continuous wave (FMCW),

      3 stepped‐frequency continuous wave (SFCW),

      4 short pulse, and

      5 chirp (linear frequency modulated [LFM]) pulse.

      Next, these waveforms will be investigated while their time and frequency characteristics are demonstrated and their common usages and applications are addressed.

      2.6.1 Continuous Wave

      A CW radar system transmits radio wave signals at a particular frequency. If both the radar and the target are stationary, then the frequency of the received CW signal is the same as the transmitted signal. On the other hand, the returned signal's frequency components are shifted from the transmitted frequency if the target is in motion with respect to the radar. This type of shift in the frequency spectrum is called Doppler frequency shift and plays an important role in finding the velocity of the target in most radar applications. The concept of Doppler frequency shift is also important for ISAR imaging. We shall see the use of Doppler frequency shift concept in Range‐Doppler ISAR imaging applications in Chapter 6.

      The time‐domain signal of the CW radar is as simple as

(2.42)

where f_o is the operating frequency. The frequency spectrum of this CW signal can be readily found by applying the forward Fourier transform (FT) operation to Eq. 2.42 to get

      (2.43)

An example of a CW radar signal is shown in Figure 2.9. In Figure 2.9a, a purely sinusoidal signal that has a frequency of 1 kHz is drawn. The frequency spectrum of this signal is plotted in Figure 2.9b where two impulses at f_o = ±1 kHz can be easily seen.

As opposed to pulsed radar systems that use the time delay of the transmitted pulses to find the range of the target, CW radars measure the instantaneous rate of change in the target's range from the radar. This change causes the Doppler shift in the frequency content of the returned EM wave due to the motion of the radar, target, or both. One of the best uses of CW radar is the police radar system that estimates the speed of motor vehicles. A demonstration of CW police radar is shown in Figure 2.10. Assuming that the radar is stationary and transmitting a CW signal with a frequency of f_o, the frequency of the reflected wave from a stationary target is the same as the transmitting frequency f_o. If the target is approaching the radar, the frequency of the reflected wave increases with a shifted amount of f_D which is known as Doppler frequency shift (Mahafza 2005) and is given by Figure 2.10b:

Figure 2.9 An example of CW radar waveform in (a) time domain, (b) frequency domain.

      (2.44)

Here, v_r is the radial speed of the moving target, and λ_o is the wavelength corresponding to the frequency of the transmitted wave. In a dual situation, if the target is moving away from the radar, the frequency of the reflected wave is altered such that the Doppler frequency shift produces a negative value. Therefore, the wavelength of the reflected wave increases and the frequency decreases with an amount of f_D (see Figure 2.10c).

Figure 2.10 Operation of police radar: (a) returned wave has the same frequency as the transmitted signal for the stationary target, (b) returned wave's frequency is increased for the approaching target; (c) returned wave's frequency is decreased for the target going away.

      The use of CW waveform in various radar applications provides the following advantages. First of all, the radars that use CW waveforms are easy to manufacture, thanks to their simple waveform shapes. Second, they can detect any target on the range as far as the power level permits. Therefore, there is no range constraint for detection. In addition, they can be used in both very low‐frequency band (e.g. radio altimeters) and very high‐frequency band (e.g. early warning radars).

      CW radars have the following disadvantages. They cannot estimate the range of a possible target. Range is normally measured by the time delay between different pulses created by the radar. In CW radars, however, the waveform is continuous and not pulsed. Furthermore, they can only detect moving targets. Reflected energy from stationary targets is filtered out since their basic operation is based on measuring the Doppler shift in the frequency.

      Another disadvantage comes from the fact that they maximize the power consumption since they continuously broadcast the outgoing signal.

      2.6.2 Frequency‐Modulated Continuous Wave

      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