Linear Frequency Modulation Waveform Research Articles

Filter Design for Steady-State Tracking of Maneuvering Targets with LFM Waveforms

Modern radars employ linear frequency modulated (LFM) waveforms for target tracking as the range-Doppler coupling enables better track accuracy in range. This paper derives expressions for the sensor-noise only (SNO) covariance matrix and the position and velocity lags during maneuvers for an alphabeta-filter processing measurements from LFM waveforms. These expressions were confirmed through computer simulations. An analysis of the maximum root-mean-square error (RMSE) in position and velocity estimates is performed, and the gains that minimize the maximum RMSE in either position or velocity are plotted versus the tracking index. For deterministic maneuvers, the paper introduces the concept of the deterministic tracking index and shows its relation to the typical tracking index generally used for random maneuvers. Using these relations, the paper also proposes a method to calculate the optimal process noise variance to be used in the tracking filter for a deterministic tracking index.

SIDELOBES REDUCTION USING SIMPLE TWO AND TRI-STAGES NON LINEAR FREQUENCY MODULATION (NLFM)

The Linear Frequency Modulation (LFM) waveform is the most commonly and extensively used signal in practical radar system. However a compressed LFM signal at the receiver will produce the flrst sidelobe at a level of i13dB to the peak of the main lobe. A weighting function is needed to apply in order to reduce the sidelobes. However, the penalty of mismatch loss is clearly evident. It may reduce output SNR, typically by 1 to 2dB. Every single dB of additional SNR can have great efiects in reducing false alarm rates in target detection applications. In an efiort to achieve low autocorrelation sidelobe level without applying weighting function, Non-Linear Frequency Modulation (NLFM) signal has been investigated. This paper describes the sidelobe reduction techniques using simple two-stage FM waveform, modifled two-stage FM waveform and tri-stage FM waveform. Simulation results of the proposed NLFM signal are presented. Sidelobe reduction of more than i19dB can be achieved by this design without any weighting technique applied.

A high performance UWB LFM waveform generator

In this paper, the design and implementation of a high performance Ultra-WideBand (UWB) Linear Frequency Modulation (LFM) waveform generator at Very High Frequency/Ultra High Frequency (VHF/UHF) band are introduced. Firstly, the design ideas for a high performance UWB LFM waveform generator are described. Then, a generation scheme for UWB LFM waveforms is presented according to the baseband digital generation method combining with the bandwidth extension method via frequency doubling. An experimental system has been implemented and tested. The results show that the UWB LFM waveform generator achieves very high performance.

Two-dimensional ISAR model and image reconstruction with stepped frequency-modulated signal

A two-dimensional (2-D) inverse synthetic aperture radar (ISAR) return signal model that employs stepped frequency (SF) modulation is developed. The geometry of the examined ISAR scenario is described by analytical geometrical equations. The target to be imaged is represented by a rectangular grid of point scatterers, moving along a rectilinear trajectory at constant speed, without any rotational motion. Thus, the inverse synthetic aperture results from the translational motion of the target for a short period of time. The process of ISAR signal modelling through coherent summation of the SF-modulated signals reflected from different point scatterers of the target is thoroughly described. Moreover, an efficient ISAR image reconstruction approach, including cross-correlation-based range compression and fast-Fourier-transform-based azimuth compression, is presented through analytical mathematical expressions. Numerical simulations are carried out for various SF ISAR scenarios and high-resolution ISAR images are obtained by applying the proposed ISAR image reconstruction approach. Simulation results (ISAR images and corresponding entropy values) indicate the validity of the proposed 2-D SF ISAR return signal model and the efficiency of the proposed imaging algorithms. Finally, a numerical simulation result is illustrated, which shows the comparison of the performance of the proposed ISAR image reconstruction algorithms based on SF and linear frequency modulation waveforms. It is shown that the two waveforms attain almost the same ISAR image resolution.

AN INTRODUCTION TO SYNTHETIC APERTURE RADAR (SAR)

This paper outlines basic principle of Synthetic Aperture Radar (SAR). Matched filter approaches for processing the received data and pulse compression technique are presented. Besides the SAR radar equation, the linear frequency modulation (LFM) waveform and matched filter response are also discussed. Finally the system design consideration of various parameters and aspects are also highlighted.

Radar Sensor Networks: Algorithms for Waveform Design and Diversity with Application to ATR with Delay-Doppler Uncertainty

Automatic target recognition (ATR) in target search phase is very challenging because the target range and mobility are not yet perfectly known, which results in delay-Doppler uncertainty. In this paper, we firstly perform some theoretical studies on radar sensor network (RSN) design based on linear frequency modulation (LFM) waveform: (1) the conditions for waveform coexistence, (2) interferences among waveforms in RSN, (3) waveform diversity in RSN. Then we apply RSN to ATR with delay-Doppler uncertainty and propose maximum-likeihood (ML) ATR algorithms for fluctuating targets and nonfluctuating targets. Simulation esults show that our RSN vastly reduces the ATR error compared to a single radar system in ATR with delay-Doppler uncertainty. The proposed waveform design and diversity algorithms can also be applied to active RFID sensor networks and underwater acoustic sensor networks.

Analysis of a true time delay photonic beamformer for transmission of a linear frequency-modulated waveform

A generalized conversion matrix (GCM) and numerical analysis are used to study the distortions suffered by a linear frequency-modulated radio frequency (RF) pulse while propagating through photonic links to be used in wideband phased arrays. The analysis shows the effects of dispersion of all orders, coherent crosstalk and nonlinearity of the optical components on the RF pulse, and the high performance needed to achieve acceptable RF performance of the temporal (impulse) response. The effects of the electrical-to-optical (E/O) and optical-to-electrical (O/E) conversions are also considered. Using the GCM, the optical amplitude and phase fluctuations are converted into their RF counterparts, thereby reducing the optical problem into the well-understood RF domain. A photonic wavelength-controlled true delay device is experimentally shown to achieve good RF performance over a 4-GHz bandwidth, with predicted sidelobe levels below 30 dB.

FOPEN SAR imaging using UWB step-frequency and random noise waveforms

The detection and identification of targets obscured by foliage have been topics of great interest. Several synthetic aperture radar (SAR) experiments have demonstrated promising images of terrain and man-made objects obscured by dense foliage, by using either linear frequency modulation (LFM) or step-frequency waveforms. We present here the methodology and results of a comparative study on foliage penetration (FOPEN) SAR imaging using ultrawideband (UWB) step-frequency and random noise waveforms. A statistical-physical foliage transmission model is developed for simulation applications. The foliage obscuring pattern is analyzed by means of the technique of paired echoes. The results of the comparative study demonstrates the ability of a UHF band UWB random noise radar to be used as a FOPEN SAR. Advantages of the random noise radar system include covert detection and immunity to radio frequency interference (RFI).

Steady-state tracking with LFM waveforms

The steady-state gains and error covariance are derived for a two-state Kalman filter (i.e., an /spl alpha/, /spl beta/ filter) for tracking with linear frequency modulated (LFM) waveforms. A procedure is given for calculating the /spl alpha/, /spl beta/ gains from the tracking index /spl Gamma/, the sample period T, and the range-Doppler coupling coefficient /spl Delta/t. The steady-state error covariance is found to be a simple function of /spl alpha/, /spl beta/, /spl Delta/t, T and the measurement noise variance /spl sigma//sub v//sup 2/. The expressions for the steady-state gains and error covariance were confirmed numerically with the Kalman filtering equations. A gain scheduling technique for /spl alpha/ and /spl beta/ during initialization is also given.

Wide-band airborne radar operating considerations for low-altitude surveillance in the presence of specular multipath

Reliable detection of low-altitude platforms while simultaneously maintaining a desired search rate can be extremely difficult due to the presence of multipath. Wide-band operation in combination with frequency diversity is a sensible approach to not only mitigate, but in some cases exploit multipath channel characteristics. While a great deal of knowledge exists for characterizing the frequency dependencies of complicated multipath channels, relatively little attention has been given to examining how this knowledge could be exploited with wide-band radar sensors. The utilization of multipath channel characteristics is considered for the scenario of an airborne wide-band radar sensor performing low-altitude surveillance in a maritime environment. A brief overview of applicable multipath phenomenology is presented leading to a description of the propagation conditions selected for the construction of a representative channel. A generalized wide-band model of the sensor engagement applicable to the resolved and unresolved domains of the interference regime is utilized in combination with the simulated channel. Wide-band short pulse and linear frequency modulation waveforms are employed to consider waveform modulation characteristics in combination with desirable sensor bandwidth and frequency diversity for nominal operation at X-band. A brief discussion on implementation possibilities is also included.

On detecting linear frequency-modulated waveforms in frequency- and time-dispersive channels: alternatives to segmented replica correlation

In modern active sonars, so-called high-gain waveforms are used to obtain processing gain for improved detection performance in reverberation. In time and frequency spread channels, the full processing gain of these waveforms is not achievable and robust detectors are needed. It is common practice to use a segmented replica correlator (SRC) detector for robust detection in such environments. In this paper, we show that an alternative processor formed by integrating the full replica correlator output magnitude squared, denoted RCI for replica correlator integrator, has advantages over the SRC when the waveform is linear frequency modulated (LFM). The RCI is better suited to the case of unknown time spreading through the use of a bank of integrators tuned for a wide range of spreading widths. The SRC, on the other hand, may be designed only for a fixed amount of distortion. Computer simulations are used to show how a multihypothesis RCI processor improves upon the fixed SRC by up to 4 dB over a realistic range of time spreading widths. >

Swept frequency reflectometer design for in-situ permittivity measurements

A prototype, broadband vector reflectometer for in-situ field measurements of permittivity is presented. The system was designed primarily to measure permittivity of sea ice in the 2-18-GHz frequency range but works equally well on other materials. The reflectometer design is based on FM-CW radar concepts. A linear frequency-modulated waveform is generated, and a portion of it is coupled off and passed through a delay line to serve as the local oscillator for the incident and reflected channels which receive most of the generated waveform. The reflectometer measures the complex reflection coefficient of a short monopole antenna probe. Permittivity is obtained by constructing a normalized input impedance of the probe. The impedance measured in a standard medium is based to construct a fourth-order rational function for the normalized input impedance, which is used with the measured impedance in the medium under test to obtain the permittivity. Measured permittivity data for air, 1-Butanol, and Teflon are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An extended Frank code and new technique for implementing P3 and P4 codes

A method is presented for generating a class of polyphase pulse compression codes of length other than N/sup 2/ using an efficient digital implementation technique. The structure, called extended Frank (EF) code, can be applied to linear frequency-modulation waveforms for compression ratios of N*M where N and M are arbitrary integers. The phase matrix of the EF code has the same properties as that of the Frank code, but the restriction of identical numbers of columns and rows for the Frank code is removed. A special case N= kappa M, where kappa is an integer, is discussed. The disadvantage of high sidelobes that results from the ED code is removed when P3 and P4 codes are implemented. By comparing the phase matrices of the P3 and P4 codes with the EF code, it is found that only (N-1) phase shifters are required to convert the EF code to P3 or P4 code. Hence, an effective implementing technique for the P3 or P4 polyphase code is obtained by using the simple EF code structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Delay‐Doppler resolution performance of large time‐bandwidth product linear FM signals in a multipath ocean environment

Active sonar systems that transmit large time‐bandwidth (TW) product linear frequency‐modulated (LFM) waveforms and receive echoes from targets of unknown speed can suffer considerable correlation losses that cannot be predicted from conventional (narrow‐band) ambiguity function theory. As is well known, the theory can be modified to include the effects of Doppler distortion on large TW‐product signals by correlating the received signal against a reference that is a time‐compressed version of the transmitted signal. In this paper, the effects of multipath (or target highlight structure) and Doppler on the correlation process for rectangular weighted large TW‐product LFM waveforms are examined. When the received echo contains no multipath, the correlator peak output is a maximum for the reference channel that is closest in Doppler to the target. However, in a multipath environment, the correlator output peak does not generally occur at the correct Doppler reference channel. The spreading of the cross‐ambiguity function as a result of Doppler mismatch and multipath is calculated in terms of the delay‐Doppler coordinates and magnitude of the extrema. It is shown that, under multipath conditions, correct estimates of target parameters can be recovered through integration of the correlator output.

Delay-Doppler resolution performance of large time-bandwidth-product linear FM signals in a multipath ocean environment

Active sonar systems that transmit large time-bandwidth (TW)-product linear frequency modulated (LFM) waveforms and receive echoes from targets of unknown range and speed can suffer considerable correlation losses that cannot be predicted from conventional (narrow-band) ambiguity function theory. As is well known, the theory can be modified to include the effects of Doppler distortion on large TW-product signals by correlating the received signal against a reference that is a time-compressed version of the transmitted signal. In this article, the effects of multipath (or target highlight structure) and Doppler on the correlation process for rectangular-weighted large TW-product LFM waveforms are examined. Gaussian-weighted waveforms are also considered to examine sidelobe behavior. It is shown that in a multipath environment, the correlator output peak does not generally occur at the correct Doppler reference channel. This is due to the constructive/destructive interference of the summation of complex delay-Doppler autocorrelation functions associated with each return. A summation technique that identifies the appropriate Doppler reference channel is proposed; this technique allows the target parameters to be estimated if the signal-to-noise ratio is sufficiently high.

Cross correlation of two hyperbolic‐frequency‐modulated (HFM) waveforms

In a multi‐user radar/sonar environment, or in the case of a single user but with different pulses transmitted, it is important to know the cross correlation of the waveforms as a function of time delay. The cross‐correlation property of two differently swept LFM (linear‐frequency‐modulated) waveforms is straightforward from the view point of using the stationary‐phase approximation. There, as one waveform's frequency‐time curve slides against the other's, the intersecting angle remains constant over an interaction interval in time delay corresponding to the common frequency interval of the two waveforms. The picture changes vastly when the two LFM waveforms are replaced by two HFM (hyperbolic‐frequency‐modulated) ones. In this paper, the cross correlation over such an interval is established. Using examples, the analytical approximation is shown to compare favorably with numerical simulation results. The difference between the analytic and numerical results is further characterized using the unity volume constraint for narrow‐band cross‐ambiguity function which is lesser known than the auto‐ambiguity counterpart.

Sidelobe level of hyperbolic frequency modulated (HFM) waveforms

As large time‐bandwidth products are employed for the widely used LFM (linear frequency‐modulated) waveforms, the loss due to the phase mismatch of the peak output of a single matched filter becomes excessive even for very moderate target radial speeds. HFM (hyperbolic frequency modulated) waveforms can eliminate this loss. An early result on sidelobe level of HFM waveform [J. J. Kroszczynski, Proc. IEEE 57, 1260–1266 (1969)] apparently has errors in its derivation in applying asymptotic approximation techniques. The only numerical result provided there did not agree well with the analytically derived result, despite the claim to the contrary. In the present paper, new asymptotic results have been derived using integration by parts in the correct direction, so that terms discarded are smaller than the quantity being approximated. Computer simulations using several sets of parameters, including the one mentioned above, compare well with the new analytic approximations. The increased sidelobe level of HFM waveform over that of the LFM one is much less than indicated by the early approximation.

Error-Signal Response of a Phase-Locked Loop to a Coherent Chirp Signal

A new theory which describes the transient response of a PLL to a periodic ramp voltage applied to the VCO for generating a coherent chirp signal has been presented. With the appropriate choice of loop parameters and the ramp voltage rate to make the value of the normalized loop natural frequency within the range (0, 1), the PLL's equation can be simplified to a nearly linear differential equation. Its asymptotic solution can be obtained by the perturbation method as ε is a rather small value. Computer simulation results in agreement with the analysis have been obtained. Its application to generate a coherent linear frequency modulation waveform using a high-gain second-order PLL is considered.