power spectral density of a radar system can be described as the following equation:
(2.36)
Here, k = 1.381 × 10−23 W/K° is the well‐known Boltzman constant, and Teff is the effective noise temperature of the radar in degrees Kelvin (K°). Teff is not the actual temperature but is related to the reference temperature via the noise figure, Fn, of the radar as
(2.37)
where the reference temperature, To, is usually referred to as room temperature (To ≈ 290 K°). Therefore, noise power spectral density of the radar is then being equated to
(2.38)
To find the value of the noise power, Pn, of the radar, it is necessary to multiply No with the effective noise bandwidth, Bn, of the radar as shown below:
Here, Bn may not be the actual bandwidth of the radar pulse; it may extend to the bandwidth of the other electronic components such as the matched filter at the receiver. Provided that the noise power is determined, it is easy to define the SNR of radar by combining Eqs. 2.28 and 2.39 as below:
(2.40)
The above equation is derived for the bistatic radar operation. The equation can be simplified to the following for the monostatic radar setup:
(2.41)
2.6 Radar Waveforms
The selection of the radar signal type is mainly decided by the specific role and the application of the radar. Therefore, different waveforms can be utilized for the various radar applications. The most commonly used radar waveforms are
1 continuous wave (CW),
2 frequency‐modulated 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
where fo 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 fo = ±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 fo, the frequency of the reflected wave from a stationary target is the same as the transmitting frequency fo. If the target is approaching the radar, the frequency of the reflected wave increases with a shifted amount of fD 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, vr is the radial speed of the moving target, and λo 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 fD (see Figure 2.10c).
