP for high PRF radar

Due to the range ambiguity of high pulse-repetition frequency (HPRF) radars, echoes from far-range fold over near-range returns. This effect may cause low Doppler targets to compete with near-range strong clutter. Another consequence of the range ambiguity is that the sample support for estimating the array covariance matrix is reduced, leading to degraded performance. It is shown that space-time adaptive processing (STAP) techniques are required to reject the clutter in HPRF radar. Four STAP methods are studied in the context of the HPRF radar problem: low rank approximation sample matrix inversion (SMI), diagonally loaded SMI, eigencanceler, and element-space post-Doppler. These three methods are evaluated in typical HPRF radar scenarios and for various training conditions, including when the target is present in the training data     

Constrained Improvement MTI Radar Processors

A new class of staggered PRF MTI radar processors is developed in this paper. These processors are constrained to achieve a specified value of MTI improvement and, subject to this constraint, minimize variations in processor response as a function of target Doppler frequency. The selection of both filter weights and PRF stagger sequences is discussed and a number of representative designs are presented.     

Synthetic Aperture Processing with Limited Storage and Presumming

The number of transmitted pulses associated with the Doppler histories of a side-looking radar may greatly exceed the desired azimuth compression ratio of the system. This discrepancy is taxing if the storage required for the azimuth processing is provided by cores, magnetic drums, and the like. Thus, as a practical matter, one considers presumming of the data prior to correlation in an attempt to achieve the desired performance with a minimum amount of digital storage. In this paper, the optimum (in terms of resolution) presummer is derived, along with the optimum apportionment of the available storage capacity between the presumming and correlation operations. Under the condition (or generally pessimistic approximation) that the illumination pattern of the antenna uniformly illuminates a Doppler bandwidth equal to the PRF of the radar, the optimum presumming coefficients are the first Np Fourier coefficients of a function which is one of the Doppler bandwidth to be correlated and zero on the remainder of the PRF bandwidth, where Np is the number of transmitted radar pulses over which presumming is provided. Increasing Np reduces the degradation due to presumming, but may leave inadequate storage for correlation. Hence, we optimize the apportionment between the two operations and present the obtainable resolution as a function of total storage and the number of transmitted pulses in the received Doppler history.     

The ‘MOB’ project: towards methods to support e-design across Europe

The development of the MDO approach presented in this paper is based on extensive programmes of research undertaken in the aerospace sector. Some of this work has resulted from in-house development of systems to support the creation of actual production aircraft of which references (1) and (2) are typical examples. Other studies have focused on the development of methods to support the application of MDO using a variety of optimisation approaches mainly in the conceptual or early preliminary design phases (2–6) and in the opportunities provided by large scale computing (7). The most detailed application for a realistic aircraft component was undertaken in an earlier EU funded research programme (BE95-2056) reported in references (8,9) with potential developments of this work explored in (10). However, the concept of creating a system able to fully cover the total design process and to include the concept that the teams involved are distributed has not been previously considered and is the focus for the MOB project.