Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 70

As explained in the previous paragraph, it will not be possible to use a sufficiently wide pulse and achieve a wide bandwidth. If a broadband spectrum is achieved with an unmodulated, or constant‐frequency pulse (as in Figure 2.19a), its time duration has to be quite small such that it may not be possible to put enough energy on it. A solution to this problem is to use a modulated pulse of sufficient duration such that this modulated waveform provides the required frequency bandwidth for the operation of radar.

Figure 2.16 A short‐duration rectangular pulse in (a) time domain, (b) frequency domain.

Figure 2.17 A short‐duration single‐frequency pulse in (a) time domain, (b) frequency domain.

Figure 2.18 A short‐duration Mexican‐hat pulse in (a) time domain, (b) frequency domain.

Figure 2.19 Comparison 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 T_PR intervals for most common radar applications, especially for localization of targets in the range. T_PR is called the pulse repetition interval (PRI) or pulse repetition period. The inverse of this interval gives the pulse repetition frequency (PRF), defined as

(2.60)

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

(2.61)

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

(2.62)

For the downward chirp pulse, the instantaneous frequency is then equal to f_i(t) = f_o − Kt.

To demonstrate the broad spectrum of the LFM waveform, the FT of single‐tone and LFM pulse signals in Figure 2.19 is taken and plotted in Figure 2.20. It is clearly seen from this figure that chirp signal provides much wider bandwidth when compared to constant‐frequency pulse.

In radar applications, LFM pulse waveforms are mainly utilized in finding range profiles, and also for synthetic aperture radar (SAR) and ISAR processing as will be discussed in Chapters 3 and 6, respectively.

Figure 2.20 Comparison of the spectrum of (a) single‐tone pulse and (b) LFM pulse. Although both signals use the same time duration, frequency bandwidth of the Chirp waveform is much wider than the single‐tone waveform.