Radar Signal Design Research Articles

Bi-alphabetic pulse compression radar signal design

Ternary sequences have superior merit factors but they cannot be transmitted with existing technology. It is proposed that a ternary sequence be coded into a binary sequence for the purpose of transmission. On reception it can be processed as a binary sequence as received and also decoded into a ternary sequence. These two interpretations provide a coincidence detection scheme for efficient target detection provided that the corresponding signal design problem is solved. Such an algorithm is developed by taking the merit factor as desideratum and the Hamming scan as optimization technique. Merit factor values obtained in some cases are further improved by implementing a back-tracking algorithm for bi-alphabetic sequence.

Untrapping techniques for radar signal design

Ternary sequences with a good merit factor obtained earlier using the S-K-H algorithm, are improved by algorithms called the backtrack and sidetrack algorithms. A merit factor of >10 has been obtained at more than 100 lengths greater than 1000. The best merit factor for a binary sequence has been exceeded by ternary sequences at 40 lengths greater than 100.

Nonsinusoidal radar signal design for stealth targets

The detection of stealth point targets challenges the design of conventional radars using sinusoidal carriers since the objective of stealth technology is to reduce the radar cross section (RCS) of targets to a level where the radar receiver cannot detect the target. While there are a number of techniques employing different technologies to reduce the RCS of targets, shaping and coating the target with absorbing material are the most useful ones. The analysis and design of nonsinusoidal radar signals is based on modeling stealth point targets by a two-layer structure consisting of a metal surface covered with a coat of absorbing material. The design is presented for two classes of signals: uncoded signals and pulse compression signals using Barker codes. The relationship between target response, absorbing material time delay, time variation of transmitted pulses and coding features are determined and analyzed. While sliding correlators are used for detection and selection of various target responses, their output autocorrelation functions are determined analytically in terms of transmitted signal autocorrelation functions. Thumbtack range-velocity resolution functions are obtained for transmitted signal characters with a single pulse and characters with coded waveforms, for different pulse duration. It is shown that the range resolution can be improved by the proper choice of the transmitted signal duration relative to absorbing material time delay. Thumbtack range-velocity resolution functions similar to those of conventional point targets can also be realized. >

Carrier-free signal design for look-down radars

The detection of low flying targets with small radar cross section (RCS), known as low observables, such as cruise missiles and stealth airplanes adds a new dimension to radar signal design and radar signal processing. A high resolution look-down radar is very attractive since it takes advantage of target shape to overcome difficulties encountered with small RCS. The look-down geometry, however, imposes three requirements: 1) the radar should detect targets with small relative velocities from almost zero to about the velocity of sound with no blind speeds, 2) it should minimize ground clutter by using short pulses, and 3) the radar signal must have a thumbtack ambiguity function. We investigate a look-down radar that eliminates time side lobes of compressed signal correlation functions to improve range resolution, reduces ground clutter to enhance receiver dynamic range, and uses thumbtack resolution function to resolve moving low observable targets from the surface of the Earth. The side lobe elimination technique transforms the correlation function of a coded waveform, based on complementary codes, to the correlation function of a single pulse. Features of side lobe elimination technique along with clutter cancellation circuits are presented in terms of blind speeds and range-velocity resolution function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Carrier-free radar signal design with MTI Doppler processor

Doppler processors with feedback delay line circuits can produce thumbtack range-velocity resolution functions by processing carrier-free radar signals consisting of a large number of characters. The moving target indicator (MTI) Doppler processor, which is a generalisation of the two-pulse canceller circuit, can produce thumbtack range-velocity resolution functions by processing only two characters of the received signal, provided that each character has a correlation function with a main lobe and no time sidelobes. The two-pulse canceller circuit is modified to produce maximum output when the pulse separation time of the returned signal, from a stationary or moving target, is identical with the delay time of the MTI circuit, whereas conventional MTI produces no output in such a case. The processor is analysed in terms of the time difference between the Doppler shift of the received signal and the Doppler time of the processor. Blind speeds defined for MTI response to sinusoidal carriers do not exist in the output of the MTI Doppler processor. Sidelobe-free thumbtack range-velocity resolution functions for signal characters with beta time variations are presented. The two-pulse canceller circuit is analysed for returned signals from extended targets.

Wigner distribution and FM radar signal design

The Wigner distribution is a bilinear distribution originally developed in the field of quantum mechanics. It has recently attracted considerable attention as a time-frequency distribution for use in signal processing. The properties of the Wigner distribution are reviewed and its relationship to other distributions, in particular the ambiguity function, is described. Wigner distributions for frequency-modulated pulse-compression radar signals are presented and the effect of Doppler shift is demonstrated. Its use in the design of radar signals is discussed. The Wigner distribution provides an elegant way of qualitatively describing the effects of Doppler shift in pulse-compression radar, but is unlikely to provide a basis for the design of frequency-modulated radar signals.

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.

Design of Optimal Radar Signals Subject to a Fixed Amplitude Constraint

The problem of designing finite-pulse-train radar signals and receivers to maximize the detectability of targets masked by thermal noise and clutter returns is considered in this paper. A practical constraint is introduced: the amplitude of each subpulse in the transmit waveform is taken to be fixed. The need for such a constraint is dictated in most radar applications, because the transmitter is most efficiently utilized by saturating its amplifying tube. An algorithm for generating optimal waveforms subject to this new constraint is presented, and the performance of the resulting waveforms is compared with those obtained using existing optimization techniques.

Technical Note—An Application of Witzgall’s Algorithm to a Problem in Radar Signal Design

The problem of finding a binary pulse-compression code with arbitrary side-lobe levels is cast as a quadratically constrained integer program. Witzgall's algorithm is then applied, after a suitable manipulation, to put the constraints into a convex form.

Computer Evaluation of Radar Ambiguity Functions Using Fast Fourier Transform Techniques

The ambiguity function is a useful tool for the design of radar signals. It is well known that the matched filter receiver is the optimum receiver for the detection and parameter estimation of signals corrupted by Gaussian noise. The ambiguity function represents the matched filter response in the absence of noise. For a given radar environment, the proper choice of an ambiguity function is necessary to minimize self-clutter while maintaining the required measure of local accuracy and resolution.No efficient methods are known for determining the signal given an ambiguity function. It is, therefore, customary for radar designers to evaluate the ambiguity functions for a number of likely signals before a choice is made. Closed form solutions for the ambiguity function are known only for a few simple signals, and computational methods need to be used in most cases. A direct approach to the computational problem is extremely tedious. In this paper a novel solution to this problem is discussed. We define a dis...

Design of radar signals and receivers subject to implementation errors

The problem of designing finite-pulse-train radar signals and receivers to maximize the detectability of targets in the presence of clutter has recently been solved. In practice, the performance of these optimum signal-receiver pairs is often degraded seriously by implementation errors. The purpose of this paper is to present an iterative procedure for designing signal-receiver pairs, which takes into account the effects of implementation errors. This method is compared with the error-free design technique by means of two examples.

The design of clutter-resistant radar waveforms with limited dynamic range

The problem of designing radar signals and receivers that are optimum for detecting a point target masked by thermal noise and clutter returns is considered. In a previous paper, the authors described an iterative algorithm for designing such signals subject to an energy constraint. This paper describes an algorithm for the case where the energy constraint is replaced by a dynamic-range constraint, that is, the ratio of maximum to minimum signal amplitude is limited. The signal to which the algorithm converges satisfies the Kuhn-Tucker conditions, which are necessary for optimality. Examples of the application of both algorithms to radar signal design problems are given.

Radar signal design subject to simultaneous peak and average power constraints

Optimal amplitude modulations for a radar signal are derived and then used to calculate the efficiencies of various sub-optimal modulations. The choice of modulation is constrained by the total energy transmitted and the peak power (amplitude) of the transmitted signal. The peak power constraint is handled by the use of Pontryagin's Maximum Principle, an extension of the calculus of variations recently developed in the U.S.S.R. that is enjoying wide application in optimal control theory. The criterion of optimality is based on the error variances of estimates of the range motion parameters of a reflecting body, where the errors are caused by additive, white, zero mean, Gaussian noise. Explicit results are provided for bodies with constant velocity and bodies with constant acceleration. The analysis covers: 1) incoherent processing of a sequence of many range measurements; 2) coherent processing assuming the RF phase is known, 3) certain aspects of coherent processing assuming the RF phase is unknown. The optimal modulations turn out to be of the "on-off" type, requiring either no transmission or transmission at the maximum allowable power level.

Radar signal design for target resolution

Target resolution involves the recognition of a particular target in an arbitrary target environment. While pulse compression methods have solved the problem of separating two closely spaced targets of about the same cross section, this separation is usually accomplished at the expense of introducing sidelobes in the matched filter response, which may mask weak targets and prevent their detection altogether. The paper investigates the nature of the constraints on combined range and range rate resolution in a matched filter radar and establishes a clear tie between the uncertainty relation and the practical limitations on the resolution performance of radar. It is found that, in general, an optimum radar waveform for target resolution cannot exist. Radar signal design for target resolution consists of matching the waveform to the characteristics of the target environment, and a signal can be optimum only in that it achieves the best match. These findings are illustrated by examples of matching the radar waveform to a given target environment.

The Design of Radar Signals Having Both High Range Resolution and High Velocity Resolution

Radar systems that yield simultaneous information regarding the range and velocity of a target would be useful in certain applications. A discussion is presented of some fundamental limitations on simultaneous range-velocity determination in terms of ambiguity diagrams, with the aid of a quantum mechanical analog to the Wigner distribution function. A sequence of signals is found in which the signals yield both range and velocity information with increasing accuracy. However, this desired property is not accompanied by a waveform suitable for maximum operating efficiency.