RCS in Radar Range Calculations for Maritime …

1 1 RCS in Radar Range Calculationsfor Maritime TargetsbyIngo Harre,Bremen, Germany( )1 AbstractThis web page deals with the RCS ( Radar Cross Section) parameter and its application inradar Range Calculations for the detection of Maritime targets . It is the intention of the authorto compile the basic facts, which are spread in the technical literature and difficult to find, andto comment them where necessary. RCS data of ships quoted even in technical standards,are often incomplete in that their conditions, such as Radar frequency, applicable targetaspect Range , and statistical properties, are missing. These conditions should be taken intoaccount when performing Radar Range Calculations in order to obtain meaningful results. Inthis paper the basic facts related to RCS shall be elucidated. Where there are openquestions yet, these will be What is DefinitionsIn Radar reference books we find various definitions for RCS, :BARTON1, Measure of the reflective strength of a target.

2 The E. W. Handbook of Navy defines, A measure of the Radar reflection characteristicsof a target. It is equal to the power reflected back to the Radar divided by power density of thewave striking the target. For most targets , the Radar cross section is the area of the crosssection of the sphere that would reflect the same energy back to the Radar if the sphere weresubstituted. RCS of sphere is independent of frequency if operating in the far field region .SKOLNIK2 provides the following short and concise definition, The Radar cross section of atarget is the (fictional) area intercepting that amount of power which, when scattered equallyin all directions, produces an echo at the Radar equal to that from the target . PhysicsRadiation theory teaches us the energy intercepted by an object can be reflected, absorbed,or transmitted through the target.

3 The respective shares of the energy add up to 100 %. Withthe Maritime targets of interest here, we can assume that most of the energy is , as understood in this paper, shall represent the reflective strength of a Radar , denoted by the Greek letter and measured in m , is defined as3:isPP 4 =Pi := power density, or intensity, of a plane wave striking the target, (W/m ),Ps := power per unit solid angle reflected by the target, (W/sr = W).RCS has a wide spread ranging from 10-5 for small insects to 106 for large ships. Hence,RCS is often stated in the logarithmic decibel scale: =2dBsqmm1 log10 RCS is a function of:4 Position of transmitter/receiver relative to target, Target geometry and material composition, Angular orientation of target relative to transmitter/receiver, Frequency or wavelength, Antenna The Importance of RCS in Radar Range CalculationsThe following formula is used in the author's Blanket algorithm5 and makes it possible todetermine the free space Range of a Radar system, the hypothetic maximum Radar Range .

4 ( )( )4/1sn0322pfsLN/SFBTk 4 GPR =The parameters in the formula are predominantly either physical constants or equipmentparameters with well defined values, see Table 1 below. In practical applications the twoparameters and SN have distinct statistical properties so that the calculated Range itselfinherits statistical properties: the Range is related to a certain detection , the theories of handling signals with noise and fluctuating Radar targets are wellresearched since a long time. Common Radar Range prediction programs, such as CARPET,are taking appropriate care of the two statistical not all Range calculation formulae or programs, however, it becomes evident that RCS offluctuating targets must be handled in a proper way to achieve meaningful data. Eq. 3Eq. 1Eq. 3Eq. 23above, for instance, S/N must be increased to take care of target echo fluctuations using theappropriate Swerling DescriptionCommentPpPeak pulse powerEquipment parameterGAntenna gainEquipment parameter Radar cross section of targetParameter with large statistical variationsfor complex Radar targets .

5 A ship Wavelength of Radar frequency Equipment parameterKBoltzmann's constantPhysical constantT0 Absolute temperature of the radarreceiver circuitryPhysical variableBBandwidthEquipment parameterFnNoise figure of the Radar receiver Equipment parameterS/NSignal-to-noise ratio required fordetectionEquipment parameter dependent on thedesired detection probability for a givenfalse alarm rateLsSystem lossesEquipment parameter dependent on thelosses of microwave radiation on thepath from the transmitter to the antennaand vice versaTable 1: Radar Range calculation Parameters4 RCS of Objects and its determinationSKOLNIK states in his RCS definition that RCS is a fictional area. The term area refers tothe unit being m . Fictional means that RCS can actually be much larger than the reflectivesurface, as the following formula shows:DRA: p =Ap : = projected object surface,R : = Reflectivity, re-radiated fraction of intercepted power,D : = Directivity, ratio of the maximum intensity of the radiator to theintensity of an isotropic the reflectivity is usually smaller than unity and material dependent, the directivitycan be much larger and depends on the shape of the RCS of Simple Target ObjectsFor simple target objects, such as flat rectangular plates, cylinders, spheres, RCS can becalculated using Maxwell s equations with certain boundary conditions.

6 Figure 1 shows threesimple objects with the principal dimension of 1 m and their 44 Rectangular Plate CylinderSphereaahdd24 a 4 = hd 2 =22d = for a = 1m: for h= 1m and d = m: for d = 1 m:X band: 12,300 m X band: 50 m X band: m S band: 1,300 m S band: 16 m S band: m Figure 1: Simple RCS of Complex Objects and its determinationA complex target is one that consists of several reflectors within a Radar resolution Radar resolution cell is delineated by the Radar pulse s length and width of arc in the this definition, almost all real-world Maritime targets are complex targets . For suchtargets there is no firm relationship between a target s surface and RCS. Hence, the RCSmust be determined in other obvious method of determining RCS is to put the object of interest, be it a ship or anaircraft, into a controlled environment and to use a calibrated Radar system to measure theecho power.

7 The target s RCS can then be established using the Radar Range equation takingcare of all system parameters and environmental losses. This is basically the procedureperformed in so-called 'measuring ranges '. Measurements are usually performed for a 360 aspect arc, at various grazing angles, and often for different Radar frequencies. Figure 2: Aspect and grazing angles5 The aspect of a target is its orientation to the axis of the Radar beam.. The nearer the anglebetween the reflecting area and the beam axis is 90 , the greater is the strength of the echo returnedto the antenna 7. Grazing angle is the angle measured in the vertical plane between the ray and areflecting surface. 1 When performing Range Calculations , the orientation of a target with respect to the Radar isoften just roughly known. This is, for instance, frequently the case in ship encounters at theopen sea.

8 In order to provide a singleRCS value representing a certain type and size of shipone should define a value with a firm statistical significance4. The median value derived fromthe measurement data set is often used for this purpose. ( chapter 6).This single RCS value can then be conceived as that of a Radar reflector representing theship. The ideal Radar reflector is a sphere, due to its non-directivity and frequencydependence, RCS definitions in chapter This RCS value representing the ship isoften accompanied by a height ( chapter 9).The larger and less mobile a target, the more expensive is the determination of RCS in ameasuring Range . To save cost, a size-reduced model with appropriately scaled radarfrequencies can be used. Another possibility is to simulate the measurements usingcomputer-based methods. By means of construction plans, the target can be decomposedinto simple computable reflector elements.

9 The RCS at each aspect angle is then determinedby summation of the RCS of the reflecting Statistical Properties of RCSIt has been mentioned above that the echo strength of Maritime targets fluctuates a greatdeal from one echo received to the next. This fluctuation is caused by several effects: predominantly random effects, target scintillation, multipath effects,environmental effects, as caused by atmosphere and seastate, systematic effects related to the scattering characteristics, target strengthvariations due to aspect and grazing angle practice these types of fluctuation can hardly be separated from each other and, hence,are treated statistically in common. If an RCS data set with sufficiently large number ofmeasurements exists, its statistical properties can be determined: the RCS mean or median value and the shape of the probability density function (PDF), the autocorrelation function (ACF).

10 In 1954 Peter Swerling has published five model cases6 describing typical Radar echofluctuations. These models can be used in Radar Range Calculations to determine additionalS/N margins taking care of the fluctuations6,2 . In order to determine the applicable Swerlingcase the PDF and the ACF should be targets are usually characterised by echoes, which do not fluctuate much from oneradar pulse to the next, successive echoes have significant similarity, whereas echoesfrom two successive scans are independent from each other (uncorrelated). Such type offluctuations is described by Swerling case 1, which is characterised by the following PDF:6 =avav exp 1) (p av := RCS mean valueA Swerling case 1 target is characterised by many scatterers of comparable size. Case 1 isthe basic model for most complex scatterers, including Maritime targets (ships and radarreflectors).