Clutter Performance of Coherent Pulse Trains for Targets with Range Acceleration

The clutter performance of coherent pulse trains is examined when the duration of the pulse train is increased to values for which range acceleration effects must be taken into account. The problem of target detection against a clutter background with differential Doppler is studied in terms of the range acceleration effects on the conventional Doppler response. Specifically considered are the consequences on the sidelobe level and width of the main Doppler lobe. The analysis shows that the sidelobe level remains essentially unchanged when the range acceleration mismatch becomes significant. However, the main Doppler response broadens in proportion to the magnitude of the acceleration mismatch. Thus, an increase of the signal duration for better Doppler resolution is useful only until acceleration effects spread the Doppler spectrum of the clutter and eliminate the differential Doppler between targets and clutter.     

Clutter Suppression by Complex Weighting of Coherent Pulse Trains

Uniform coherent pulse trains offer a practical solution to the problem of designing a radar signal possessing both high range and range-rate resolution. The Doppler sensitivity provides some rejection of off-Doppler (clutter) returns in the matched filter receiver. This paper considers the use of a processor in which members of the received pulse train are selectively weighted in amplitude and phase to improve clutter suppression. The techniques described are particularly suitable for rejecting interference entering the processor through ambiguous responses (range sidelobes) of the signal. The complex weights which are derived are optimum in the sense that they produce the maximum clutter suppression for a given detection efficiency. In determining these weights, it is assumed that the distribution of clutter in range and range rate relative to targets of interest is known. Thus, clutter suppression is achieved by reducing the sidelobe levels in specified regions of the receiver response. These techniques are directly applicable to array antennas; the analogous antenna problem would be to reduce sidelobe levels in a particular sector while preserving gain. Complex weighting is most successful when the clutter is limited in both range and velocity.     

Group-Complementary Array Coding for Radar Clutter Rejection

A radar waveform design technique which utilizes Lagrange's method of multipliers to control temporal sidelobes and to reduce Doppler sidelobes is described. This classical method of constrained optimization is applied to the problem of synthesizing a radar wave-form where mismatch loss is the objective function to be minimized. The associated constraints are taken from expressions for the composite temporal sidelobes of the cross-correlation response and the peak correlation response where sets of code words are used to modulate a series of radar pulses. The resulting code sets and receiver reference sets are called group-complementary and produce a trench parallel to or on the range axis of the cross-ambiguity surface.     

Clutter Suppression Properties of Weighted Pulse Trains

A common but troublesome requirement on radar sensors is the detection of a target in the interference from undesired scatterers, or clutter. Systems with coherent processing of pulse trains are uniquely suited for the purpose because, with pulse trains, it is possible to concentrate the receiver output for particular values of Doppler and thus suppress the clutter by Doppler filtering. This paper discusses to what degree the effectiveness of the method can be enhanced by tapering, or weighting, of the pulse amplitudes. The general results are illustrated by computer-plotted response functions for weighted pulse trains. The clutter suppression efficiency of weighting is calculated both for unilateral weighting in the receiver and for bilateral weighting in both receiver and transmitter. The significance of additional phase weighting is discussed and the results for pure amplitude weighting are compared with publishedwork on phase and amplitude weighting.     

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.     

Doppler Properties of Polyphase Coded Pulse Compression Waveforms

Doppler properties of the Frank polyphase code and the recently derived P1, P2, P3, and P4 polyphase codes are investigated and compared. An approximate 4 dB cyclic variation of the peak compressed signal is shown to occur as the Doppler frequency increases. The troughs in the peak-signal response occur whenever the total phase shift across the uncompressed pulse, due to Doppler, is an odd multiple of ? radians. It is shown that while the P3 and P4 codes have larger zero-Doppler peak sidelobes than the other codes, the P3 and P4 codes degrade less as the Doppler frequency increases. Also, the effects of amplitude weighting and receiver bandlimiting for both zero and nonzero Doppler are investigated.     

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.     

Rotating Blades Radio Interference in a Helicopter-Borne CW Doppler Radar

Radio interference generated in a helicopter-borne continuous wave (CW) Doppler radar system due to the rotating blades is analyzed. This problem has been previously treated for the case of pulse Doppler radar systems with very narrow (near zero) beamwidth. In this case the strong interference component returning directly from the blades (with no ground reflection) need not be considered as it reaches the receiver when it is still blinded. In the case of a CW Doppler radar, however, this interference component must be included. Numerical calculations show that the total blade interference power level, dominated by the direct component, is higher than that of the direct ground clutter in the radar clutter region. It decreases approximately as (f - fo)-4 in the radar clear region. It stays, however, well above the thermal noise level which might cause false alarm and degrade the radar performance.     

A Generalized Clutter Computation Procedure for Airborne Pulse Doppler Radars

A general procedure for analyzing ground clutter effects in airborne pulse Doppler radars is described. The quantity computed is the expected clutter power at the output of any specified range gate/ Doppler filter processing cell. The procedure has been computerized and is quite general with respect to antenna gain pattern, clutter cross section variation, PRF, pulse and range gate shapes, and the various receiver processing functions. It is applicable only to distributed ground clutter and linear processing, and excludes the dynamic effects of continuous antenna scanning. To exemplify the use of the procedure, two studies conducted for a postulated high PRF radar are described, and the results are presented.     

GEO星弹双基SAR多普勒分辨率特性分析

通过对地球同步轨道（GEO）卫星运动特点的分析，阐明其对多普勒分辨率的影响。传统的双基合成孔径雷达（SAR）多普勒分辨率表达式由于不考虑雷达平台加速度矢量带来的影响，并不适用于GEO星弹双基SAR系统。根据收发平台的双曲线轨迹对目标的回波多普勒特性影响，首先利用梯度方法推导了GEO星弹双基SAR系统的多普勒分辨率表达式；随后详细地分析了GEO卫星与导弹的空间几何关系及多普勒参数，特别是加速度矢量对多普勒分辨率的影响。仿真结果验证了所推导多普勒分辨率表达式的有效性，其有助于双基SAR理论系统完整性的提高，为后续系统设计及应用实践提供理论支撑。     

Resolution Performance of Pulse Trains with Large Time-Bandwidth Products

The coherent pulse train has good clutter suppression performance because the energy in its matched-filter response is essentially concentrated within sharp ambiguous spikes. However, this is so only when the Doppler distortions are neglected, so that the Doppler effect is taken as a simple translation of the carrier frequency. This paper analyzes the consequences of Doppler distortions on the resolution performance of pulse trains. It is found that Doppler distortions widen the Doppler ambiguities of the pulse train response, with the widening factor proportional to the order of the Doppler ambiguity. This reduces the interval between Doppler ambiguities, and hence the Doppler width of a clutter space that can be accommodated without severe clutter interference. For an operation in a Doppler-ambiguous mode, it also degrades nominal Doppler resolution performance. A detailed analysis of the effects is presented, and numerical results on the widening of the Doppler ambiguities are obtained.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Comparison between monostatic and bistatic antenna configurationsfor STAP

The unique characteristics of bistatic radar operation on the performance of airborne/spaceborne moving target indicator (MTI) radars that use space-time adaptive processing (STAP) are discussed. It has been shown that monostatic STAP radar has the following properties. 1) For a horizontal flight path and a planar Earth the curves of constant clutter Doppler (isodops) are hyperbolas. 2) For a sidelooking antenna geometry the clutter Doppler is range independent. 3) Clutter trajectories in the cosφ-F plane (F=normalized Doppler) are in general ellipses (or straight lines for a sidelooking array). We demonstrate that these well-known properties are distorted by the displacement between transmitter and receiver in a bistatic configuration. It is shown that even for the sidelooking array geometry the clutter Doppler is range-dependent which requires adaptation of the STAP processor for each individual range gate. Conclusions for the design of STAP processors are drawn     

An experiment with an S-band radar using pulse compression andrange sidelobe suppression for meteorological measurements

A major technology barrier to the application of pulse compression for the meteorological functions required by a next generation ATC radar is range/time sidelobes which mask and corrupt observations of weak phenomena occurring near areas of strong extended meteorological scatterers. Techniques for suppressing range sidelobes are well known but without prior knowledge of the scattering medium's velocity distribution their performance degrades rapidly in the presence of Doppler. Recent investigations have presented a “doppler tolerant” range sidelobe suppression technique. The thrust of the work described herein is the extension of previous simulations to actual transmitted dispersed/coded waveforms using the S-band surveillance radar located at Rome Laboratory Surveillance Facility. The objectives of the experiment are: 1) to extend the verification of the simulation of the Doppler tolerant technique; and 2) to demonstrate that the radar transmitter, waveform generator, and receiver imperfections do not significantly degrade resolution, performance or reliability of meteorological spectral moment estimates     

Design of MTI Radar on the Basis of Detection Probability

A single (quadrature) channel moving target indicator (MTI) radar system employing a tapped delay line filter is analyzed. The point of view taken is that of optimal clutter rejection in conjunction with subsequent receiver decision operations. The random nature of the spread of target Doppler shifts is taken into account. Based on the above, a procedure is presented by means of which the detection probability can be numerically evaluated for an optimized filter frequency response.     

Frequency-Agile Radar Signal Processing

Modern radars may incorporate pulse-to-pulse carrier frequency modulation to increase probability of detection, to reduce Vulnerability to jamming, and to reduce probability of interception. However, if coherent processing is used for clutter rejection, the frequency of N consecutive pulses must be held constant for N-pulse clutter cancellation or Doppler filtering. If M pulses are transmitted during the time the antenna illuminates a target, there are M/N coherently integrated echoes available for noncoherent integration in the computer or the operator's display to further improve the signal-to-noise ratio (SNR). In this paper, analytical and simulation methods are employed to determine the balance between coherent and noncoherent integration that yields the greatest SNR improvement. Attention is focused upon a model using peak selection of fast Fourier transform (FFT) Doppler channels and is compared to a reference model involving only a single Doppler channel. Curves of detectable SNR as a function of M and N are presented for both models.     

机载相控阵雷达中抑制杂波的线性预测法

从一个多通道自回归过程拟合杂波信号的概念出发 ,提出了用线性预测法实现机载相控阵雷达的时空二维自适应信号处理。研究表明 ,杂波过程可以用一个低阶的多通道自回归过程很好地拟合 ,从而使用一个低阶的线性预测处理器以较低的代价实现准最优的处理。同时 ,这种低阶的线性预测处理器还具备冗余的自由度以对付除杂波外的其他有色噪声和干扰     

Optimum Processing of Unequally Spaced Radar Pulse Trains for Clutter Rejection

A train of radar pulses from one resolution cell can be processed coherently to reject echoes from external clutter and detect targets moving radially with respect to the clutter. Optimum methods of signal processing are defined for systems in which the interpulse spacings are multiply staggered to avoid target blind speeds. Likelihood ratio tests are developed for systems in which the target Doppler frequency is known a priori and for systems employing a bank of filters to cover the target Doppler band. To implement such tests, the N pulses in the train are added with complex weights and the amplitude of the sum compared with a detection threshold. The set of weights which maximizes the average signal-to-clutter ratio is also computed for a single-filter system with unknown target Doppler frequency. When the clutter autocorrelation function is exponential, the clutter covariance matrix can be inverted analytically. This latter result is useful for comparing different interpulse-spacing codes for a particular system application.     

Low sidelobe radar waveforms derived from orthogonal matrices

Novel waveforms are described that have low sidelobes when individual or multiple waveforms are approximately processed. They are related to orthogonal matrices that may be associated with complementary sequences and also with periodic waveforms having autocorrelation functions with constant zero-amplitude sidelobes. Also described are sets of sequences whose cross-correlation functions sum to zero everywhere. A potential application is the elimination of ambiguous range stationary clutter     

An effect of range-heterogeneous clutter on adaptive Dopplerfilters

The practical implementation of adaptive Doppler filters requires estimates of clutter parameters to determine the adaptive weights. A method of deriving the estimate via the sample matrix inversion (SMI) algorithm using multiple data snapshots from adjacent range cells is presented. For homogeneous clutter environments, the results of this technique asymptotically approach the optimum (a priori known covariance matrix) as the number of snapshots approaches infinity; this asymptotic behavior does not occur for heterogeneous clutter environments. An equation for the decrease in improvement factor is derived. To promote understanding, the simplified special case of narrowband clutter is considered in detail. In almost all cases, the loss is small