Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir


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the Matlab routine “Figure 2.15.m” to the synthetic backscattered data, the range profile of this point target can be obtained as plotted in Figure 2.15. It is clearly seen from the figure that the point target at the range of 50 m is perfectly pinpointed.

      2.6.4 Short Pulse

      One of the simplest radar waveforms is the short pulse (or impulse) whose time duration is usually on the order of a few nanoseconds. As calculated in Eq. 2.54, the range resolution of a pulsed radar is equal to

      (2.56)equation

      (2.57)equation

      which means that the range resolution is proportional to its pulse duration as

      (2.59)equation

      Since this signal is much smoother than the previous short pulse waveforms that we have presented, the frequency extent of this wavelet is extremely broad. Therefore, it provides an ultrawide band (UWB) spectrum as most of the other short‐duration wavelets do as shown in Figure 2.18b.

      While these short pulses are good for providing a wide spectrum, they are not practical in terms of providing sufficient energy. This is because of the fact that it is not possible to put great amount of power onto a very small pulse. To circumvent this problem, the pulse is modulated by altering the frequency as time continues to pass. The common practice is to use a chirp waveform to be able to put enough energy onto the pulse, as will be investigated next.

      

      2.6.5 Chirp (LFM) Pulse

Graphs depicts short-duration rectangular pulse in (a) time domain, (b) frequency domain. Graphs depicts short-duration single-frequency pulse in (a) time domain, (b) frequency domain. Graphs depict short-duration Mexican-hat pulse in (a) time domain, (b) frequency domain. Graphs depict of the time-domain pulse waveforms: (a) single-tone pulse, (b) LFM (Chirp) pulse.

      The common waveform is the LFM pulse, also known as the chirp pulse, whose waveform is shown in Figure 2.19b. In practice, this waveform is repeated in every TPR intervals for most common radar applications, especially for localization of targets in the range. TPR is called the pulse repetition interval (PRI) or pulse repetition period. The inverse of this interval gives the pulse repetition frequency (PRF), defined as

      The mathematical expression of the upward chirp signal whose frequency is increasing as time passes along the pulse is given as

      (2.61)equation

      where n is an integer, τ is the pulse width, and K is the chirp rate. The instantaneous frequency of the pulse is fi(t) = fo + Kt. It is also possible to form another LFM pulse by decreasing the frequency along the pulse width as shown below:

      (2.62)equation

      For the downward chirp pulse, the instantaneous frequency is then equal to fi(t) = foKt.


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