Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 68

Another popular radar waveform used to determine the range is the SFCW. This signal is formed by emitting a series of single‐frequency short continuous subwaves. In generating the SFCW signal, the frequencies between adjacent subwaves are increased by an incremental frequency of Δf as demonstrated in Figure 2.14. For one burst of SFCW signal, a total of N CW signals, each having a discrete frequency of f_n = f_o + (n − 1)·Δf, is sent. Each subwave has a time duration of τ and is of T distance away from the adjacent subwave. The total frequency bandwidth, B, and the frequency increment (or resolution), Δf, can be readily calculated as below:

(2.51)

(2.52)

The SFCW signal can be used to estimate the range of a possible target in the following manner. Suppose that the target is at the range distance of R_o from the radar. With a single measurement of monostatic SFCW radar, the phase of the backscattered wave is proportional to the range as given in the following equation:

Figure 2.14 SFCW signal in time‐frequency plane.

(2.53)

Here, E^s is the scattered electric field, A is the scattered field amplitude, and k is the wavenumber vector corresponding to the frequency vector of f = [f_o f₁ f₂⋯f_N−1]. The number 2 in the phase corresponds to the two‐way propagation between radar‐ to‐ target and target to radar. It is obvious that there is FT relationship between (2k) and (R). Therefore, it is possible to resolve the range, R_o, by taking the inverse Fourier transform (IFT) of the output of the SFCW radar. The resulted signal is nothing but the range profile of the target. The range resolution is determined by the Fourier theory as

(2.54)

where BW_k and BW_f ≜ B are the bandwidths in wavenumber and frequency domains, respectively. The maximum range is then determined by multiplying the range resolution by the number of SFCW pulses:

Figure 2.15 Range profile of a point target is obtained with the help of SFCW radar processing.

(2.55)

We will demonstrate the operation of SFCW radar with an example. Let us consider a point target which is 50 m away from the radar. Suppose that the SFCW radar's frequencies change from 2 to 22 GHz with the frequency increments of 2 MHz. Using Eqs. 2.54 and 2.55, one can easily find the range resolution and the maximum range as 0.75 cm and 75 m, respectively. Applying 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.