Ulrawideband Normalized Radar Cross Secions o Disribued Cluer Ram M. Narayanan Deparmen o Elecrical Engineering The Pennsylvania Sae Universiy Universiy Park, PA 68, USA ram@engr.psu.edu Absrac Theoreical and empirical ormulas have been derived o compue he normalized radar cross secion (NRCS) o disribued cluer arges or remoe sensing applicaions. These ormulas are usually parameerized in erms o he cener requency, and are hereore requency-dependen. In recen years, high resoluion measuremens are being invesigaed or improved errain characerizaion using ulrawideband () radar sysems. In such cases, he NRCS value a he cener requency is generally used or calculaions. This approximaion does no cause oo grea an error when he sysem operaes over a narrow requency band, ypically less han %. However, under condiions, errors as large as a ew decibels can occur under his assumpion. We derive an expression or he NRCS o disribued cluer as a uncion o he NRCS value a he cener requency and he racional bandwidh. We show he applicaion o hese resuls in deducing he signal-o-cluer raio (SCR) or represenaive arges. I is seen ha he SCR increases wih increasing racional bandwidh iniially, and hen ends o level o a higher racional bandwidhs. I. RADAR RANGE EQUATION FOR ULTRAWIDEAND WAVEFORMS The power received by a radar sysem P r is obained using he amiliar radar range equaion, given by [] PG λ σ P =, () r 3 4 64π R where P is he ransmi power, λ is he wavelengh, G is he anenna gain, R is he range o he arge, and σ is he radar cross secion (RCS) o he arge. In he above ormulaion, we neglec sysem and propagaion losses o keep he analysis simple. Equaion () is applicable a a single requency = c λ, where c is he speed o ligh. I mus be noed ha boh he anenna gain G and he arge RCS σ are, in general, uncions o requency. Assume ha a wideband signal is now ransmied wih a uniorm power specral densiy over he requency band {, }. The oal power, P r,, received by he radar over he range {, } can be expressed as [] r, = dpr = 3 4 64π R P P c G ( ) σ( ) d, () where = ( ) is he bandwidh. We also deine he racional bandwidh as β =, where he cener requency is denoed as = + ). ( We now consider wo cases or he anenna ype: (a) Aperure anenna, and Frequency independen anenna. A. Aperure Anenna Case Examples o aperure anennas are horn anennas and dish anennas. In such an anenna, he power gain is proporional o he square o he requency, since he anenna becomes elecrically larger as he requency increases and he wavelengh shrinks. The RCS o he arge when using aperure anennas, denoed as σ (A), can be derived as σ (A) σ( ) d =. (3). Frequency Independen Anenna Case Examples o requency independen anennas are logperiodic anennas and Yagi anennas. The radar cross secion (RCS) o he arge when using requency independen anennas, denoed as σ (F), can be derived as σ ( ) (F) = σ d. (4) 978--4673-658-4//$3. IEEE 796
II. FREQUENCY DEPENDENCE OF RADAR CROSS SECTION AND ITS EFFECTS In general, a disribued arge s NRCS dependence wih respec o requency can be expressed as n σ ( ) = σ, (5) where σ is he NRCS a he cener requency and n is assumed known via heory, simulaions, or measuremens. The value o n is generally observed o lie beween and or land cluer [3], wih a value o n = ½ recommended or requencies rom UHF o W-and [4]. Since σ = σ A, where A is he area illuminaed, we have σ σ. Subsiuing he above expression or σ ( ) in (3) and (4) and canceling A on boh sides, we obain and σ n+ (A) n+ σ = d, (6) σ n (F) n σ = d. (7) As, i.e. as, we obain σ σ or boh anenna cases, as expeced. The error in d on using he incorrec NRCS value a insead o using he correc value o σ is given by σ Error (d) = log. (8) σ. Vegeaion Year: 975 Type: Fields o corn, milo, soybeans, alala, whea, grass, and clover (and bare soil a planing ime) Polarizaion: HH Angle o Incidence: A plo o he wideband NRCS or he seleced cluer suraces is shown in Fig.. We noe ha he value o n, given in (5), varies wih boh cluer ype and requency. IV. TARGET CHARACTERISTICS Radar arges have a requency response similar o cluer. Their RCS can be expressed as n σ( ) = σ, (9) where σ is he RCS a he cener requency and n is an ineger normally in he range { 4, + } depending upon he arge geomery and viewing aspec [7]. Three dieren arge ypes were considered based upon heir requency response: Corner relecor (n = ), sphere (n = ), and apex (n = ). Their characerisics were seleced as ollows: A. Corner Relecor Lengh o edge l : m Targe range: m. Sphere Radius r : m Targe range: m C. Apex Apex angle θ : 3 Targe range: 5 m The magniude o he error depends on boh he cener requency and he bandwidh, and i increases wih bandwidh a a given cener requency. III. CLUTTER CHARACTERISTICS Several reerences were sudied in order o obain he requency characerisics o land cluer over a wide range o requencies or analysis. We used published daa on hree cluer ypes: dry snow and we snow [5] and vegeaion [6]. Daa were available over he requency range 6 GHz, as ollows: A. Dry and We Snow Year: 977 Polarizaion: HH Angle o Incidence: 5 Snow Deph: 48 cm Waer Equivalen:.5 cm Fig. : Specral response o NRCS or dry snow, we snow, and vegeaion cluer exraced rom [5] and [6]. 978--4673-658-4//$3. IEEE 797
In our simulaions, requency independen anennas wih consan gain over he requency range were assumed. For his scenario, he RCS o he seleced arges are given by [] Corner Relecor: σ(f) = σ (a) 4 Sphere: σ = σ (F) ( 4 β ) (b) 64 β Apex: σ(f) = σ + 3 ( 4 β ) (c) where β is he racional bandwidh and σ is he RCS o he arge a he cener requency. The SCR is deined as he raio o he power received rom he arge o ha received rom he cluer. Since he received power is proporional o he RCS, we can wrie RCS o arge SCR = RCS o cluer Fig. : Geomery or he pulse lengh limied case. The RCS o above arges are given by: 4 πl Corner Relecor: σ = 3λ (a) Sphere: σ = πr (b) λ 4 Apex: σ = an θ 6π (c) V. SIGNAL-TO-CLUTTER RATIO (SCR) AS A FUNCTION OF RELATIVE ANDWIDTH We compued he SCR or each arge agains each cluer ype a 3 GHz and GHz as a uncion o racional bandwidh β. The anenna beamwidh was assumed o be in all cases. A ypical pulse lengh limied scenario, as shown in Fig., was considered. In Fig., R is he range o he arge, τ is he pulse lengh, θ is he hal-power anenna beamwidh, γ is he depression angle given by (9 θ) where θ is he incidence angle, and Δ x is he ground range resoluion or he pulse lengh limied case. The ground area illuminaed is given by ( θ ) A= R Δ x. () Alhough he above geomery holds or a pulse radar, i can be adoped or he requency-modulaed radar case by replacing he pulse lengh wih he reciprocal o he bandwidh, i.e. by seing τ =. σ o arge =. (3) A σ o cluer Since he racional bandwidh aecs all erms in (), SCR is a uncion o boh he cener requency and he racional bandwidh, i.e. SCR = SCR(, β ). Plos o he SCR are shown in Figs. 3 5. VI. DISCUSSION We noe rom he SCR plos ha he SCR increases iniially as racional bandwidh increases, and hen levels o a higher racional bandwidhs (greaer han abou 3%). In (3), he numeraor increases or a bes remains consan wih increasing β. On he oher hand, in he denominaor, while he illuminaed area A decreases, he NRCS o cluer increases as β increases. Thus, i is possible ha under some condiions, he denominaor may increase aser han he numeraor, causing he SCR o level o and even decrease under cerain condiions (see dry snow plos or corner relecor and sphere a β values greaer han abou 6%. The implicaions o hese resuls are quie signiican. Wih he available elecromagneic (EM) specrum becoming increasingly scarce, a crucial requiremen is one o mulimodal sensor operaion wih ully adapive waveorm capabiliy [8], [9]. Operaing a radar a he highes bandwidh (and he bes resoluion) a all imes has he disadvanage o requiring more processing and no leaving any bandwidh or oher applicaions, such as communicaions or elemery. I SCR enhancemen is he goal, hen i appears ha no much advanage is gained beyond a racional bandwidh o approximaely 35%. 978--4673-658-4//$3. IEEE 798
(a) (a) Fig. 3: SCR as a uncion o racional bandwidh or corner relecor a a cener requency o (a) 3 GHz, and GHz. Fig. 4: SCR as a uncion o racional bandwidh or sphere a a cener requency o (a) 3 GHz, and GHz. 978--4673-658-4//$3. IEEE 799
(a) REFERENCES [] M.I. Skolnik, Inroducion o Radar Sysems, 3 rd ed. New York, NY: McGraw-Hill,. [] R.M. Narayanan, Ulrawideband radar cross secions o radar calibraion arges, Proc. NATO Specialis Meeing on Ulra- Wideband-Radar Sysems (RTO-MP-SET-), Toulouse, France, pp. 8-8-8, Ocober 8. [3] J.P. Reilly, R.L. McDonald, G.D. Dockery, and J. Sapleon, RF- Environmen Models or he ADSAM Program, JHU/APL Final Repor AA97U-7, Augus 997. [4] F.E. Nahanson, J.P. Reilly, and M.N. Cohen, Radar Design Principles: Signal Processing and he Environmen, nd ed. New York, NY: McGraw-Hill, 99. [5] F.T. Ulaby and W.H. Siles, Microwave response o snow, Advances in Space Research, vol., pp. 3 49, 98. [6] F.T. Ulaby, Vegeaion cluer model, IEEE Transacions on Anennas and Propagaion, vol. AP-8, no. 4, pp. 538 545, 98. [7] E.F. Kno, EM waves and he releciviy process, Chaper in Principles o Modern Radar, J.L. Eaves and E.K. Reedy, eds. New York, NY: Van Nosrand Reinhold, 987. [8] D.M. Manners, ART An adapive radar esbed, Proc. IEE Colloquium on Real-Time Managemen o Adapive Radar Sysems, London, UK, pp. 6/ 6/7, June 99. [9] E. Adler, J. Clark, M. Conn, P. Phu, and. Scheiner, Low-cos echnology or mulimode radar, IEEE AES Sysems Magazine, vol. 4, no. 6, pp. 3-7, June 999. Fig. 5: SCR as a uncion o racional bandwidh or apex a a cener requency o (a) 3 GHz, and GHz. 978--4673-658-4//$3. IEEE 8