Effect of Radar Amplitude and Phase Weighting Errors on Clutter Rejection by Burst Waveforms

This correspondence derives simple expressions for the ambiguity function X and the Q function of uniformly spaced burst waveforms that are subject to independent random errors in the transmitter and receiver pulse phase and amplitude weightings. The expressions are similar to those in [1], but have been put in more simplified form, and are valid for more general sources of error.     

Design of Zigzag FM Signals

Since no practical method is available for synthesizing radar waveforms, a sizable effort has been directed into studies of the matched-filter response, or ambiguity function, of many waveforms. In this paper, we investigate the class of FM signals whose instantaneous frequency varies in a zigzag pattern. The waveforms thus consist of linear FM segments and are relatively easy to generate and process. The paper discusses the relation between the characteristics of the waveform and the features of the associated ambiguity function. The effects studied include those of signal repetition, changes in the FM slope, phase-shift and frequency-shift coding, and staggering of frequency step and segment duration. Ambiguity functions of interesting waveforms illustrate the general results. These ambiguity functions are computer-plotted projections of the three-dimensional surface above the delay-Doppler plane.     

Fourier Transform and Ambiguity Function of Piecewise Polynomial Functions

A general systematic procedure is described for computing the Fourier transform and the ambiguity function of waveforms that are piecewise polynomial. The procedure can be implemented by hand or programmed for execution by a digital computer. The main advantage of the technique is that integration is replaced by a finite summation. Examples include the computation of characteristic function, moments, and the ambiguity function of an amplitude modulated linear FM signal.     

Self-Clutter Cancellation and Ambiguity Properties of Subcomplementary Sequences

In radar signal design it is well known that a fixed volume under the ambiguity surface representing signal energy can only be shifted but not eliminated in the delay-Doppler plane because of the constraint imposed by Woodward's total volume invariance. Rihaczek has shown that periodic signal repetition, though appealing to increased energy, increases the time-bandwidth product at the expense of introducing pronounced ambiguities in the delay-Doppler plane, and thus self-clutter is generated when signals are repeated in the time domain to increase energy. The undesirable self-clutter has a masking effect on targets in different resolution cells thereby limiting performance. An analysis is presented to show that a class of waveforms described in an earlier paper as the subcomplementary set of sequences which are basically repetitive and Hadamard coded, exhibit the property of cancelling self-clutter completely in the delay-Doppler plane if their ambiguity functions are combined. By this technique it is possible to repeat contiguously a basic waveform N times in a prescribed manner to increase signal energy and to cancel totally the resulting self-clutter by combining the ambiguity functions of N different repetitive waveforms which are Hadamard coded. A convenient matrix method to combine the ambiguity functions of subcomplementary sequences, which is an extension of known methods to derive the ambiguity function of repetitive waveforms, is presented. Radar implementation considerations and comparison of performance with various forms of linear frequency modulation (FM) are also discussed.     

Small Aperture Angle Measurement for Active Echo Location Systems

The problem of bearing estimation for active systems is examined from the point of view of the generalized wideband ambiguity function (GAF). The maximum likelihood (ML) estimator is derived and its local and global properties are discussed. A structure is proposed which searches the three-dimensional ambiguity surface in two stages first, in range-Doppler, and then, in bearing with the goal of reducing search complexity when utilizing highly resolvent waveforms. Comparisons are made between the ML estimators and structures utilizing phase information which generate closed form estimators. The beneficial results of full bandwidth utilization are discussed in terms of both local and global properties of the GAF.     

The hit array: an analysis formalism for multiple access frequencyhop coding

A formalism is presented for the analysis of general frequency hop waveforms, such as those suitable for use in coherent active radar and sonar echolocation systems as well as multiple-access spread-spectrum communications. This formalism is based on the concept of coincidence, or `hit', between two frequency hopping patterns. The collection of all possible hits, together with their locations, is recorded in time-frequency space, which produces the high array associated with the two patterns considered. If the code length is sufficiently small with respect to the time-bandwidth product chosen, the hit array can be viewed as a digital representation of the corresponding ambiguity function. Salient properties of the hit array formalism are derived, including simple relationships between hit arrays resulting from basic symmetry-preserving transformations. These properties make it possible to predict the performance of a given set of frequency hop waveforms directly from the associated set of frequency hopping patterns     

Pseudorandom Frequency Modulation in Range-Doppler Radar

In many radar systems, efficient use of transmitter power requires the transmission of a constant-amplitude signal for a substantial fraction of time; for a monotonic transmission, however, the range resolution is restricted by the length of the transmitted pulse. Linear frequency modulation removes this constraint for targets with negligible, or known, radial velocities; it is not suitable, however, for simultaneous observations of range and radial velocity (Doppler shift). This paper describes a class of waveforms suitable for simultaneous measurement of range and Doppler shift. These waveforms are characterized by a uniform distribution in frequency and by pseudorandom frequency changes. Uniform frequency distribution is attained by a uniform spacing of frequencies with each frequency present for an identical length of time. Frequency changes are effected by sequencing the frequencies with a pseudorandom number generator. Ambiguity functions are computed for pseudorandom frequencymodulated waveforms designed for ionospheric backscatter studies. By suitable choice of parameters, the ambiguity function becomes a narrow central peak surrounded by a plateau whose height varies randomly between zero and approximately twice its average. Waveform generation by means of a digital frequency synthesizer and data reconstruction considerations are described.     

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.     

Constrained bandwidth waveforms with minimal dilation sensitivity

Bandpass waveforms which have envelopes which are insensitive to this velocity-induced time dilation can be efficiently processed by narrowband receivers in which envelope correlation is fixed and Doppler tested using fast Fourier transform (FFT) processing. The peak level of the waveform ambiguity function (AF) can be used to gauge the distortion of the waveform induced by dilation. The degree of AF attenuation is shown to be proportional to the dilation parameter or velocity, waveform traveling wave (TW) product, and a sensitivity parameter which depends on the envelope function utilized. Classes of symmetric, constrained bandwidth, phase modulated envelope functions which are minimally dilation sensitive (Doppler tolerant) are derived. When the resulting waveforms are used with a simple correlation receiver structure and the echo data is derived from slowly fluctuating point scattering in white Gaussian noise, the receiver becomes an uncoupled joint estimator of delay and dilation (Doppler). In the case of the bandpass waveforms, only odd symmetry of the phase modulation (PM) yields an uncoupled estimator     

Optimum Signals for Radar

The research reported herein deals with the general problem of the selection of radar waveforms. The investigation is specifically concerned with the synthesis of radar signals which are optimum in the sense that they are characterized by ambiguity surfaces minimized over certain predetermined regions of the ambiguity plane. The weighted ambiguity surface is utilized as the weighted error criterion. This error criterion is mathematically tractable and pertinent to radar system performance but is not unduly restrictive as some orientation parameters are left unspecified for subsequent cost or penalty function analysis. The signal optimization is approached by variational techniques augmented by equality and inequality constraints, for example, limiting the amount of bandwidth or frequency modulation to be less than some system requirement. Several examples are presented demonstrating the optimization techniques and providing a minimum error for the stated problem. It is shown that for any given type of amplitude modulation of the radar signal, the variance or dispersion of the ambiguity surface is not decreased for any type of phase modulation added. The optimum signal for an elliptical weighting function is derived for several cases. The minimum error is shown to depend upon the constraints and the unspecified orientation parameters and, for one case, on the second moment of the signal.     

A Logarithmic Frequency Allocation Algorithm for Wideband Discrete Frequency Pulse Trains

It is shown that signal waveforms utilizing discrete frequency modulation (DFM) which are generated using a narrowband or frequency shift algorithm have ambiguity sidelobe distortion which is caused by the approximation of time compression by frequency shift. A logarithmic frequency allocation algorithm is presented which couches the signal design problem in terms of band and step ratios, rather than in terms of bandwidth and frequency steps, and is consistent with the wideband formulation of the ambiguity function. The algorithm makes use of the same basic code generating sequence used for narrowband frequency allocation, but the resulting signal will have invariant ambiguity sidelobe positions for any receiver realization in the delay-time compression 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.     

Detection of polyphase pulse compression waveforms using the radon-ambiguity transform

The recently developed Radon-ambiguity transform (RAT) detects unknown linear frequency modulated (LFM) signals by computing line integrals through the origin of the signal's ambiguity function (AF) magnitude. It is shown that this method also detects the step LFM and frequency-derived polyphase pulse compression waveforms with varying performance degradation. Simulations are provided to estimate the detection loss relative to the LFM.     

Costas array generation and search methodology

Costas arrays are permutation matrices that provide sequencing schemes for frequency hop in FSK waveforms. Such frequency-shift keying (FSK) waveforms can be designed to have nearly ideal ambiguity function properties in both the time and frequency directions: the Costas property permits at most one coincident tone in autocorrelations in both time and frequency. Costas arrays are found by number-theoretic generators and their extensions, and by exhaustive search methods. Two new extensions of number-theoretic methods are introduced here that find two new Costas arrays. All Costas arrays for orders 24, 25, and 26 are disclosed here, including previously unknown examples.     

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。     

Radar Waveforms for Suppression of Extended Clutter

A common problem in waveform design is to adapt the transmitted signal to the target environment in order that the interference from extended fields of scatterers is reduced. This problem is investigated here for the special case of detection of a single target in the ``vicinity' of an extended clutter space. The paper considers the possibility of confining the matched-filter response in delay and Doppler, or ambiguity function, to a narrow strip with arbitrary orientation in the delay-Doppler plane. It is shown that strict confinement of the response is achievable only with waveforms that are unlimited in both time and frequency domain. With practical waveforms, which are necessarily of finite extent, one merely can trade close-target separability against detectability in the background clutter. Thus, one form of the resolution problem is exchanged against the other. The paper examines these effects quantitatively.     

Monopulse Resolution of Interferometric Ambiguities

Ambiguities in interferometers with high angular accuracy must be resolved to achieve a practical system design. A new technique for ambiguity resolution is described and is based on monopulse circuitry used with the interferometric elements. The overall angular accuracy of the system is achieved by the interferometer; the angular accuracy of the monopulse subsystem is used to resolve interferometric ambiguities. An expression for the probability of correct ambiguity resolution is derived as a function of element size and monopulse accuracy which indicates that high probability of ambiguity resolution results when the size of the interferometric elements are a fraction of the interferometric baseline. Finally, a comparison between conventional monopulse and interferometric system designs is made for the three principal parameters, signal sensitivity, angular accuracy, and field of view, that dictate the appropriate choice for a particular application. Interferometric systems are more appropriate than monopulse systems for those applications in which angular accuracy and field of view are more important than signal sensitivity.     

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.     

ECCM capabilities of an ultrawideband bandlimited random noise imaging radar

Investigated here is high-resolution imaging of targets in noisy or unfriendly radar environments through a simulation analysis of the ultrawideband (UWB) continuous-wave (CW) bandlimited random noise waveform. The linear FM chirp signal was selected as a benchmark radar waveform for comparison purposes. Simulation of the recovery of various types of target reflectivity functions (TRFs) for these waveforms were performed and analyzed. In addition, electronic counter-countermeasure (ECCM) capabilities for both types of systems were investigated. The results are compared using the error between the interference (jamming)-free recovered TRF and the recovered TRF under noisy conditions as a function of the signal-to-interference/jamming ratio (SIR/SJR). Our analysis shows that noise waveforms possess better jamming immunity (of the order of 5-10 dB improvement over the linear FM chirp) due to the unique radar correlation processing in the receiver.     

Algorithms for Multitarget Ambiguity Removal after Coincidence Detection

A first cut at the difficult problem of the identification and removal of ambiguous responses to radar burst waveforms is presented. Assuming that two bursts are used, algorithms for multitarget ambiguity removal after coincidence detection are presented and illustrated by examples. The results may have significant application in ballistic missile defense surveillance radars.