CHAPTER SEVEN Radar and Sensor Systems 7.1 INTRODUCTION AND CLASSIFICATIONS Radar stands for radio detection and ranging. It operates by radiating electromag- netic waves and detecting the echo returned from the targets. The nature of an echo signal provides information about the target—range, direction, and velocity. Although radar cannot reorganize the color of the object and resolve the detailed features of the target like the human eye, it can see through darkness, fog and rain, and over a much longer range. It can also measure the range, direction, and velocity of the target. A basic radar consists of a transmitter, a receiver, and a transmitting and receiving antenna. A very small portion of the transmitted energy is intercepted and reflected by the target. A part of the reflection is reradiated back to the radar (this is called back-reradiation), as shown in Fig. 7.1. The back-reradiation is received by the radar, amplified, and processed. The range to the target is found from the time it takes for the transmitted signal to travel to the target and back. The direction or angular position of the target is determined by the arrival angle of the returned signal. A directive antenna with a narrow beamwidth is generally used to find the direction. The relative motion of the target can be determined from the doppler shift in the carrier frequency of the returned signal. Although the basic concept is fairly simple, the actual implementation of radar could be complicated in order to obtain the information in a complex environment. A sophisticated radar is required to search, detect, and track multiple targets in a hostile environment; to identify the target from land and sea clutter; and to discern the target from its size and shape. To search and track targets would require mechanical or electronic scanning of the antenna beam. For mechanical scanning, a motor or gimbal can be used, but the speed is slow. Phased arrays can be used for electronic scanning, which has the advantages of fast speed and a stationary antenna. 196 RF and Microwave Wireless Systems. Kai Chang Copyright # 2000 John Wiley & Sons, Inc. ISBNs: 0-471-35199-7 (Hardback); 0-471-22432-4 (Electronic) For some military radar, frequency agility is important to avoid lock-in or detection by the enemy. Radar was originally developed during World War II for military use. Practical radar systems have been built ranging from megahertz to the optical region (laser radar, or ladar). Today, radar is still widely used by the military for surveillance and weapon control. However, increasing civil applications have been seen in the past 20 years for traffic control and navigation of aircraft, ships, and automobiles, security systems, remote sensing, weather forecasting, and industrial applications. Radar normally operates at a narrow-band, narrow beamwidth (high-gain antenna) and medium to high transmitted power. Some radar systems are also known as sensors, for example, the intruder detection sensor=radar for home or office security. The transmitted power of this type of sensor is generally very low. Radar can be classified according to locations of deployment, operating functions, applications, and waveforms. 1. Locations: airborne, ground-based, ship or marine, space-based, missile or smart weapon, etc. 2. Functions: search, track, search and track 3. Applications: traffic control, weather, terrain avoidance, collision avoidance, navigation, air defense, remote sensing, imaging or mapping, surveillance, reconnaissance, missile or weapon guidance, weapon fuses, distance measure- ment (e.g., altimeter), intruder detection, speed measurement (police radar), etc. 4. Waveforms: pulsed, pulse compression, continuous wave (CW), frequency- modulated continuous wave (FMCW) Radar can also be classified as monostatic radar or bistatic radar. Monostatic radar uses a single antenna serving as a transmitting and receiving antenna. The transmitting and receiving signals are separated by a duplexer. Bistatic radar uses FIGURE 7.1 Radar and back-radiation: T=R is a transmitting and receiving module. 7.1 INTRODUCTION AND CLASSIFICATIONS 197 a separate transmitting and receiving antenna to improve the isolation between transmitter and receiver. Most radar systems are monostatic types. Radar and sensor systems are big business. The two major applications of RF and microwave technology are communications and radar=sensor. In the following sections, an introduction and overview of radar systems are given. 7.2 RADAR EQUATION The radar equation gives the range in terms of the characteristics of the transmitter, receiver, antenna, target, and environment [1, 2]. It is a basic equation for under- standing radar operation. The equation has several different forms and will be derived in the following. Consider a simple system configuration, as shown in Fig. 7.2. The radar consists of a transmitter, a receiver, and an antenna for transmitting and receiving. A duplexer is used to separate the transmitting and receiving signals. A circulator is shown in Fig. 7.2 as a duplexer. A switch can also be used, since transmitting and receiving are operating at different times. The target could be an aircraft, missile, satellite, ship, tank, car, person, mountain, iceberg, cloud, wind, raindrop, and so on. Different targets will have different radar cross sections ðsÞ. The parameter P t is the transmitted power and P r is the received power. For a pulse radar, P t is the peak pulse power. For a CW radar, it is the average power. Since the same antenna is used for transmitting and receiving, we have G ¼ G t ¼ G r ¼ gain of antenna ð7:1Þ A e ¼ A et ¼ A er ¼ effective area of antenna ð7:2Þ FIGURE 7.2 Basic radar system. 198 RADAR AND SENSOR SYSTEMS Note that G t ¼ 4p l 2 0 A et ð7:3Þ A et ¼ Z a A t ð7:4Þ where l 0 is the free-space wavelength, Z a is the antenna efficiency, and A t is the antenna aperture size. Let us first assume that there is no misalignment (which means the maximum of the antenna beam is aimed at the target), no polarization mismatch, no loss in the atmosphere, and no impedance mismatch at the antenna feed. Later, a loss term will be incorporated to account for the above losses. The target is assumed to be located in the far-field region of the antenna. The power density (in watts per square meter) at the target location from an isotropic antenna is given by Power density ¼ P t 4pR 2 ð7:5Þ For a radar using a directive antenna with a gain of G t , the power density at the target location should be increased by G t times. We have Power density at target location from a directive antenna ¼ P t 4pR 2 G t ð7:6Þ The measure of the amount of incident power intercepted by the target and reradiated back in the direction of the radar is denoted by the radar cross section s, where s is in square meters and is defined as s ¼ power backscattered to radar power density at target ð7:7Þ Therefore, the backscattered power at the target location is [3] Power backscattered to radar ðWÞ¼ P t G t 4pR 2 s ð7:8Þ A detailed description of the radar cross section is given in Section 7.4. The backscattered power decays at a rate of 1=4pR 2 away from the target. The power 7.2 RADAR EQUATION 199 density (in watts per square meters) of the echo signal back to the radar antenna location is Power density backscattered by target and returned to radar location ¼ P t G t 4pR 2 s 4pR 2 ð7:9Þ The radar receiving antenna captures only a small portion of this backscattered power. The captured receiving power is given by P r ¼ returned power captured by radar ðWÞ¼ P t G t 4pR 2 s 4pR 2 A er ð7:10Þ Replacing A er with G r l 2 0 =4p,wehave P r ¼ P t G t 4pR 2 s 4pR 2 G r l 2 0 4p ð7:11Þ For monostatic radar, G r ¼ G t , and Eq. (7.11) becomes P r ¼ P t G 2 sl 2 0 ð4pÞ 3 R 4 ð7:12Þ This is the radar equation. If the minimum allowable signal power is S min , then we have the maximum allowable range when the received signal is S i;min . Let P r ¼ S i;min : R ¼ R max ¼ P t G 2 sl 2 0 ð4pÞ 3 S i;min ! 1=4 ð7:13Þ where P t ¼ transmitting power ðWÞ G ¼ antenna gain ðlinear ratio; unitlessÞ s ¼ radar cross section ðm 2 Þ l 0 ¼ free-space wavelength ðmÞ S i;min ¼ minimum receiving signal ðWÞ R max ¼ maximum range ðmÞ This is another form of the radar equation. The maximum radar range ðR max Þ is the distance beyond which the required signal is too small for the required system 200 RADAR AND SENSOR SYSTEMS operation. The parameters S i;min is the minimum input signal level to the radar receiver. The noise factor of a receiver is defined as F ¼ S i =N i S o =N o where S i and N i are input signal and noise levels, respectively, and S o and N o are output signal and noise levels, respectively, as shown in Fig. 7.3. Since N i ¼ kTB,as shown in Chapter 5, we have S i ¼ kTBF S o N o ð7:14Þ where k is the Boltzmann factor, T is the absolute temperature, and B is the bandwidth. When S i ¼ S i;min , then S o =N o ¼ðS o =N o Þ min . The minimum receiving signal is thus given by S i;min ¼ kTBF S o N o  min ð7:15Þ Substituting this into Eq. (7.13) gives R max ¼ P t G 2 sl 2 0 ð4pÞ 3 kTBF S o N o  min 2 6 6 4 3 7 7 5 1 4 ð7:16Þ where k ¼ 1:38  10 À23 J=K, T is temperature in kelvin, B is bandwidth in hertz, F is the noise figure in ratio, (S o =N o Þ min is minimum output signal-to-noise ratio in ratio. Here (S o =N o Þ min is determined by the system performance requirements. For good probability of detection and low false-alarm rate, ðS o =N o Þ min needs to be high. Figure 7.4 shows the probability of detection and false-alarm rate as a function of ðS o =N o Þ.AnS o =N o of 10 dB corresponds to a probability of detection of 76% and a false alarm probability of 0.1% (or 10 À3 ). An S o =N o of 16 dB will give a probability of detection of 99.99% and a false-alarm rate of 10 À4 % (or 10 À6 ). FIGURE 7.3 The SNR ratio of a receiver. 7.2 RADAR EQUATION 201 7.3 RADAR EQUATION INCLUDING PULSE INTEGRATION AND SYSTEM LOSSES The results given in Fig. 7.4 are for a single pulse only. However, many pulses are generally returned from a target on each radar scan. The integration of these pulses can be used to improve the detection and radar range. The number of pulses ðnÞ on the target as the radar antenna scans through its beamwidth is n ¼ y B _ yy s  PRF ¼ y B _ yy s 1 T p ð7:17Þ where y B is the radar antenna 3-dB beamwidth in degrees, _ yy s is the scan rate in degrees per second, PRF is the pulse repetition frequency in pulses per second, T p is FIGURE 7.4 Probability of detection for a sine wave in noise as a function of the signal-to- noise (power) ratio and the probability of false alarm. (From reference [1], with permission from McGraw-Hill.) 202 RADAR AND SENSOR SYSTEMS the period, and y B = _ yy s gives the time that the target is within the 3-dB beamwidth of the radar antenna. At long distances, the target is assumed to be a point as shown in Fig. 7.5. Example 7.1 A pulse radar system has a PRF ¼ 300 Hz, an antenna with a 3-dB beamwidth of 1:5  , and an antenna scanning rate of 5 rpm. How many pulses will hit the target and return for integration? Solution Use Eq. (7.17): n ¼ y B _ yy s  PRF Now y B ¼ 1:5  _ yy s ¼ 5 rpm ¼ 5  360  =60 sec ¼ 30  =sec PRF ¼ 300 cycles=sec n ¼ 1:5  30  =sec  300=sec ¼ 15 pulses j FIGURE 7.5 Concept for pulse integration. 7.3 RADAR EQUATION INCLUDING PULSE INTEGRATION AND SYSTEM LOSSES 203 Another system consideration is the losses involved due to pointing or misalignment, polarization mismatch, antenna feed or plumbing losses, antenna beam-shape loss, atmospheric loss, and so on [1]. These losses can be combined and represented by a total loss of L sys . The radar equation [i.e., Eq. (7.16)] is modified to include the effects of system losses and pulse integration and becomes R max ¼ P t G 2 sl 2 0 n ð4pÞ 3 kTBFðS o =N o Þ min L sys "# 1=4 ð7:18Þ where P t ¼ transmitting power; W G ¼ antenna gain in ratio ðunitlessÞ s ¼ radar cross section of target; m 2 l 0 ¼ free-space wavelength; m n ¼ number of hits integrated ðunitlessÞ k ¼ 1:38  10 À23 J=K ðBoltzmann constantÞðJ ¼ W=secÞ T ¼ temperature; K B ¼ bandwidth; Hz F ¼ noise factor in ratio ðunitlessÞ ðS o =N o Þ min ¼ minimum receiver output signal-to-noise ratio ðunitlessÞ L sys ¼ system loss in ratio ðunitlessÞ R max ¼ radar range; m For any distance R,wehave R ¼ P t G 2 sl 2 0 n ð4pÞ 3 kTBFðS o =N o ÞL sys "# 1=4 ð7:19Þ As expected, the S o =N o is increased as the distance is reduced. Example 7.2 A 35-GHz pulse radar is used to detect and track space debris with a diameter of 1 cm [radar cross section ðRCSÞ¼4:45  10 À5 m 2 ]. Calculate the maximum range using the following parameters: P t ¼ 2000 kW ðpeaksÞ T ¼ 290 K G ¼ 66 dB ðS o =N o Þ min ¼ 10 dB B ¼ 250 MHz L sys ¼ 10 dB F ¼ 5dB n ¼ 10 204 RADAR AND SENSOR SYSTEMS Solution Substitute the following values into Eq. (7.18): P t ¼ 2000 kW ¼ 2  10 6 W k ¼ 1: 38  10 À23 J=K G ¼ 66 dB ¼ 3:98  10 6 T ¼ 290 K B ¼ 250 MHz ¼ 2:5  10 8 Hz s ¼ 4:45  10 À5 m 2 F ¼ 5dB¼ 3:16 l 0 ¼ c=f 0 ¼ 0:00857 m ðS o =N o Þ min ¼ 10 dB ¼ 10 L sys ¼ 10 dB ¼ 10 n ¼ 10 Then we have R max ¼ P t G 2 sl 2 0 n ð4pÞ 3 kTBFðS o =N o Þ min L sys "# 1=4 ¼ 2  10 6 W Âð3:98  10 6 Þ 2  4:45  10 À5 m 2 Âð0:00857 mÞ 2  10 ð4pÞ 3  1:38  10 À23 J=K  290 K  2:5  10 8 =sec  3:16  10  10 "# 1=4 ¼ 3:58  10 4 m ¼ 35:8km j From Eq. (7.19), it is interesting to note that the strength of a target’sechois inversely proportional to the range to the fourth power ð1=R 4 Þ. Consequently, as a distant target approaches, its echoes rapidly grow strong. The range at which they become strong enough to be detected depends on a number of factors such as the transmitted power, size or gain of the antenna, reflection characteristics of the target, wavelength of radio waves, length of time the target is in the antenna beam during each search scan, number of search scans in which the target appears, noise figure and bandwidth of the receiver, system losses, and strength of background noise and clutter. To double the range would require an increase in transmitting power by 16 times, or an increase of antenna gain by 4 times, or the reduction of the receiver noise figure by 16 times. 7.4 RADAR CROSS SECTION The RCS of a target is the effective (or fictional) area defined as the ratio of backscattered power to the incident power density. The larger the RCS, the higher the power backscattered to the radar. The RCS depends on the actual size of the target, the shape of the target, the materials of the target, the frequency and polarization of the incident wave, and the incident and reflected angles relative to the target. The RCS can be considered as the effective area of the target. It does not necessarily have a simple relationship to the physical area, but the larger the target size, the larger the cross section is likely to be. The shape of the target is also important in determining the RCS. As an example, a corner reflector reflects most incident waves to the incoming direction, as shown in Fig. 7.6, but a stealth bomber will deflect the incident wave. The building material of 7.4 RADAR CROSS SECTION 205 [...]... search radar or acquisition radar provides the target coordinates for the tracking radar The tracking radar acquires the target by performing a limited search in the area of the designated target coordinates provided by the search radar There are two major types of tracking radar: continuous-tracking radar and trackwhile-scan radar The continuous-tracking radar provides continuous-tracking data on a... optimal performance, the pulse width is designed such that [1] Bt % 1 ð7:23Þ where B is the bandwidth Example 7.3 A pulse radar transmits a train of pulses with t ¼ 10 ms and Tp ¼ 1 msec Determine the PRF, duty cycle, and optimum bandwidth Solution The pulse repetition frequency is given as 1 1 ¼ 103 Hz ¼ Tp 1 msec t 10 msec  100% ¼ 1% Duty cycle ¼  100% ¼ Tp 1 msec 1 B ¼ ¼ 0:1 MHz t PRF ¼ j Figure... signal is amplified by multiple-stage power amplifiers (solid-state devices or tubes) and passed through a 7.5 PULSE RADAR 211 duplexer to the antenna for transmission to free space The duplexer could be a circulator or a transmit=receive (T=R) switch The circulator diverts the signal moving from the power amplifier to the antenna The receiving signal will be directed to the mixer If it is a single-pole,... transmitting and receiving can be used Since fd is generally less than 1 MHz, the system suffers from the flicker noise ð1=f noise) To improve the sensitivity, an intermediate-frequency receiver system can be used Figure 7.14 shows two different types of such a system One uses a single antenna and the other uses two antennas FIGURE 7.14 CW radar using superheterodyne technique to improve sensitivity: (a) singleantenna... noise leaked to the receiver limits the receiver sensitivity and the range performance For these reasons, the CW radar is used only for short or moderate ranges A two-antenna system can improve the transmitter-to-receiver isolation, but the system is more complicated Although the CW radar can be used to measure the target velocity, it does not provide any range information because there is no timing... for transmitter–receiver isolation improvement The returned signal is f1 Æ fd The plus sign stands for the target moving toward the radar and the minus sign for the target moving away from the radar Let us consider the following two cases: The target is stationary, and the target is moving 7.7.1 Stationary-Target Case For simplicity, a stationary target is first considered In this case, the doppler frequency... can be determined by measuring fR , which is the IF beat frequency at the receiving time (i.e., t2 ) FIGURE 7.15 Block diagram of an FMCW radar 218 RADAR AND SENSOR SYSTEMS FIGURE 7.16 An FMCW radar with a triangular frequency modulation waveform for a stationary target case 7.7.2 Moving-Target Case If the target is moving, a doppler frequency shift will be superimposed on the range beat signal It... the output frequency from the mixer is f2 À f1 Ç fd , as shown in Fig 7.15 The minus sign is for the target moving toward the radar, and the plus sign is for the target moving away from the radar 7.7 FREQUENCY-MODULATED CONTINUOUS-WAVE RADAR 219 Figure 7.17(b) shows the waveform for a target moving toward radar For comparison, the waveform for a stationary target is also shown in Fig 7.17(a) During the... ð7:33Þ During the period when the frequency is decreased, the beat frequency is fb ðdownÞ ¼ fR þ fd ð7:34Þ FIGURE 7.17 Waveform for a moving target: (a) stationary target waveform for comparison; (b) waveform for a target moving toward radar; (c) beat signal from a target moving toward radar 220 RADAR AND SENSOR SYSTEMS The range information is in fR , which can be obtained by fR ¼ 1 ½ fb ðupÞ þ fb ðdownފ... obviously an influence on the RCS If the target is made of wood or plastics, the reflection is small As a matter of fact, Howard Hughes tried to build a wooden aircraft (Spruce Goose) during World War II to avoid radar detection For a metal body, one can coat the surface with absorbing materials (lossy dielectrics) to reduce the reflection This is part of the reason that stealth fighters=bombers are invisible . Monostatic radar uses a single antenna serving as a transmitting and receiving antenna. The transmitting and receiving signals are separated by a duplexer and weapon control. However, increasing civil applications have been seen in the past 20 years for traffic control and navigation of aircraft, ships, and automobiles,