Radar transient signals are usually transient in time domain and wide-band in frequency domain.
Since classical methods ( such as Fourier transform ) have difficulty to handle transient signal
analysis, time-frequency or time-scale analysis is more suitable for
preserving high-frequency contents of the information carried by
transient signals.
Comparing with the Fourier transform, the
time-frequency/time-scale transform of a transient signal may
detect and locate rapid changes of the signal better than
Fourier transform.
One of the important applications of time-frequency/time-scale transform is
the detection and extraction of unknown radar signals in noise.
The localization of the time and frequency by time-frequency/time-scale
transform makes it possible for de-noising, signal detection and extraction
in the time-frequency domain.
Feature extraction in the time-frequency domain refers to the
identification of specific feature attributes from the transform domain.
To recover and isolate specific signal features, the transform pairs
must be not only effective, but also computationally efficient.
Radar transmits electromagnetic waves to a target
which consists of a number of point scatterers
and receives the scattered waves from the target.
The scattering properties of the target describe the features of the target.
The integrated effect of the scattered fields can be measured
directly by the radar, thus, the spatial distribution of the reflectivity
corresponding to the target can be reconstructed by a radar processor.
The distribution of the reflectivity is referred to as the radar image
of the target. The target's reflectivity is usually mapped onto a range
(or down-range) and cross-range plane and is viewed as a radar image of the target.
The range is the dimension along the radar line-of-sight to the target.
The cross-range is the dimension transverse to the line-of-sight.
High resolution radar images are always demanded. The range resolution is directly related to the bandwidth of the transmitted radar signal. Stepped-frequency waveforms and linear frequency-modulated chirp waveforms are examples of wide-band radar signals which are commonly used in radar imaging systems. The cross-range resolution is determined by the antenna beamwidth, which is inversely proportional to the length of the antenna aperture. To achieve high cross-range resolution without using a large antenna aperture, synthetic array processing is widely employed. Synthetic array radar processing coherently combines signals obtained from sequences of small apertures to emulate the result from a large aperture.
Synthetic array radar includes both synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR). Traditionally, SAR refers to the situation where the radar is moving and the target is stationary; ISAR refers to the geometrical inverse in which the target is moving and the radar is stationary. For ISAR, the synthetic aperture is formed by coherently combining signals obtained from a single aperture as it observes a rotating target. The rotation of the target emulates the result from a larger circular aperture focusing at the rotation center of the target.
ISAR uses Doppler information to obtain the cross-range resolution. Due to the target's rotation, which can be characterized as a superposition of pitch, roll, and yaw motions, different parts of the target have slightly different velocities relative to the radar and, hence, produce slightly different Doppler frequencies in the radar receiver. The differential Doppler shift of adjacent point scatterers can be observed in the receiver; therefore, the distribution of the target's reflectivity can be measured by the Doppler spectrum. The conventional method to retrieve Doppler information is the Fourier transform.
The objective of radar processing is to estimate
the target's reflective density function from received baseband signal samples,
the so-called frequency signature.
If the target's range is known exactly and the velocity and acceleration of
the target's motion are constant and known exactly over the imaging
time duration,
then the extraneous phase term of the motion can
be exactly removed.
Therefore, the reflective density function of the target can be
obtained simply by taking the inverse Fourier transform of the phase compensated
frequency signature.
The process of estimating the target's range and removing the extraneous
phase term is called focusing or
gross translational motion compensation.
Then, the inverse Fourier transform can be used to construct
the reflective density function of the target.
For SAR, the motion compensation is facilitated
by measuring the actual motion of the radar platform.
In ISAR, the actual motion can be measured by a range-tracker,
or estimated by a motion compensation algorithm
which estimates motion parameters and
compensates motion with respect to the target's range, velocity, acceleration and
other higher order terms.
The radar processor uses the frequency signatures as the raw data to perform range processing and Doppler processing. Range processing functions as a matched filter for use with pulse compression, which removes frequency or phase modulation and resolves range. For each range cell, the range profiles constitute a new complex time history series. Then, Doppler processing takes Fourier transform for the time history series and generates its Doppler spectrum, or profile. By combining the Doppler spectra for all range cells, finally, the range-Doppler image is formed. Therefore, the radar image is the target's reflectivities mapped onto the range-Doppler plane.
Motion compensation is a very important step to achieve
the requirements of using Fourier processing and to have a clear radar image.
Conventional motion compensation is a gross compensation for the whole target. It performs mainly range and the Doppler tracking. While a target is moving smoothly, conventional motion compensation is good enough to produce a clear image of the target.
However, when a target exhibits complex motion, such as pitching, yawing, rolling, or maneuvering, conventional motion compensation for the whole target is not sufficient to produce an acceptable image for viewing and analysis. In this case, more sophisticated motion compensation procedures for each individual scatterer such as polar reformatting and sub-aperture approach are needed. It keeps each scatterer within its range cell and maintains constant Doppler frequency shift for each of them. Thus, the Fourier transform may be applied properly to construct a clear image of the target.
In case a target exhibits significant maneuvering, even sophisticated motion compensation is still not sufficient, and the residual of the motion is still large. With large motion residuals or phase errors, individual scatterers may still drift through their range cells; thus, the Doppler spectrum may still be time-varying and image is still blurred.
Conventional approach to retrieve Doppler spectrum is the Fourier transform.
To use the Fourier transform adequately, some restrictions must be applied:
the Doppler frequency contents of the data should not change within
the time duration of the data.
If the Doppler contents do change with time, the Doppler spectrum by using
the Fourier transform becomes smeared and, thus, the cross-range
resolution is degraded.
However, the restrictions can be lifted if the Doppler information
can be retrieved with time-frequency transforms which
do not require stationary Doppler spectrum.
Replacing the conventional Fourier transform with the joint time-frequency transform,
a 2-D range-Doppler Fourier frame becomes a 3-D time-range-Doppler cube.
By sampling in time, a time sequence of 2-D range-Doppler images can be viewed.
Each individual time-sampled image from the cube
provides not only superior resolution but also excellent noise performance with
enhanced signal-to-noise ratio.
For radar pulse data:
The data consists of 10 complex (inphase and quadrature) signals each. There are 3 tests from each of 4 sources called A2, CCC2, F2, and H2. Each ASCII file contains a sequence of 20 concatenated signals of length 180 samples. The first 10 signals are the real-part (inphase) and the last 10 signals are the imaginary-part (quadrature). There is a total of 20x180 = 3600 samples in the data. The SNR of this data is higher. The purpose of analysis is to classify the source of the signals.
For noisy radar pulse data:
The data consists of a complex (inphase and quadrature) signal with 3120 samples. The SNR of this data is lower. The purpose of analysis is to detect and to classify the source of the signals.
For simulated noisy chirp data:
The data consists of 15,000 samples. The SNR of this data is about -5dB. The purpose of analysis is to detect and to extract the signal embedded in noise.
For simulated B-727 data:
The Stepped Frequency Radar operates at 9GHz and has a bandwidth of 150 MHz. For each pulse, 64 complex range samples were saved. The file contains 256 successive pulses. The Pulse repetition frequency is 20KHz. Motion compensation and range processing have been applied to the data. Radar image can be reconstructed by taking 1-D FFT of 256 pulses for each range sample. The B727s is high SNR with fluctuation in velocity which causes the image blurring. The B727s0 is high SNR without blurring. The B727sn is low SNR without blurring.
For simulated MIG-25 data:
The Stepped Frequency Radar operates at 9GHz and has a bandwidth of 512MHz. For each pulse, 64 complex range samples were saved. The file contains 512 successive pulses. The Pulse repetition frequency is 15KHz. Basic motion compensation processing without polar reformation has been applied to the data without pulse compression. Radar image can be reconstructed by taking 2-D FFT of the data.
For real B-727 data:
The Stepped Frequency Radar operates at 9GHz and has a bandwidth of 150 MHz. For each pulse, 128 complex range samples were saved. The file contains 128 successive pulses. Motion compensation and range processing has been applied to the data. Radar image can be reconstructed by taking 1-D FFT of 128 pulses for each range sample.
File Access
The files listed below can be obtained by your browser, the links in the table below can be
used to download the desired files.
| File Name | Format | Size | Dimensions | Description |
|---|---|---|---|---|
| PULSE01.MAT | MATLAB | 34 KB | 180 x 10 | Radar pulses (complex) |
| PULSE01.DAT | ASCII | 60 KB | 180 x 20 | Radar pulses (real+imag.) |
| PULSE02.MAT | MATLAB | 34 KB | 180 x 10 | Radar pulses (complex) |
| PULSE02.DAT | ASCII | 60 KB | 180 x 20 | Radar pulses (real+imag.) |
| PULSE03.MAT | MATLAB | 34 KB | 180 x 10 | Radar pulses (complex) |
| PULSE03.DAT | ASCII | 60 KB | 180 x 20 | Radar pulses (real+imag.) |
| PULSE04.MAT | MATLAB | 34 KB | 180 x 10 | Radar pulses (complex) |
| PULSE04.DAT | ASCII | 60 KB | 180 x 20 | Radar pulses (real+imag.) |
| PULSE05.MAT | MATLAB | 51 KB | 3120 x 1 | Noisy radar pulses (complex) |
| PULSE05.DAT | ASCII | 102 KB | 3120 x 2 | Noisy radar pulses (real+imag.) |
| CHIRPM5DB.MAT | MATLAB | 119 KB | 1 x 15000 | Radar chirp signal in noise |
| CHIRPM5DB.DAT | ASCII | 238 KB | 1 x 15000 | Radar chirp signal in noise |
| B727S.MAT | MATLAB | 264 KB | 64 x 256 | Simulated ISAR data with blurring (complex) |
| B727S.DAT | ASCII | 519 KB | 64 x 512 | Simulated ISAR data with blurring (real+imag.) |
| B727S0.MAT | MATLAB | 264 KB | 64 x 256 | Simulated ISAR data without blurring (complex) |
| B727S0.DAT | ASCII | 519 KB | 64 x 512 | Simulated ISAR data without blurring (real+imag.) |
| B727SN.MAT | MATLAB | 264 KB | 64 x 256 | Simulated ISAR data without blurring (complex) |
| B727SN.DAT | ASCII | 519 KB | 64 x 512 | Simulated ISAR data without blurring (real+imag.) |
| RECON1D.M | Matlab M-file for 1-D processing | |||
| MIG25.MAT | MATLAB | 519 KB | 64 x 512 | Simulated MIG-25 with blurring (complex) |
| MIG25.DAT | ASCII | 1 MB | 64 x 1024 | Simulated MIG-25 with blurring (real+imag.) |
| RECON2D.M | Matlab M-file for 2-D processing | |||
| B727R.MAT | MATLAB | 264 KB | 128 x 128 | Real B-727 data (complex) |
| B727R.DAT | ASCII | 519 KB | 128 x 256 | Real B-727 data (real+imag.) |