Nasser J. Mohamed

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. >

Target signature using nonsinusoidal radar signals

A target recognition method that utilizes both target length determined from target signature duration for target classification and target shape determined from target signature amplitude variation for target identification is presented. The transformation of the target axes coordinate system into a rotated coordinate system enables target recognition at any aspect angle. The information obtained about target shape and size, in addition to the velocity information supplied by the Doppler effect, can be used to generalize Woodwards ambiguity function to a range-velocity-shape resolution function. Thumbtack range-velocity-shape resolution functions are easily obtained by increasing the number of pulses in the transmitted radar signal. >

Resolution function of nonsinusoidal radar signals. I. Range-velocity resolution with rectangular pulses

A generalization of a previously published ambiguity function that applies to radar known as large-relative-bandwidth radar, carrier-free radar, impulse radar, or nonsinusoidal radar is discussed. This radar has attracted attention because of its ability to penetrate absorbing materials used in the stealth technology. Another good application is the detection of moving targets with a small radar cross section by a look-down radar, which calls for a thumbtack ambiguity function. Since a small radar cross section in this application is typically due to the small size of the target that is coated with absorbing material, the antistealth feature of the nonsinusoidal radar is implicitly being used. The principle is presented of a resolution function (tentatively called the range-velocity or the range-Doppler resolution function) based on processing a nonsinusoidal signal consisting of N characters with a time separation T/sub D/ and each character consisting of a sequence of L binary pulses of duration T. It is shown that range-velocity resolution functions approaching the ideal thumbtack function are easy to obtain. The blind speeds of the pulse-Doppler radar with sinusoidal carrier do not inherently occur, and all velocities are observed as true velocities rather than as velocities modulo the first blind speed (velocity ambiguity). >

Two-Dimensional Beamforming with Nonsinusoidal Signals

A two-dimensional beamforming technique is presented for two-dimensional arrays of (N × N) sensors receiving plane wavefronts with nonsinusoidal time variations in the form of a single rectangular pulse of duration T or in the form of a coded sequence of rectangular pulses with nominal time duration T. The three-dimensional energy pattern has a main beam for small angles of incidence and a number of sidelobes for large angles of incidence. For wavefronts with rectangular time variations, the maximum sidelobe has the magnitude 1/N and, for coded time variations, the maximum sidelobe exceeds 1/N. The magnitude of the sidelobes of the energy pattern can be decreased by increasing the number of sensors in the array. The resolution angle can be decreased by the ratio (N1/N2) when the number of sensors is increased from (N1 × N1) to (N2 × N2) and it can be decreased by the ratio (T1/T2) when the nominal time duration is decreased from T2 to T1. Waveform distortion results in a degradation of the resolution angle.

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. >

Beam Forming with Nonsinusoidal Coded Waveforms

The principle of beam forming based on a line array of sensors for nonsinusoidal signals with rectangular time variations is advanced to include beam forming of coded nonsinusoidal signals. The energy patterns of coded waveforms using complementary codes have a narrow main beam for small angles of incidence, a large number of sidelobes forming minor beams for large angles of incidence, and a constant value of 1/N, where Nis the number of sensors in the line array. Arrays with a large number of sensors N ¿ 64 have array gains that reduce the large amplitudes of the sidelobes significantly, eliminate the sidelobes with small amplitude, and decrease the final value to 1/N. The resolution angle e can be reduced by increasing the array length L or by increasing the bandwidth ¿f = 1/2T, where T is the nominal pulse duration of the coded waveform.

Target course recognition using nonsinusoidal look-down radars

The target signature of an airplane as viewed by a nonsinusoidal look-down radar is obtained analytically as a function of target shape, azimuth orientation, look-down angle, and transmitted pulse duration. The information contained in the target signature can be used for detection of stationary and moving targets in heavy clutter, as well as the recognition of target shape and orientation. The relation between target signature and target azimuth orientation shows that pulse lengths shorter than airplane length are required to perform target recognition at all azimuth angles. Target course recognition in the radar ground plane is the process of determining the azimuth angle by selecting from the database the target signature that is most similar to the observed one. The effect of look-down angle on the target signature is also analyzed. At small look-down angles, target shape information is obtained with pulse lengths shorter than aircraft length. However, at large look-down angles pulse lengths much shorter than the airplane length are required. The variation of the target signature with azimuth and look-down angles are utilized for determining two-dimensional target course recognition. Cruise missile radars operating in a lookdown mode can utilize the very-high-resolution nonsinusoidal radar to enhance target shape recognition in addition to target course recognition. >

Range-velocity resolution function of nonsinusoidal radar signals with Gaussian time variations

Signal design for carrier-free radars calls for the calculation of a range-velocity resolution function of nonsinusoidal signals consisting of a number of pulses with Gaussian time variations; this is a generalization of P.M. Woodwards (1953) ambiguity function that includes signals that do not have a sinusoidal carrier. Doppler processing of nonsinusoidal signals is investigated in terms of the Doppler effect of pulses with Gaussian time variation and Doppler resolutionl. Doppler resolution is determined in terms of signal parameters. The range-velocity resolution function is obtained analytically and represented by a three-dimensional surface as a function of target range and velocity. Methods for approaching the thumbtack range-velocity resolution function are determined in terms of signal parameters. Several plots for range-velocity resolution function are shown. >

Resolution function of nonsinusoidal radar signals. II. Range-velocity resolution with pulse compression techniques

For pt.I see ibid., vol.32, no.2, p.153-60 (May 1990). The thumbtack range-velocity resolution function of nonsinusoidal radar signals has been realised with signals having a large number of characters with triangular correlation functions. In reality, a radar signal rarely consists of one pulse; rather, it consists of thousands of pulses structured by various coding techniques. Pulse compression is a technique for obtaining high range resolution with long coded signals. The thumbtack range-velocity resolution function based on the pulse compression principle is realized by coding the transmitted signal using complementary codes. Increasing the code length will increase the pulse compression ratio and the time-sidelobe-free region, Doppler processing of correlation functions based on the pulse compression technique can realize the thumbtack range-velocity resolution function. The range-velocity resolution function is obtained by computer simulation and represented by a three-dimensional surface as a function of target range and velocity for signals with a different number of characters. Plots of range-velocity resolution functions for characters with different code lengths are presented. >

Lines of Force for a Hertzian Electric Dipole

The generation of electromagnetic waves by a Hertzian electric dipole having a current with a nonsinusoidal time variation is described in terms of magnetic flux lines called lines of force. The magnetic flux depends on the time variation of the current, the normalized distance from the radiator and the time variation of the integral of the current. The radiation of electromagnetic waves and their propagation is described by the lines of force in the near zone and the far zone, respectively. When the large-distance approximation is made, the magnetic flux depends on the time variation of the current only, and the lines of force generated will propagate away from the radiator. Plots of lines of force at several observation times are presented where the near zone and the far zone identified.