AREQUIPA – PERÚ
2.2 ESTOMATITIS AFTOSA:
2.2.1 PERÍODOS
In this chapter, I have described a simple technique (Range Standoff diagrams) for calculating and graphically presenting the effects of phase and amplitude error on the PSF of an FMCW radar. I have also described a simple formula for calculating the ideal PSF given signal window weighting for the cosine family of window weighting functions.
The ability of the Range Standoff method to highlight detailed and subtle effects on the PSF for a variety of errors was demonstrated, illustrating the
Figure 3.28: A photograph of the radar test range. The radar can be seen in the open laboratory window.
points that, firstly, simple metrics of PSF quality are not always ideal mea- sures of image quality and, secondly, numerical methods can provide easy and accurate methods for predicting radar performance.
The ability of the technique to predict PSF degradation at a given range was demonstrated for a variety of cases.
In future work, more sensitive measurements could be made to validate the image phase prediction and the prediction of the effects of amplitude modula- tion.
Result: close target
Measured Predicted Normal performance
Figure 3.29: The measured normal, measured nonlinear, and predicted nonlinear chirp responses of the instrumentation radar to the close trihedral. It can be seen that there is good agreement between the measured PSF and that predicted using the range-standoff diagram.
Result: far target
Measured Predicted Normal performance
Figure 3.30: The measured normal, measured nonlinear, and predicted nonlinear chirp responses of the instrumentation radar to the far trihedral. It can be seen that there is good agreement between the measured PSF and that predicted using the range-standoff diagram. N.B. the noise floor in the ‘measured’ plot can be seen to be due to the swept out spurs in the ‘normal performance’ plot.
Range autofocus for FMCW radar
In this chapter, I shall describe a software-based method for estimating and compensating for chirp nonlinearity in FMCW radars. The method is based on two existing techniques: the Phase Gradient Algorithm (PGA) and time- domain warping of the dechirped signal. I shall demonstrate the new method on both typically and severely nonlinear chirps. I shall also demonstrate ret- rospective application of the method on archive radar data.Part of the work described in this chapter forms a paper accepted for publication in IET Radar Sonar Navigation under the title ‘Range Autofocus for Linearly Frequency Modulated Continuous Wave Radar’.
4.1
Introduction
FMCW radar requires a highly linear frequency chirp if the resultant imagery is to have near-ideal resolution, dynamic range, SNR, and geometric precision [10, 43, 47, 48, 77, 78].
Many methods of achieving good chirp linearity exist, including charac- terization of the chirp nonlinearity and pre-distortion of the control voltage applied to the oscillator [50]; use of feedback via delay lines to modify the voltage control [55, 56]; use of a frequency divider and a Direct Digital Syn- thesizer (DDS) to linearize the chirp[79]; and phase locked loops[80, 81].
In certain circumstances, it is necessary or desirable not to make hard- ware provision to linearize the chirp. For example, in a test radar, it might be impossible to include linearization components without modifying the per- formance of the components under test. Another example might be provision
of a correction/compensation for an existing radar that cannot be modified to include extra hardware. In some circumstances, it might be desirable to keep the hardware to a minimum, for reasons of physical size, electrical power re- quirements, or cost. In many cases, it would simply be easier not to have to use hardware linearization.
The method proposed in this chapter provides an entirely software-based autofocus technique that enables any FMCW radar to be focussed to near ideal performance.
The method comprises two existing techniques: the PGA [60, 82, 83], which is used to estimate the phase error that is defocussing the PSF of a reference reflector, and a time-domain warping of the signal[54, 58], which is used to simultaneously correct the signal for all ranges, focussing the entire range profile.
This method does not require hardware modification to measure the phase error because the reference phase error can be obtained from a real reflector in the radar’s beam. This is made possible by the ability of the PGA to pro- duce a stable estimate of the signal phase directly from the defocussed images of a reference reflector produced by the radar. The PGA achieves this by ex- ploiting both the underlying repeatable nature of the phase error due to the chirp nonlinearity and the random nature of the phase error due to noise. By combining the phase errors that defocus multiple notionally identical images of the same reference reflector, the phase error due to chirp nonlinearity can be stably estimated.
From this stable estimate of the IF phase error due to chirp nonlinearity, a time-domain signal warping can be derived that will distort all of the nonlinear phases, making them linear.
The method proposed in this chapter is called an autofocus technique be- cause the information to focus the radar’s PSF is extracted from the defocussed PSF itself. This type of technique, including the PGA, is widely used in SAR, where two-dimensional imagery is focussed in the cross-range direction to remove errors chiefly introduced by nonlinearity in the nominally linear tra- jectory of the radar.
This chapter has the following structure: in Section 4.2, the proposed method is described and explained. In Section 4.3, the method is demon- strated using a VCO-based radar: first on a deliberately (and badly) nonlinear case over a moderate chirp bandwidth and second using the same radar’s in- herent (and slight) nonlinearity over a large chirp bandwidth. Finally, the
method is demonstrated on archive data acquired with a long-range terrain- mapping radar, demonstrating retrospective application, which enables poorly focused archive data to be focussed.