of the resulting product. Fast convolution results in significant computational savin performing the time- domain convolution of returns with the filter function corresponding to the mato er. The signal processor output can be characterized in terms of range gates and Doppler filters corresp approximately to the range and Doppler resolution, respectively In contrast, the radar data processor typically consists of a general-purpose computer with a real-time operating system. Fielded radar data processors range from microcomputers to mainframe computers, depend ing on the requirements of the radar system. Data processor software and hardware requirements are signifi- cantly mitigated by off loading timing and control functions to specialized hardware. This timing and control subsystem typically functions as the two-way interface between the data processor and the other radar sub systems. The increasing inclusion of Bit (built-in-test)and built-in calibration capability in timing and control ubsystem designs promises to result in significant improvement in fielded system performance. Radar Performance Prediction Radar Line-of Sight With the exception of over-the-horizon(OTH)radar systems, which exploit either sky-wave bounce or ground wave propagation modes and sporadic ducting effects at higher frequencies, surface and airborne platfor dar operation is limited to the refraction-constrained line of sight. Atmospheric refraction effects can be closely approximated by setting the earths radius to 4/3 its nominal value in estimating horizon-limited range. The resulting line-of-sight range is depicted in Fig. 41.3 for a surface-based radar, an airborne surveillance radar and 10000 SPACE-BASED RADAR: 600 KM ALTTTUDE 0 AIRBORNE RADAR: 10KM ALTITUDE SURFACE-BASED RADAR TARGET ALTITUDE(KM) surface-based radar, an airb ased c2000 by CRC Press LLC
© 2000 by CRC Press LLC of the resulting product. Fast convolution results in significant computational saving over performing the timedomain convolution of returns with the filter function corresponding to the matched filter. The signal processor output can be characterized in terms of range gates and Doppler filters corresponding approximately to the range and Doppler resolution, respectively. In contrast, the radar data processor typically consists of a general-purpose computer with a real-time operating system. Fielded radar data processors range from microcomputers to mainframe computers, depending on the requirements of the radar system. Data processor software and hardware requirements are signifi- cantly mitigated by off loading timing and control functions to specialized hardware. This timing and control subsystem typically functions as the two-way interface between the data processor and the other radar subsystems. The increasing inclusion of BIT (built-in-test) and built-in calibration capability in timing and control subsystem designs promises to result in significant improvement in fielded system performance. Radar Performance Prediction Radar Line-of-Sight With the exception of over-the-horizon (OTH) radar systems, which exploit either sky-wave bounce or groundwave propagation modes and sporadic ducting effects at higher frequencies, surface and airborne platform radar operation is limited to the refraction-constrained line of sight. Atmospheric refraction effects can be closely approximated by setting the earth’s radius to 4/3 its nominal value in estimating horizon-limited range. The resulting line-of-sight range is depicted in Fig. 41.3 for a surface-based radar, an airborne surveillance radar, and a space-based radar. FIGURE 41.3 Maximum line-of-sight range for surface-based radar, an airborne surveillance radar, and a space-based radar
evident in the plot, airborne and space-based surveillance radar systems offer significant advantages the detection of low-altitude targets that would otherwise be masked by earth curvature and terrain features from surface-based radars. However, efficient clutter rejection techniques must be used in order to detect targets since surface clutter returns will be present at almost all ranges of interest. Radar Range Equation The radar range equation is commonly used to estimate radar system performance, given that line-of-sight onditions are satisfied. This formulation essentially computes the signal-to-noise ratio(SN) at the output the radar signal processor. In turn, SNis used to provide estimates of radar detection and position measurement performance as described in the subsections "Detection and Search"and"Estimation and Tracking. SN can be calculated in terms of the number of pulses coherently integrated over a single coherent processing interval ( CPI)using the radar range equation such that S/N PDAN° (41.1) (4)R'L,L,LsnkT where P is peak transmitter power output, D is directivity of the transmit antenna, A is effective aperture area of the receive antenna in meters squared, T, is pulse duration, o is radar cross section in square meters, N, is er of coherently inge to target meters, L, is system ohmic and nonohmic transmit losses, Lm is system nonohmic receive losses, L,p is signal processing losses, k is Boltzmanns constant(1.38 X 10-23K), and T, is system noise temperature, including At X-band and above it may also be necessary to include propagation loss due to atmospheric absorption [Blake, 1986]. This form of the radar range equation is applicable to radar systems using pulse compression or bulse Doppler waveforms as well as the unmodulated single-pulse case. In many applications, average power is a better measure of system performance than peak power since it indicates the S/N improvement achievable with pulse integration over a given interval of time. Hence, the radar range equation can be modified such that S/N= P DATO (4兀)2RL1L where P is average transmitter power and T is coherent processing interval(CPI) The portion of time over which the transmitter is in operation is referred to as the radar duty cycle. The average transmitter power is the product of duty cycle and peak transmitter power. Duty cycle ranges from less than 1%for typical noncoherent pulse radars to somewhat less than 50% for high pulse repetition frequency (PRF) Pulse Doppler radar systems. High PRF systems are sometimes referred to as interrupted continuous wave(ICW)systems because they operate essentially as a Cw radar system with transmitter and receiver alternately turned on and off. The CPI is the period over which returns are collected for coherent processing functions such as integration and Doppler filtering. The CPI can be estimated as the product of the number of coherently integrated pulses and the interval between pulses. Noncoherent integration is less efficient and alters the statistical character of Antenna Directivity and Aperture Area The directivity of the antenna is 4兀An e 2000 by CRC Press LLC
© 2000 by CRC Press LLC As evident in the plot, airborne and space-based surveillance radar systems offer significant advantages in the detection of low-altitude targets that would otherwise be masked by earth curvature and terrain features from surface-based radars. However, efficient clutter rejection techniques must be used in order to detect targets since surface clutter returns will be present at almost all ranges of interest. Radar Range Equation The radar range equation is commonly used to estimate radar system performance, given that line-of-sight conditions are satisfied. This formulation essentially computes the signal-to-noise ratio (S/N) at the output of the radar signal processor. In turn, S/N is used to provide estimates of radar detection and position measurement performance as described in the subsections “Detection and Search” and “Estimation and Tracking.” S/N can be calculated in terms of the number of pulses coherently integrated over a single coherent processing interval (CPI) using the radar range equation such that (41.1) where P is peak transmitter power output, D is directivity of the transmit antenna, A is effective aperture area of the receive antenna in meters squared, Tp is pulse duration, s is radar cross section in square meters, Np is the number of coherently integrated pulses within the coherent processing interval, R is range to target in meters, Lt is system ohmic and nonohmic transmit losses, Lrn is system nonohmic receive losses, Lsp is signal processing losses, k is Boltzmann’s constant (1.38 ¥ 10–23 K), and Ts is system noise temperature, including receive ohmic losses (kelvin). At X-band and above it may also be necessary to include propagation loss due to atmospheric absorption [Blake, 1986]. This form of the radar range equation is applicable to radar systems using pulse compression or pulse Doppler waveforms as well as the unmodulated single-pulse case. In many applications, average power is a better measure of system performance than peak power since it indicates the S/N improvement achievable with pulse integration over a given interval of time. Hence, the radar range equation can be modified such that (41.2) where Pa is average transmitter power and Tc is coherent processing interval (CPI). The portion of time over which the transmitter is in operation is referred to as the radar duty cycle. The average transmitter power is the product of duty cycle and peak transmitter power. Duty cycle ranges from less than 1% for typical noncoherent pulse radars to somewhat less than 50% for high pulse repetition frequency (PRF) pulse Doppler radar systems. High PRF systems are sometimes referred to as interrupted continuous wave (ICW) systems because they operate essentially as a CW radar system with transmitter and receiver alternately turned on and off. The CPI is the period over which returns are collected for coherent processing functions such as integration and Doppler filtering. The CPI can be estimated as the product of the number of coherently integrated pulses and the interval between pulses. Noncoherent integration is less efficient and alters the statistical character of the signal and interference. Antenna Directivity and Aperture Area The directivity of the antenna is (41.3) S N PDAT N R L L L kT p p t rn sp s / = s (4p) 2 4 S N P DAT R L L L kT a c t rn sp s / = s (4p) 2 4 D A = 4 2 p h l
TABLE 41.3 Median Target RCS (m2) Carrier Frequency, GHz Aircraft(nose/tail avg) 2.5 Small jet(Lear) T38-twin jet, F5 0/8 4-20/10 27, 707, DC8-type DC-10-type, 747 Ryan drone Standing man(180 Ib) Ships-incoming(x10 m2) 4K tons birds 0.001-0.0040.004 0.001 0.00l00010.001 Slash marks indicate different set where n is aperture efficiency and A is radar carrier wavelength. Aperture inefficiency is due to the antenna illumination factor The common form of the radar range equation uses power gain rather than directivity. antenna gain is equi to the directivity divided by the antenna losses. In the design and analysis of modern radars, directivity is a more convenient measure of performance because it permits designs with distributed active elements, such as solid-state phased arrays, to be assessed to permit direct comparison with passive antenna systems. Beamwidth and directivity are inversely related; a highly directive antenna will have a narrow beamwidth. For typical design D e 0 where Aa and ee are the radar azimuth and elevation beamwidths, respectively, in milliradians. Radar Cross section In practice, the radar cross section(RCS)of a realistic target must be considered a random variable with an associated correlation interval. Targets are composed of multiple interacting scatters so that the composite return varies in magnitude with the constructive and destructive interference of the contributing returns. The target RCS is typically estimated as the mean or median of the target RCS distribution. The associated correlation interval indicates the rate at which the target RCS varies over time. RCS fluctuation degrades target detection performance at moderate to high probability of detection. The median RCS of typical targets is given in Table 41.3. The composite RCS measured by a radar system may be composed of multiple individual targets in the case of closely spaced targets such as a bird flock. Loss and System Temperature Estimation Sources of S/N loss include ohmic and nonohmic(mismatch)loss in the antenna and other radio frequency components, propagation effects, signal processing deviations from matched filter operation, detection thresh olding, and search losses. Scan loss in phased array radars is due to the combined effects of the decrease in projected antenna area and element mismatch with increasing scan angle c2000 by CRC Press LLC
© 2000 by CRC Press LLC where h is aperture efficiency and l is radar carrier wavelength. Aperture inefficiency is due to the antenna illumination factor. The common form of the radar range equation uses power gain rather than directivity. Antenna gain is equal to the directivity divided by the antenna losses. In the design and analysis of modern radars, directivity is a more convenient measure of performance because it permits designs with distributed active elements, such as solid-state phased arrays, to be assessed to permit direct comparison with passive antenna systems. Beamwidth and directivity are inversely related; a highly directive antenna will have a narrow beamwidth. For typical design parameters, (41.4) where qaz and qel are the radar azimuth and elevation beamwidths, respectively, in milliradians. Radar Cross Section In practice, the radar cross section (RCS) of a realistic target must be considered a random variable with an associated correlation interval. Targets are composed of multiple interacting scatters so that the composite return varies in magnitude with the constructive and destructive interference of the contributing returns. The target RCS is typically estimated as the mean or median of the target RCS distribution. The associated correlation interval indicates the rate at which the target RCS varies over time. RCS fluctuation degrades target detection performance at moderate to high probability of detection. The median RCS of typical targets is given in Table 41.3. The composite RCS measured by a radar system may be composed of multiple individual targets in the case of closely spaced targets such as a bird flock. Loss and System Temperature Estimation Sources of S/N loss include ohmic and nonohmic (mismatch) loss in the antenna and other radio frequency components, propagation effects, signal processing deviations from matched filter operation, detection thresholding, and search losses. Scan loss in phased array radars is due to the combined effects of the decrease in projected antenna area and element mismatch with increasing scan angle. TABLE 41.3 Median Target RCS (m2 ) Carrier Frequency, GHz 1–2 3 5 10 17 Aircraft (nose/tail avg.) Small propeller 2 3 2.5 Small jet (Lear) 1 1.5 1 1.2 T38-twin jet, F5 2 2–3 2 1–2/6 T39-Sabreliner 2.5 10/8 9 F4, large fighter 5–8/5 4–20/10 4 4 737, DC9, MD80 10 10 10 10 10 727, 707, DC8-type 22–40/15 40 30 30 DC-10-type, 747 70 70 70 70 Ryan drone 2/1 Standing man (180 lb) 0.3 0.5 0.6 0.7 0.7 Automobiles 100 100 100 100 100 Ships-incoming (¥104 m2 ) 4K tons 1.6 2.3 3.0 4.0 5.4 16K tons 13 18 24 32 43 Birds Sea birds 0.002 0.001–0.004 0.004 Sparrow, starling, etc. 0.001 0.001 0.001 0.001 0.001 Slash marks indicate different set. D az el = 107 q q
TABLE 41.4 Typical Microwave Loss and System Temperature Budgets Mechanically Scanned Electronically Scanned Reflector Slotted Solid-State Phased Array Transmit loss, L,(dB) Nonohmic receiver loss, L,(dB) Signal processing loss, L,(dB) Scan loss(dB) N/A 30 log [cos(scan angle)I Search losses, Lps 3 Range gate straddle(dB) Doppler filter straddle(dB) Detection thresholding(dB) System noise temperature (kelvin) 600 earch operations impose additional losses due to target position uncertainty. Because the target positio unknown before detection, the beam, range gate, and Doppler filter will not be centered on the target return. Hence, straddling loss will occur as the target effectively straddles adjacent resolution cells in range and Doppler. Beamshape loss is a consequence of the radar beam not being pointed directly at the target so that there is loss in both transmit and receive antenna gain. In addition, detection threshold loss associated with radar system adaptation to interference must be included [ Nathanson, 1991]) System noise temperature estimation corresponds to assessing the system thermal noise floor referenced to the antenna output. Assuming the receiver hardware is at ambient temperature, the system noise temperature T 90(L。F-1) where T, is the antenna noise temperature, Lm is receive ohmic losses, and F is the receiver noise figure. In phased array radars, the thermodynamic temperature of the antenna receive beam-former may be signif icantly higher than ambient, so a more complete analysis is required. The antenna noise temperature is determined by the external noise received by the antenna from solar, atmospheric, earth surface, and other sources. Table 41.4 provides typical loss and noise temperature budgets for several major radar classes. In general, loss increases with the complexity of the radar hardware between the transmitter/receiver and the antenna radiator Reflector antennas and active phased arrays impose relatively low loss, while passive array antennas impose relatively high loss Resolution and Accuracy The fundamental resolution capabilities of a radar system are summarized in Table 41.5. In general, there is a trade-off between mainlobe resolution corresponding to the nominal range, Doppler, and angle resolution, an effective dynamic range corresponding to suppression of sidelobe components. This is evident in the use weighting to suppress Doppler sidebands and angle sidelobes at the expense of broadening the mainlobe and Cross range denotes either of the two dimensions orthogonal to the radar line of sight. Cross-range resolution in real-aperture antenna systems is closely approximated by the product of target range and radar beamwidth processing to generate a focused image, including correction for scatterer change in range over the CP nal in radians. Attainment of the nominal ISAR/SAR cross-range resolution generally requires comple The best accuracy performance occurs for the case of thermal noise-limited error. The resulting accuracy is the resolution of the radar divided by the square root of the SNand an appropriate monopulse or interpolation factor. In this formulation, the single-pulse SN has been multiplied by the number of pulses integrated within the CPI as indicated in Eqs. (41.1)and(41. 2) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Search operations impose additional losses due to target position uncertainty. Because the target position is unknown before detection, the beam, range gate, and Doppler filter will not be centered on the target return. Hence, straddling loss will occur as the target effectively straddles adjacent resolution cells in range and Doppler. Beamshape loss is a consequence of the radar beam not being pointed directly at the target so that there is a loss in both transmit and receive antenna gain. In addition, detection threshold loss associated with radar system adaptation to interference must be included [Nathanson, 1991]). System noise temperature estimation corresponds to assessing the system thermal noise floor referenced to the antenna output. Assuming the receiver hardware is at ambient temperature, the system noise temperature can be estimated as Ts = Ta + 290 (Lr o F – 1) (41.5) where Ta is the antenna noise temperature, Lro is receive ohmic losses, and F is the receiver noise figure. In phased array radars, the thermodynamic temperature of the antenna receive beam-former may be significantly higher than ambient, so a more complete analysis is required. The antenna noise temperature is determined by the external noise received by the antenna from solar, atmospheric, earth surface, and other sources. Table 41.4 provides typical loss and noise temperature budgets for several major radar classes. In general, loss increases with the complexity of the radar hardware between the transmitter/receiver and the antenna radiator. Reflector antennas and active phased arrays impose relatively low loss, while passive array antennas impose relatively high loss. Resolution and Accuracy The fundamental resolution capabilities of a radar system are summarized in Table 41.5. In general, there is a trade-off between mainlobe resolution corresponding to the nominal range, Doppler, and angle resolution, and effective dynamic range corresponding to suppression of sidelobe components. This is evident in the use of weighting to suppress Doppler sidebands and angle sidelobes at the expense of broadening the mainlobe and S/N loss. Cross range denotes either of the two dimensions orthogonal to the radar line of sight. Cross-range resolution in real-aperture antenna systems is closely approximated by the product of target range and radar beamwidth in radians. Attainment of the nominal ISAR/SAR cross-range resolution generally requires complex signal processing to generate a focused image, including correction for scatterer change in range over the CPI. The best accuracy performance occurs for the case of thermal noise-limited error. The resulting accuracy is the resolution of the radar divided by the square root of the S/N and an appropriate monopulse or interpolation factor. In this formulation, the single-pulse S/N has been multiplied by the number of pulses integrated within the CPI as indicated in Eqs. (41.1) and (41.2). TABLE 41.4 Typical Microwave Loss and System Temperature Budgets Mechanically Scanned Electronically Scanned Reflector Slotted Solid-State Antenna Array Phased Array Nominal losses Transmit loss, Lt (dB) 1 1.5 0.5 Nonohmic receiver loss, Lr (dB) 0.5 0.5 0.1 Signal processing loss, Lsp (dB) 1.4 1.4 1.4 Scan loss (dB) N/A N/A 30 log [cos (scan angle)] Search losses, LDS Beam shape (dB) 3 3 3 Range gate straddle (dB) 0.5 0.5 0.5 Doppler filter straddle (dB) 0.5 0.5 0.5 Detection thresholding (dB) 1 1 1 System noise temperature (kelvin) 500 600 400