Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 67

While the CW radar can only estimate the Doppler shift created by the movement of the target with respect to radar, FMCW radar can be used to determine the range of a possible target. The common way to modulate the frequency is done by simply increasing the frequency as the time passes. This type of modulation is also known as linear frequency modulation or chirp modulation.

The waveform of an LFM CW signal is simply given by

(2.45)

where A is the signal amplitude, f_o is the starting frequency, and K is the chirp rate (or frequency increase/decrease rate). In the above equation, the “+” sign indicates an upchirp signal and the “−” sign is for a downchirp signal. The instantaneous frequency of this signal can be easily found by taking the time derivative of the phase as

(2.46)

A simple upchirp time‐domain signal is illustrated in Figure 2.11. As obvious from the figure, the frequency of the wave increases as time progresses.

Figure 2.11 A linear frequency‐modulated continuous wave signal.

In FMCW radar operation, consecutive LFM signals are transmitted by the radar. If the period of serial LFM waves is T, the frequency variation of such waveforms can be represented as in Figure 2.12a. The received signal arrives with a time delay of t_d. This time delay can be determined in the following manner: The difference in the frequency between the transmitted and the received signals, Δf, can be found as below:

(2.47)

Of course, time delay t_d is related to the range, R, of the target by the following equation:

(2.48)

where c is the speed of light in the air. Combining Eqs. 2.47 and 2.48, it is easy to determine the range of the target via

(2.49)

Figure 2.12 Operation of LFMCW radar: (a) time‐frequency display of the transmitted and received LFMCW signals, (b) the difference in the frequency between the transmitted and the received signals.

The block diagram of linear frequency‐modulated continuous wave (LFMCW) radar is shown in Figure 2.13. The LFMCW generator produces the LFM signal to be broadcasted by the transmitter. The receiver collects the returned wave that is multiplied with the transmitted signal. The output has both the sum and the difference of the transmitted and the received frequencies. As shown in Figure 2.12b, only the positive frequency difference, Δf is selected. Then the signal is fed to a discriminator that contains a differentiator plus an envelope detector. The output of the discriminator is proportional to the frequency difference, Δf. Once Δf is obtained, the range, R, of the target can be easily obtained via Eq. 2.50.

It is also obvious from Figure 2.12 that range ambiguity occurs when t_d > T. Therefore, the maximum difference in frequency can be Δf_max = KT, which means that the maximum unambiguous range can be determined as

(2.50)

Figure 2.13 LFMCW radar block diagram.

The above equation suggests that FMCW radar can only be used for short‐ or mid‐range detection of objects. Therefore, it is not suitable for long‐range detection.