Ultra-Wideband Radio Systems. Their Peculiarities and Capabilities

Transcription

1 PACS : x I.Ya. Immreev Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Cntents 1. Intrdutin Terminlgy UWB Wavefrm Variatin during Transmissin-Reeptin. General Apprah Wavefrm Variatin during Radiatin 8 5. Diretinal Pattern t Radiative Radiatin Wavefrm Variatin during Reeptin Peuliarities f UWB Wavefrm Detetin Determinatin f Target EDS while Emplying UWB Wavefrms 9 9. Passive Interferene Immunity 93 1.Range Equatin. Partiulars f Appliatins Sme f Examples f UWB Radars Created by the Russian UWB Grup f Msw Aviatin Institute Cnlusins 98 Abstrat Thery and appliatins f Ultrawide Band UWB) radisystems whih belng t a new intensively develping area in radar and mmuniatins are nsidered in the paper. Main distinguishing features f UWB radisystems are systematized, while differene between suh systems and traditinal narrw-band nes is analyzed. Sientifi and tehnial hallenges faed by UWB radar designers are shwn. Sme new tehnial and iruit slutins used in UWB radisystems are nsidered n examples f UWB radars. Pssible diretins in develpment f UWB tehnlgy and tehnique fr suh systems are suggested. 1. Intrdutin The nventinal radi-tehnial systems perate at a narrw frequeny band and emply harmni sinusidal) signals at their arrier sillatin frequeny fr data transmissin. It ame abut this way histrially, beause a simple LC iruit allwed fr easy generatin f the sillatin at the needed frequeny, the sinusid being the natural sillatin f this iruit. The frequeny seletin has sine remained the main tehnique fr radi hannel divisin, with the majrity f radi-tehnial systems perating at suh a band f frequenies, whih is substantially smaller than their enter frequeny. All thery and applied pratie f the mdern radi engineering is based n this feature fr suessful peratin. Hwever, the narrwband peratin restrits the infrmatinal apabilities f the radi-tehnial systems. As shwn by Shannn C. [1], the amunt 76

2 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities f data transmitted per unit time H is diretly prprtinal t the data transmissin hannel bandwidth f: H = f lg 1 + ) pwer f signal. pwer f nise Inreasing f the data transmissin apabilities f a system alls fr widening f its perating band. The alternative t it wuld be a mere inreasing f the data transmissin time. A dramati grwth in data transmissin flws in the mdern wrld makes this prblem espeially hallenging. The nventinal radi-tehnial systems, in whih the perating bandwidth des nt exeed 1 % f the enter frequeny, have atually exhausted their apabilities as regards data transmissin. And fr this reasn alne, ne f the ways t develp further infrmatin netwrks wuld be the using f signals arss wide and UWB frequeny bands [2 1]. Creatin f UWB radi systems, like any ther relevant tehnlgies, mandates pstulatin f ertain theretial fundamentals that shuld enable t mpute their perfrmanes aurately and define the requirements fr radi system mpnents while designing the hardware. Fr all that, despite the grwing number f published papers that have seen light f late, an rderly UWB system thery is, pratially, nn-existent. The reasn fr this is quite bjetive. The presses f transmissin f radi signals differ nsiderably in the narrwband systems and UWB systems. A study that uld be made n thse differenes shall allw ne t understand when the traditinal thery uld be appliable t design the UWB radi systems r when this thery is unusable and sme nvel tehniques shuld be in rder. This review paper brings int sharp fus bth state-f-the-art infrmatinal apabilities that the radi-tehnial systems aquire when using UWB wavefrms and basi features f suh UWB radi systems that emerge with emplyment f thse signals. 2. Terminlgy In 199, Defense Advaned Researh Prjets Ageny DARPA) under US Department f Defense DD) intrdued the definitin [5] f the s-alled fratinal frequeny band 1 : η = f upper f lwer f upper + f lwer. In ardane with this definitin, the UWB systems embrae thse systems and wavefrms fr whih 1 The very same expressin multiplied by a fatr f tw beame knwn as relative frequeny band. a) b) Fig. 1. Example f signals f equal duratin. a) f = 1/τ = 1 MHz; τ = 1 ns; f arrier = 1 MHz; η =.5 UWB signal). b) f = 1/τ = 1 MHz; τ = 1 ns; f arrier = 5 MHz; η =.1 Narrwband signal)..25 < η 1. This definitin is widely referred in literature at present. Nnetheless, this definitin as intrdued by DARPA has nt met with muh suess. A mere ase in pint Fig. 1) and a diagram Fig. 2) indiate that signals, at the same frequeny range f = 1/τ, that have similar data transmissin apaities 2 fall, in ardane t DARPA, under different lasses f=.4 GHz f=.6 GHz f=.8 GHz f=1. GHz f=1.2 GHz Fig. 2. Classifiatin f signals. f GHz UWB Nt UWB At the same time, a feature mmn t all UWB wavefrms is their apability f reslving bjets ver distane, determining, in this way, their struture. In this nnetin, it might be expedient t atalg signals arding t this feature and refer t ultrawideband wavefrms, nly if their spatial duratin τ is the speed f light) bemes smaller than the size L f bjet illuminated mre ften than nt, 2 Frm here n, τ a simple signal duratin r the autrrelatin funtin width f a signal with hirp mdulatin. 3 The absene f larity in the definitin f UWB wavefrms emplyed in radars prmpted establishment within the framewrk f the Siety IEEE f an Internatinal Wrking Grup UWBR Wrking Grup), whih arries n R&D n a speial referene standard IEEE Standard P 1672 UWBR Terms and Definitins. Eletrmagneti Phenmena, V.7, 1 18), 27 77

3 I.Ya. Immreev smaller than the antenna size) 4 : τ L. This kind f definitin brings abut ertain innvenienes, sine a lass f signal and a lass f radi system) bemes dependent n the dimensins f bjet plaed under illuminatin. Hwever, the inequality τ L plays a majr rle in mre than just frmal referene f signals and systems) t the UWB lass. Fulfilling f this inequality makes apparent an imprtant peuliar feature f all UWB systems: UWB wavefrm hanges in the urse f illuminatin f target, its refletin and reeptin. It is this very feature that preludes sme methds f the nventinal radi engineering frm being used in UWB radi systems design. Belw, the nsideratin is given t suh wavefrms and systems, in whih the inequality τ L is fulfilled. 3. UWB Wavefrm Variatin during Transmissin- Reeptin. General Apprah The narrwband signals have a unique prperty. With suh widely used transfrmatins as additin, subtratin, differentiatin and integratin the narrwband signal shape, whih is determined by the harmni referene arrier wave law, remains atually unhanged. What really takes plae is just a hanging f the amplitude f the signal and its shift ver time phase variatin). The UWB wavefrms underg hanges nt nly in their parameters, but in their shapes as well, during thse and ther) transfrmatins. Let us nw take a lk, as an example, at hw the UWB wavefrm hanges during radar target surveillane. A shemati f the radar is given in Figure 3. Arding t this shemati, a multibeam antenna, made as an array f N radiating elements, is used fr transmissin, while the reeiver is nneted t a single-beam hrn r mirrr) antenna. The signal f transmitter in the frm f the urrent pulse S t) with the duratin τ mes t eah radiating element f the array, the aperture f whih being f the size L. During radiatin the first hange in the signal wavefrm urs, namely its differentiatin, beause with the majrity f simple radiating elements the eletrmagneti field pulse shape S 1 t) is a derivative f the urrent pulse shape in the radiating element. The urrent pulse in the radiating element has the spatial extent τ, where is a harge mtin velity in the radiating element material. Fr the UWB wavefrm τ L. This makes the press f differentiatin extended ver 4 Frm this standpint, it might be mre lgial t name the nsidered wavefrms as ultra-shrt impulse nes, whih is dne by several authrs [11]. Yet, the term ultra-wideband has lng sine gne dwn as suh in literature the wrld ver, and its renaming an hardly be aunted fr at present. time, running n until the urrent pulse mpletes its yle in the radiating element. As a result, an additinal send) UWB wavefrm hange urs S 2 t), sine during the time f this yle, in the spae appear mre than ne K) eletrmagneti field pulses separated by the intervals t k. Sine the visible radiating element wavelength L hanges relative t the angle θ between the plane f the muth and diretin tward the reeiving pint, then the signal wavefrm S 2 t) shuld differ at different angles f surveillane. As a result, the radiating element spatial field distributin in the far zne diretinal pattern ver field) hanges its psitin and shape during the press f urrent pulse mtin arss the radiating element, i.e. it bemes transient this issue is nsidered in a mre detail in Chapter 4). The wavefrm S 2 t) is emitted simultaneusly by all radiating elements N f the multi-element antenna. In the press, a delay urs, in the diretins that are different frm nrmal t the antenna muth, between field pulses, whih me in frm different radiating elements. Fr adjaent radiating elements this delay wuld be d/)s θ, where d - a distane between the radiating elements. Resulting frm the additin N f the delayed signals S 2 t), a new third) shape is reated f the UWB wavefrm S 3 t). While perfrming surveillane at different angles θ, the resulting wavefrm S 3 t) shall have variable, smetimes rather mpliated, shape. Fig. 4 frm referene [2] shws an instane f the wavefrm variatin f this signal relative t the angle θ fr an array f fur radiating elements. The field fr the individual radiating element S 2 t) is shwn in this figure fr the sake f simpliity as retangular videpulse. The furth hange in the UWB wavefrm urs during its return frm lal refletive elements M brilliant speks ) f target, arranged arbitrarily ver the length f the target L 1. The wavefrm S 3 t) returns frm eah f these elements with a different delay t m. The sum f the displaed signals vs. time S 3 t) frms the wavefrm S 4 t), the shape f whih the number f maximums, intervals between them t m and their amplitudes) depends n gemetry and materials f the target. This wavefrm is als dependent n impulse respnse f the target brilliant speks h m, whih may turn ut t be frequeny filters fr this signal. This kind f signal is alled the prtrait f the target. The entire prtrait is frmed in the time T = 2L 1 /, its wavefrm varying vs. target surveillane angle. The fifth hange in the UWB wavefrm S 5 t) urs during signal reeptin. Belw, Chapter 5 will deal with auses f thse hanges. They have t d with the dependene f a reeiving antenna diretinal pattern frm n that f a field pulse returning frm target and n the tempral shift f urrent pulses, whih is indued by the field in near and far ends f the antenna 78 Электромагнитные Явления, Т.7, 1 18), 27 г.

4 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Transmitter S t) Kimpulses ds t) S 1t)= dt K 1 k=1 S t)= S t - t ) 2 k N radiatrs N S t)= S t - nd s ) 3 2 n=1 Target Mrefletrs Reeiver S t) 3 S 4= M S t - t m) m=1 3 h t - t - t)dt m Fig. 3. Variatin f UWB wavefrm during transmissin and reeptin. Sin = Sin 3d Sin 2d Sin d Sin d Fig. 4. Field pulse shapes at varius angles θ. relative t target. One shuld als take int aunt the variatin f UWB wavefrm during its travel t target and bak wing t variable deay f different parts f its spetrum in atmsphere. Fig. 5 illustrates examples f real wavefrms btained in the urse f radar target surveillane. The wavefrm variatin makes it diffiult n several unts t evaluate the radar parameters. The lassial ptimum pressing f this wavefrm using mathed filter r rrelatr is impssible t perfrm here. The determinatin f the effetive dissipative surfae EDS) pses the fllwing questin: whih exatly value f the signal shuld be taken as eletrmagneti field amplitude in the reeiving pint, n reeiving antenna this issue is dealt with in a mre detail in Chapter 7)? In this way, ne f the mst hallenging tasks in designing UWB systems remains determinatin f their parameters, ating in nsideratin f the abve features, and searh fr the ptimum pressing tehniques f wavefrm reeived t allw fr a maximum signal-t-nise rati SNR) this issue is nsidered in a mre detail in Chapter 6). Let us nsider in a mre detail several auses fr the abve wavefrm variatins. Eletrmagneti Phenmena, V.7, 1 18), 27 79

5 I.Ya. Immreev First BP Send BP Refleted signal Radiated signal Signal f the transmitter t, ns t, ns Radiated signals Change f the signals refleted frm different brilliant pints BP) f the target Fig. 5. Variatin f shapes f real UWB wavefrms. M vetr f the harge. L Li i R L Sine it) = dq/dt, the harge aeleratin in the radiating element is indued by the field whih is prprtinal t the first urrent derivative. When the urrent pulse has appeared, the exitatin f the first elementary radiatr urs in the pint O. In the time R/, an eletrmagneti field will arise in the far zne, whih will lk like as fllws [14]: Fig. 6. Mdel f diple shulder. 4. Wavefrm Variatin during Radiatin Let us nsider the ultimate radiating element f UWB wavefrm as linear antenna a length f wire r a shulder f diple) and present the physial interpretatin f the presses that ause the hanges in the wavefrm S 1 t) and S 2 t) [12]. A mdel f this radiating element f the length L is given in Figure 6. Let us separate it int elementary radiatrs with the linear size L. Designatins in this Figure are as fllws: L j a j-th elementary radiatr; L j its rdinate; R a distane as far as the pint f surveillane M; θ - an angle between diretin t the pint f surveillane and plane f the muth. The urrent pulse it) arises in the pint O and prpagates alng the radiating element. In this way, a series exitatin f its aperture takes plae. The eletrmagneti field arising in the far zne f the radiating element is assiated with the mvement f harges thrugh radiating element wire via the knwn relatinship [13]: Et) = q 4πε [ 1 d 2 ] e r 2 dt 2 where the speed f light; q a harge; e r a unit E 1 t,θ) = Z sin θ 4π [ i d dt 1 R t L 1 R L 1 s θ )] L 1) where Z a harateristi impedane f free spae. The send summand in parentheses determines the delay f the signal in this wire and the third ne indiates the delay f the signal in spae. In the time L/, the urrent pulse will exite the send elementary radiatr. The send eletrmagneti field E 2 t,θ) will emerge that wuld be similar t 1), replaing L 1 with L 2. Travelling alng the wire, the urrent pulse will exite ne by ne the subsequent elementary radiatrs. T get a relatively plain physial piture f the presses taking plae in the radiating element, we shall intrdue ertain simplifiatins. We shall neglet lsses in the radiating element wire and lsses t radiative radiatin; we shall assume that there is n refletin frm the end f the radiating element, and upn exitatin f the last, N-th, elementary radiatr the urrent pulse will be absrbed by the lad, and we will at n assumptin, as well, that there is n delay in the wire and thus =. This kind f radiating element will be further knwn as mathed ne. The ttal field f all elementary radiatrs in the far 8 Электромагнитные Явления, Т.7, 1 18), 27 г.

6 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities It), di/dt dit)/dt It) Fig. 7. Current pulse shape and its derivative. zne aquires the fllwing frm: E Σ t,θ) = Z sin θ 4π N [ d i dt j=1 1 R t L j R L j s θ t )] L. 2) We shall nw use, instead f the disrete representatin f radiating element, the ntinuus ne. Fr this purpse, we shall get the length f elementary radiatrs t strive t zer L and their number t strive t infinity N. Then, in 2) the summatin turns int integratin: E Σ t,θ) = Z sin θ 1 4π R L [ i d dt t L R Ls θ )] dl. 3) The expressin 3) desribes the eletri mpnent f eletrmagneti field in the far zne fr extended radiating element exited at ne end by the urrent f arbitrary shape. The field that is determinable by derivative f the urrent ver time is frmed by varius pints f the radiating element as far as the pulse travels alng the wire. The expressin fund in parentheses determines its running time, taking int aunt this delay. By assuming the derivative f this time ver dl, we shall raise a pssibility t make in 3) a replaement f the variables [15]: dt = s θ 1 dl. As a result, we btain the integral f derived funtin ver the same variable, whih is equal t the funtin itself. Then, E Σ t,θ) = Z sin θ 4πR [ i 1 s θ 1 t L R Ls θ = Z sinθ 4πR [ i t L R Ls θ 1 s θ 1 ) i )] L t R )]. 4) One an see frm this expressin that, in the general ase, the radiating element field must nsist f tw fields, psitive and negative, eah f whih fllws the shape f the exiting urrent. The shape f ttal field hinges n the relatinship between radiating element length L and spatial duratin f the exiting pulse τ. This shape will als depend n the angle f surveillane θ. We shall nsider thse relatinships by iting a speifi instane when the exiting urrent pulse appears as Gaussian urve with unitary amplitude Figure 7, slid urve): [ ) ] 2 t it) = exp 4, 5) τ where τ a pulse duratin at level.5. The derivative f this pulse is a symmetrial biplar pulse Figure 7, dtted urve). By substituting 5) in 3) and perfrming the differentiatin and integratin, we shall btain: E Σ t,τ,θ) = Z sin θ 4πR exp 4 1 s θ + 1 t L R Ls θ τ t R exp 4 τ ) The frmula 6) indiates that the radiating field is indeed a sum f tw fields, ne f whih is radiated at the mment when the urrent pulse enters the radiating element exitatin pint and the ther exatly at the mment when this pulse reahes the end f the radiating element. This press is smetimes explained as radiative radiatin frm the exitatin pint and frm the radiating element end. Hwever, the physis f phenmena urring in the radiating element will be smewhat different. We shall nw nsider frmatin f the field E Σ t,τ,θ) by using the disrete radiating Eletrmagneti Phenmena, V.7, 1 18), 27 81

7 I.Ya. Immreev Et) r/ E t) 1 E t) 2 E t, =9 ) I E t) N r/ +L/ Fig. 8. Fields exited by elementary radiatrs at L/τ 1. r/ E 1 t) E 2 t) E Nt) r/ +L/ E t, =9 ) Fig. 9. Fields exited by elementary radiatrs at L/τ 1. E,t) =1 =15 =3 =45 =6 I =75 t 4 t 5 t 6 t 7 t =9 Fig. 1. Field pulse shapes at varius angles θ. element mdel Fig. 6). In Figure 8, the slid urve stands fr fields exited by elementary radiatrs in the pint M at the angle θ = 9, the value f L/τ being 1. One an gather frm this Figure that the fields f the elementary radiatrs are shifted ver time due t the urrent pulse delay and that they have psitive and negative half-waves the areas f whih are equal. That is why they will be partially mpensated during the summatin. The degree f this mpensatin depends n the rati between t t radiating element length L and pulse duratin τ. The mplete field mpensatin starts ff at the mment f time t k = τ. Unmpensated will remain nly a part f the elementary radiatr fields that are lated in the viinity f the exitatin pint and tward the radiating element end Figure 6, dtted urve). Fr this reasn, at L/τ 1 the radiating element field will lk like radiatin ff the pwer pint and ff the end. By mparing the urrent in Figure 7 and field in Figure 8, it is evident that the shape f the field that lingers after the mpensatin inides with the shape f the urrent that exites the radiating element. As the rati L/τ dereases, the tempral interval during whih the field mpensatin takes plae bemes lesser and lesser, as mpared t the field pulse duratin. The gap between field pulses in Figure 8 bemes ever shrter. In the lng run, at L/τ 1 the mpensatin atually stps altgether Figure 9). All f the aperture radiates simultaneusly, while the shape f the field resembles mre and mre the frm f the derivative f the urrent that exites the radiating element. In this way, at L/τ 1 the shape f the field inides with that f the urrent, while at L/τ 1 it inides with its derivative. Figure 1 shws eletri mpnents f the radiating element field pulse fr varius angles f surveillane θ. One an dedue here that, upn hanging f the angle f surveillane, the field pulse shape des s as well, sine the radiating element prjetin size varies at a given angle. The angle, at whih the field shape an still be viewed as tw separate different-plarity pulses with the duratin that is equal t the urrent pulse duratin, is determinable by using the expressin: [ τ ] θ gr = π ars L 1. The angle θ gr depends n the rati τ/l. At τ > 2L, the angle θ gr takes n negative values. This bservatin stands t mean that the field in the far zne is nt separated int tw pulses at any angles whatsever and, in its shape, it rrespnds t the derivative f the Gaussian pulse. As a matter f fat, we have here transitin frm UWB wavefrm t narrwband signal. 5. Diretinal Pattern t Radiative Radiatin The variatin f the field pulse shape at different angles f surveillane auses transient tempral behavir f the diretinal pattern ver field. T prve it, we shall use the expressin 6). The fatr befre the square brakets is diretinal pattern DP) f the elementary radiatr. Inside the square brakets ne 82 Электромагнитные Явления, Т.7, 1 18), 27 г.

8 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities E,t) t t 1 t 2 t 3 t 4 t t1 t 5 t*** W ) W max,8, L =.1 t 5,4 t ****, degrees degrees Fig. 11. Instantaneus diretinal patterns antenna with series exitatin). Fig. 12. Energy diretinal patterns antenna with series exitatin). shall find the fatr f elementary radiatr array. It depends n time, angular diretin, exiting signal shape and antenna length. The exiting signal shape and antenna length in ur ase are fixed. T determine the dependene f DP n time, we shall separate several mments f time t,t 1,t 2,t 3,... in the interval, during whih the urrent pulse exists in the antenna Figure 1) and, emplying the expressin 6), we shall nstrut the dependene f field n angular rdinates, i.e. instantaneus DPs. Figure 11 shws a family f instantaneus DPs fr the shulder f diple being exited by the Gaussian urrent pulse at L/τ 1. As ne an see frm this Figure, the DP maximum hanges its diretin in the urse f existene f the field. Initially, it is direted atually alng the axis f the antenna. As the urrent pulse travels alng the wire, this maximum shifts tward the nrmal t the antenna, with the field amplitude dereasing. The DP sans the spae, hanging its psitin frm the antenna axis t its nrmal. During the sanning the DP width and amplitude derease. The nature f the instantaneus DP family presented in Figure 11 agrees well with the results reprted in referene [16] where a rigrus linear antenna mdel was used fr the simulatins. The transient behavir f DP ver field makes it unsuitable fr mputatins f the parameters f a radi-tehnial system, sine it des nt allw ne t determine the diretive gain DG), beam width, et. Early literature fr example, referene 17) desribed different ptins f DP that are used relative t peak amplitude, t peak pwer, t steepness. Hwever, the mst suitable seems t be the energy DP Wθ). This DP is btained by way f averaging the pwer radiated in eah angular diretin ver the time f the urrent pulse travel thrugh the radiatr, desribing the density distributin f energy flw being radiated in spae [17,18]. W T θ) = 1 Z + E 2 t,θ) dt, where Z = 12π 377 Ohm is the harateristi impedane f free spae. The endless limits f integratin ver time allw ne t apply this expressin t urrent pulses f any shape and duratin. T mpare the antenna perfrmanes, the nrmalized energy DP mes in very handy: W TN = W Tθ) W T max, where the value f DP in the diretin f maximum radiatin is alulated arding t the frmula: W T max = 1 Z + E 2 maxt) dt. Figure 12 shws a family f nrmalized energy DPs fr the ase abve and varius values f the rati L/τ. At L/τ 1, the energy DP is a DP f the half-wave diple. As the rati L/τ inreases, the DP maximum deflets frm the nrmal and, at L/τ 1, the linear antenna begins t radiate axially, the DP maximum value inreasing and antenna width dereasing. The DG f UWB wavefrm radiating elements is defined as the rati f energy density flw f the radiating element, as studied in the diretin f the maximum radiatin W T max, t energy density flw f equivalent istrpi radiating element W T at equal energy fed t the istrpi radiating element and the ne studied: D T = W T max W T. Cnsidering that fr the mathed antenna the radiatin resistane wuld be R em = Z, the ttal field energy radiated by the antenna thrugh sphere Eletrmagneti Phenmena, V.7, 1 18), 27 83

9 I.Ya. Immreev E,t) t 4 t 3 t 2 t 1 t t t t t t 1,8,6,4 W ) W max L/ = , degrees Fig. 13. Instantaneus diretinal patterns aperture antenna). f the radius R shuld be equal t: W = R2 Z 2π π + E 2 θ,ϕ,t)sin θ dθdϕdt. By dividing this energy by the surfae area f the sphere surrunding the antenna, we shall btain the energy density flw f equivalent istrpi radiating element: W T = W 4πR 2 = 1 4πZ 2π π + E 2 θ,ϕ,t)sin θ dθdϕdt. The btained expressins nw permit t determine the DG f radiating element energy: D T = 4π 2π π + + E 2 maxt) dt. E 2 θ,ϕ,t)sin θ dθdϕdt The abve linear radiating element fr UWB wavefrms Fig. 6) is, as a matter f fat, an antenna with a series exitatin. Upn simultaneus exitatin f the entire aperture with ultra-shrt UWB impulse τ L), the antenna radiatin als aquires unusual prperties a TEM pyramidal hrn may be ited as an example f this antenna). The DP fr the antenna f this type an be derived frm the expressin 4) by exluding frm the parentheses the summand L/ that determines the urrent pulse delay due t its travel arss the aperture. Figure 13 shws a family f instantaneus DPs ver field fr several mments f time t,t 1,t 2,t 3,... in the interval, during whih the exiting urrent is running thrugh the antenna. As different frm the preeding ase, the DP axis des nt hange its diretin, althugh the DP itself, during the urrent degrees Fig. 14. Energy diretinal patterns aperture antenna). pulse travel thrugh the radiating element, splits int tw diverging rays. This has t d with the fat that, in an antenna with a parallel exitatin, like in an antenna with a series exitatin, the field in the far zne hanges its shape at different angles. Figure 14 presents a family f nrmalized energy DPs fr an antenna with a parallel exitatin at different values f the rati L/τ. The abve variatins f UWB wavefrms as radiated by separate radiating element are mmn in harater. Depending n the type and gemetry f the antenna, thse hanges may me up differently. The mre mpliated the antenna, the mre mpliated the field shape f radiated UWB wavefrms. Even transitin frm ne diple shulder t entire diple and nsidering f the signal refletins frm its ends makes the piture f radiated field ntieably mre diffiult t grasp, bsuring the understanding f the press f frmatin f the field pulse and that f the antenna DP. Fr this reasn, the abve physial interpretatin f the presses urring in the ultimate antenna during radiatin f a shrt UWB wavefrm is bund t help understand the prblems ne has t fae while designing UWB radi systems. Results prdued in many referenes see, fr instane, review in [14]) allw us t generalize the differenes in antenna parameters during radiatin f narrwband single-frequeny) signals and during radiatin f UWB wavefrms Table 1): 6. Wavefrm Variatin during Reeptin Frm Figure 1 ne an see that the pulse shape f the field inident n reeiving antenna varies vs. angle, at whih it is dispsed relative t transmitting antenna figure 15). As a result, bth the pulse shape f the urrent indued by this field in reeiving antenna and vltage pulse shape in antenna s lad, as indued by this urrent, will depend n arrangement 84 Электромагнитные Явления, Т.7, 1 18), 27 г.

10 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Table 1. Single-frequeny signal Field in far zne is viewed as slitary wave radiated by the entire aperture f antenna Shape f this wave is derivative frm urrent shape in antenna Field amplitude in far zne depends n angular rdinates, nly. Shape f this field at any angles f surveillane remains sinusidal Psitin f antenna diretinal pattern ver field depends n angular rdinates, nly Lateral antenna radiatin has side-lbe struture UWB wavefrm Field in far zne is viewed as several waves radiated frm the enter and ends f antenna Shape f these waves inides with urrent shape in antenna Amplitude and shape f the field in far zne depend n angular rdinates, time and shape f exiting signal Psitin f antenna diretinal pattern ver field depends n angular rdinates, time and shape f signal emitted N side-lbe struture in lateral antenna radiatin f the antennas. As a nsequene, the reeiving antenna diretinal pattern shall nw depend n this arrangement and due t this the DP f this antenna will differ in the mdes f transmissin and reeptin f UWB wavefrm. This irumstane des nt allw fr the use f the reiprity therem in rder t determine the diretinal patterns f UWB reeiving antennas relative t their diretinal patterns in the transmissin mde, as it is the nrm in the nventinal narrwband antenna thery. Fig. 15. Setup f antennas. With a view f determining the dependene f the shape f UWB wavefrm reeived n the reipral rientatin f transmitting and reeiving antennas, we shall turn t Figure 15 whih shws the setup f thse antennas that are arranged as diples f the lengths L T and L R. T simplify this prblem, the arrangement has n illuminated target, exluding thereby its influene n perfrmanes f the reeiving antenna. The reeiving antenna is lated at a distane R frm the transmitting antenna in its far zne pint M in Figure 6). The lad and diple ends have been mathed arss the signal bandwidth and d nt reflet energy. The eletri mpnent f the field is radiated by the transmitting antenna in the diretin f the reeiving antenna at the angle θ T between the line f its aperture and diretin tward the reeiving antenna, being inident n the reeiving antenna at the angle θ R between the line f its aperture and diretin tward the transmitting antenna. The eletri mpnent f the field f ne shulder f radiating diple is desribed by the frmula 4), whih, nsidering new designatins, shall assume the fllwing frm the index with E stands fr the number f the shulder): E 1 t,θ T ) = Z [ sinθ T 1 4πR s θ T 1 { i t L T R L T s θ T ) i t R )}]. Fr the send diple shulder, the eletrmagneti field in the far zne is determined using the fllwing expressin: E 2 t,θ T ) = Z [ sinθ T 4πR { i t R ) i 1 s θ T + 1 t L T R + L T s θ T )}]. Then the ttal field radiated by the diple wuld be: E Σ t,θ T ) = E 1 t,θ T ) + E 2 t,θ T ) = A 1 i t L T R L ) T s θ TX A 1 i t R ) + A 2 i t R ) A 2 i t L T R + L ) T s θ T, where A 1 and A 2, respetively are the amplitude fatrs A 1 = Z sinθ T 4πR s θ T 1), A Z sin θ T 2 = 4πR s θ T + 1). Eletrmagneti Phenmena, V.7, 1 18), 27 85

11 I.Ya. Immreev Ut, ) Ut, ) Ut, ) Ut, ) t t t t =9 * =7 =5 * * =5 * Fig. 16. Vltage shapes n reeiving diple lads. W ) W max a) a) L / =1, b) L / =3, ) L / =1, * * * b) ) degrees Fig. 17. Energy diretinal patterns f reeiving diple. Let us break eah reeiver diple shulder dwn int the infinite number f elementary setins dl R. The EMF indued in the elementary setin is diretly prprtinal t the prjetin f the vetr E Σ t,θ T ) f the eletri mpnent f the field that is inident n this setin: de = E Σ t,θ T ) sinθ dl R. Upn the impat f this field, the elementary urrent begins t run thrugh the elementary setin: di = de Z A + Z L ), where Z A an antenna radiatin resistane; Z L a lad resistane. The elementary urrents that appear in eah setin run bth tward lad and tward diple ends. An assumptin was made abve that the diple ends are mathed. Fr this reasn, a part f these urrents running tward the diple ends emits sendary radiatin and is absrbed. The urrents running tward the lad prdue a vltage drp n it. As in the ase f radiative radiatin, let us take int aunt the signal delay in the reeiver diple wire and in spae relative t the pint M): ) LR + L R s θ R t 3 =. The ttal urrent running thrugh the lad f reeiver diple will be as fllws, nsidering this delay: I Σ t,θ T,θ R,L T,L R ) = R L T s θ T L R { A 1 i t L T + L R + L R s θ R ) A 1 i t R + L R s θ R + A 2 i t R + L R + L ) R s θ R A 2 i t L T R + L T s θ TX + L R + L R s θ R The vltage n reeiver diple lad will be: ) )} dl R. U Σ t,θ T,θ R,L T,L R ) = I Σ t,θ T,θ R,L T,L R ) Z L. Figure 16 shws an example f alulatins f this vltage, designated frm here n as Ut, θ) fr different angles θ R. An assumptin was made during the alulatins that the radiating diple shuld be exited by a urrent pulse with the shape 5), the 86 Электромагнитные Явления, Т.7, 1 18), 27 г.

12 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities U *** X 2 T 2 x t)dt M Threshld U *** U *** U *** U *** Fig. 18. Energy detetr with nn-herent strage. U t) T 1 T r 2 M Fig. 19. Example f peridi signal with unknwn shape. duratin f whih shuld be τ τ L T ), while L R = L T. The angle θ TX is assumed t be 3, sine at this angle the pulse shape f the field whih is inident n the reeiver diple mes lsest t the shape f the derivative f the pulse f the urrent that exites the radiating diple Figure 1), and, in this way, the nditin τ L R is met fr the reeiver diple, t. Frm Figure 16 it is evident that the vltage in the reeiver diple lad is a sum f tw pulses, eah f whih fllws the shape f the inident field pulse. Thse pulses are mirrr images f ne anther, sine diretins f the urrents running t the lad frm different diple shulders are ppsite. The pulses are espeially ntieably divided at small angles θ R, when the inident field indues urrents in the shulders with a nsiderable delay. A hange in the vltage pulse shape n diple lad, when the angle f the inident field pulse n diple hanges, is analgus t the hange in the field pulse shape f radiating diple, when the angle f surveillane has been hanged. Quite similar t it is the behavir f the reeiver diple DP ver field determinable as the dependene f n-lad vltage n angular rdinates): whilst the inident field pulse is travelling arss reeiver diple, this DP mves in spae, i.e. t say it bemes transient vs. time. As a result, the reeiver diple requires mputatins f the energy DP, whih is btained via averaging f the pwer reeived frm eah angular diretin in the urse f travel f the diple-inident field pulse arss its aperture. The energy DP desribes the density distributin f energy flw reeived by diple frm spae. W R θ) = 1 Nrmalized energy DP: + Z L U 2 t,θ)dt. W RN = W Rθ) W R max, where W R max = 1 + Z L U 2 maxt,θ)dt. Figure 17 shws a family f nrmalized energy DPs used in the abve example at different values f the rati L R /τ. At the value f L R /τ, whih is lse t unity, the energy DP inides with the DP f half-wave diple. With an inreasing rati L R /τ, the shape f DP hanges: the DP maximum bifurates and bemes narrwer. The DG f reeiving antenna D R is defined as a rati f energy density flw reeived by the antenna frm the diretin f DP maximum W R max, t energy density flw reeived frm spae: D R = W R max W R. Cnsidering that fr the mathed antenna the radiatin resistane wuld be R em = Z L, the ttal energy f the field that is inident n antenna thrugh sphere with the radius R shuld be: W = R2 Z L 2π π + U 2 θ,ϕ,t) sinθ dθdϕdt. By dividing this energy by surfae area f the sphere surrunding the antenna, we shall btain the energy density flw, as reeived by the equivalent istrpi antenna: W R = W 4πR 2 = 1 4πZ L 2π π + U 2 θ,ϕ,t) sinθ dθdϕdt. The btained expressins allw us t determine the Eletrmagneti Phenmena, V.7, 1 18), 27 87

13 I.Ya. Immreev U input T ip Tip Tip Tip 2 X Threshld U utput U *** U threshld Fig. 2. Energy detetr with herent strage. diretive gain f the reeiving antenna: D R = 4π 2π π + + U 2 maxt,θ)dt. U 2 θ,ϕ,t) sinθ dθdϕdt where u t) a returned signal impulse) f unknwn shape with the duratin T = nτ and energy E s, u 2 t)dt = E s. Individual impulses d nt verlap in the paket, i.e. 7. Peuliarities f UWB Wavefrm Detetin The highly infrmatinal UWB wavefrms allw fr target disriminatin, even radi prtrait f the target when the high reslutin is btained. Hwever, the press f target detetin preedes that f target disriminatin. While analyzing the press, it shuld be brne in mind that the shape f target-refleted signal remains unknwn. The ptimum detetr f unknwn signal in the Gaussian nise is the square-law ne energy detetr) [19] Figure 18). Having staked up a paket f M suh signals Figure 19), ne emplys nnherent aumulatin f the results f square-law detetin. The gating is perfrmed at the mments f mpletin f single signal integratin and mpletin f the paket staking-up frm M signals. The signals fund in the paket are herent, althugh f unknwn shape. The nn-herent pressing f herent signals brings abut, bviusly, sme lsses. In rder t avid thse lsses, ne has t hange the rder f staking-up and square-law detetin peratins. The setup f this energy detetr is given in Figure 2. A theretial validatin f the ptimum detetin algrithm fr signal with unknwn shape was perfrmed by V.S. Chernyak [22]. Fr synthesis f the detetin algrithm, a priri data were used nerning the prbing pulse repetitin perid T r. The target is illuminated with impulses with the duratin τ, the impulse rep rate being s high that during a relatively shrt time interval the target an be regarded as mtinless, while the returned signal u s t) an be visualized as a paket nsisting f M similar impulses Figure 19): u s t) = M 1 k= u t kt r ), u t kt r ) u t mt r ) dt = { E s, k = m,, k m. 7) The nise shall be assumed as being white, Gaussian, with the zer mean value. The lked-n signal is a mean value f the sum f signal and nise. Fr the knwn signal the lgarithm f relatin f the likelihd funtinal is as fllws: ln Λ = ln W s/n[ut)] W n [ut)] 1 2 M 1 k= M 1 l= = M 1 k= ut)u t kt r )dt u t kt r )u t lt r ) dt. 8) Here ut) a reeivable realizatin f the signalnise sum r just nise with the duratin T > M 1)T r + T. Taking 7) int aunt, a simplifiatin an be made 8): ln Λ = M 1 k= ut)u t kt r ) dt 1 2 M 1 k= u 2 t kt r ) dt. Althugh u t) is unknwn but nt randm), we shall emply the adaptive apprah. The essene f the apprah is t use an algrithm fr a signal that is ptimal at the knwn parameters, int whih, replaing the unknwn parameters, their maximum 88 Электромагнитные Явления, Т.7, 1 18), 27 г.

14 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities likelihd evaluatins are substituted [21]. In this event, ne shuld nsider the signal, as a whle, as a funtin f time, rather than individual parameters f the signal [22]. Let us nsider the likelihd funtinal lgarithm f the signal: R 1 = 1 2 [ ut) M 1 k= u t kt r )] 2 dt. The maximum R 1 as a funtin f M 1 k= u t kt r ) rrespnds t the minimum f the expressin fund in the square brakets. Sine duratin f the reeivable realizatin u t) fr the signal-nise sum embraes all inming signals, then the minimum f the expressin in the square brakets is fulfilled at the nditin when, in eah time interval where there is the signal, it is equal t the reeivable realizatin: û t kt r ) = ut) when t kt r,kt r + T) Let us replae the variable in 7): t 1 = t kt r. Then û t 1 ) = ut 1 + kt r ) when t,t). The evaluatins f the same funtin u t 1 ) btained in the time intervals that are lated ver the repetitin perid T r, as regards ne anther, are statistially independent, sine the Gaussian nise in thse intervals is independent. This means that the ptimum evaluatin û t 1 ), t 1,T) that is rendered aurate ver M measurements lks like as fllws: û t 1 ) = 1 M M 1 k= ut 1 + kt r ) when t i,t). 9) 9) By substituting in 12) the variables t 1 = t kt r, we shall btain ln Λ = M 1 k= ut 1 + kt r )u t 1 )dt M 1 k= u 2 t 1 )dt 1. 1) By replaing u t 1 ) with the btained evaluatin f û t) frm 9), while skipping the index frm t1 and nn-essential fatr 1/M, sme simple transfrms having been made, we btain frm 1) the ptimum arding t the Neumann-Piersn riterin) adaptive detetin algrithm in the frm f: R = U exit = [ M 1 k=1 ] 2 ut k T r ) dt > < U threshld, 11) where U threshld a detetin threshld. Thus, the ptimum algrithm bils dwn t the summatin f the aeptable realizatin lengths Tlng eah) in suh time intervals where signals are expeted; t mputatin f the energy f this sum and mparisn f prdued energy with the threshld that is determinable via the assigned false alarm prbability. This is the knwn energy detetr, with whih ne aunts fr nt nly the energy f eah impulse f the paket, but als fr the energy f rrelatins between the impulses. At a rather swift target mvement relative t the radar, the impulses f the paket u s t) will begin t differ frm ne anther. In this ase, ne an nsider at least tw adjaent impulses t be similar. Fr this reasn, we shall nw nsider a ase, whih is imprtant fr applied purpses, f pressing tw impulses with a small repetitin perid M = 2). The setup f the detetr in this ase is presented in Figure 21. The ptimum algrithm 11) at M = 2 an be represented as: R = U utput = 2 u 2 t)dt + u 2 t + T r )dt ut)ut + T r )dt U threshld. 12) The first and send integrals in 12) desribe the energy mputatin algrithm f suh signals that are reeived in tw adjaent perids, the third integral determining the algrithm f their reipral rrelatin pressing. Frm 12) it is bvius that the detetr under nsideratin an be represented and realized) as three sub-ptimal detetrs perating jintly Figure 22). The first tw nes are well-knwn energy detetrs f signals expeted in the first and send perid. The third ne, dubbed as alternating-perid rrelatin detetr APCD), was desribed earlier in referene [23] 5. Shematis shwn in Figures 21 and 22 permit t bring ut the partiulars f the ptimal detetr: a) The nises ming frm adjaent repetitin perids t inputs f the detetrs are nt dependent; the integratr input reeives either the square f the sum f independent segments f the nrmal presses Figure 21), r the sum f tw squares and prdut f these segments Figure 22) rrespnding t adjaent perids; the prbability distributin at the integratr input substantially differs frm the nrmal ne in bth ases. b) The prbability distributin at the integratr utput apprahes the nrmal ne, as the 5 In referene [23] the alternating-perid rrelatin detetr is wrngly ited as ptimal. Eletrmagneti Phenmena, V.7, 1 18), 27 89

15 I.Ya. Immreev U input T òp 2 X Threshld U utput U threshld Fig. 21. Energy detetr fr M = 2. U utput U input X 2 1 X1X2 U threshld U utput T *** U threshld X 2 2 U utput Uthreshld Fig. 22. Three sub-ptimal detetrs fr M = 2. integratin time inreases; this time is determined nt by the duratin f radiated signal t, but by the duratin f signal returned frm target T = nτ; in this way, the radial target length L = nτ/2 determines the integratin time, level f nrmalizatin f press distributin at the integratr utput, nise dissipatin and, as a result, the detetr threshld level. Let us mpare the effiieny f the ptimal detetr 12) and three sub-ptimal nes. Figure 23 presents the detetin harateristis fr the ptimum algrithm urve 2), APCD urve 3) and sum f energies urve 4). Fr the sake f mparisn, the Figure shws the detetin harateristi f the lassial detetr with preisely knwn determined) signal urve 1). At M = 2, urve 3 inides with urve 4. The false alarm prbability is fa = 1 3. The harateristis are nstruted fr target with radial length upn whih 16 reslutin elements are laid. With suh strage during the integratin press, the utput statistis f bth ptimal and sub-ptimal detetrs an be nsidered as Gaussian values. One an gather frm thse Figures that the ignrane f the signal shape leads t nsiderable lsses. These lsses are attributed t the absene in the reeiver f an utnised sample f the signal deteted. Frm urves shwn in Figure 23 ne an gather that the sub-ptimal detetrs effiieny is just slightly wrse than that f the ptimal ne. That is why, in ertain ases, a suffiiently unsphistiated APCD algrithm may find its way t pratial appliatins. Shemes shwn in Figures 21 and 22 are ptimum fr detetin f a mtinless target with the fixed radial length. This hypthetial ase was nsidered as standard referene enabling t evaluate the effiieny f detetin under varius nditins. T a ertain extent, this apprah is analgus t the prblem frm the lassi thery f detetin f a signal with exhaustively knwn parameters determinant). In reality, when the target velity and its extent are nt knwn a priri, a multi-hannel gemetry f the system must be in rder bth in signal delay and in integratin interval duratin. The thus-btained ptimal and sub-ptimal algrithms are realizable in digital frm. 8. Determinatin f Target EDS while Emplying UWB Wavefrms During target illuminatin with narrwband signal, when the radial target length L is nsiderably smaller than the spatial extent f the signal τ and refletins frm diverse brilliant speks frm the target verlap in spae, prduing the added-up signal in the reeiving pint, in rder t determine the EDS f a target lated in the antenna far zne, the fllwing well- 9 Электромагнитные Явления, Т.7, 1 18), 27 г.

16 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities P Q=2E/N, db Fig. 23. Charateristis f detetin f ptimal and sub-ptimal algrithms. knwn expressins is used: σ = 4πr 2 E 2 2/E 2 1, 13) where r a distane t target; 1 an amplitude value f the prbing signal field strength in the pint f target; 2 an amplitude value f field strength f a signal dissipated by target in the reeiving pint. During target illuminatin with simple UWB wavefrm L τ) the returns frm brilliant speks f the target beme divided in spae, while the signal in the reeiving pint is represented as a sequene f pulses f variable amplitude, shape and plarity, shifted ne relative t anther t arbitrary time lengths target prtrait, see, fr example, in Figure 5). The value f the amplitude 2 in the reeiving pint in this event bemes vague [24 26]. T determine the EDS in this ase [27], a ntin f generalized EDS was intrdued: σ = 2πr 2 W 2 /W 1, 14) where W 1 = τ 1 Π 1 t)dt an energy density flw f radar prbing signal in the pint f target; W 2 = τ 2 Π 2 t)dt an energy density flw f n-target dissipated signal in the reeiving pint; Π 1 t) an instantaneus value f the Pynting vetr f prbing signal whih exists during the time t1 in the pint f target; Π 2 t) an instantaneus value f the Pynting vetr f dissipated signal whih exists during the time t2 in the reeiving pint. A similar situatin with determinatin f the target EDS arises in thse ases when UWB wavefrms with hirp mdulatin are in use. In this event, the amplitude value f the unmpressed signal field in the reeiving pint Е2 and signal amplitude at the mathed filter utput, whih is mpared with threshld, differ in relative units) by times the mpressin rati. That is why using f the expressin 13) t determine the target EDS wuld nt be right. Sine the signal energy prir t and after the mpressin withut nsideratin f the lsses t pressing) remains the same, the expressin 14) enables t determine the target EDS n this sre. Nw, we shall mpare the values f the target EDS btained during illuminatin f the target with narrwband and UWB signals. Fr that purpse, we shall nsider as being target an ultimate grup sendary radiatr nsisting f tw refletrs dumbbells ). An assumptin is made t the effet that the refletrs d nt interfere with eah ther. Fr the narrwband signal L τ), this ase is very well knwn [28]. The pulse f the field illuminating target has the high-frequeny filling e 1 t) = E 1 s ωt. We shall designate the refletrt-radar distane as r 1,2 r 1 r 2 = l τ), while the mments f arrival f the refleted fields t the reeiving pint wuld be written as t 1,2 = 2r 1,2 /. The field dissipated by the sendary radiatr in the reeiving pint wuld be as fllws the index in parentheses stands fr the refletr number): e 2 t) = E 21) s ωt t 1 ) + E 22) s ωt t 2 ) = e 2 sωt ϕ), where ϕ = ωt 1 t 2 ) = 2π/λ)2r 1 r 2 ) = 4π l/λ. The ttal field amplitude in the reeiving pint E 2 : E 2 2 = E 2 21) + E2 22) + 2E 21)E 22) s ϕ. The target EDS in ardane with 1) nw wuld be: σ Σ2 = 4πr 2 E 2 2/E 2 1 = σ 1 + σ σ 1 σ 2 s ϕ. At the values f ϕ = and σ 1 = σ 2 = σ, that f the EDS will be maximal σ Σ = 4σ. Crrespndingly, with N refletrs that have equal EDS σ, if the refleted fields are synhrnus in phase, the EDS f the grup radiatr will be σ ΣN = N 2 σ. In the general ase, the phase ϕ is a randm quantity that assumes any values frm t 2π. In this ase, the EDS is determined as mean value: σ ΣN = Nσ. 15) When using UWB wavefrm L τ), the nsidered sendary radiatr has a field pulse inident upn it with the duratin τ and energy density flw Π 1 t). When r 1 r 2 = l > τ, then frm the tw refletrs in the reeiving pint me tw nn-verlapping field pulses that have, in the general ase, different energy density flws Π 21) t) and Π 22) t) and different duratins τ 1 and τ 2. In this event, the EDS f eah sendary radiatr is determined arding t the frmula 14): σ 1,2 = 4πr 2 W 21),22) /W 1, Eletrmagneti Phenmena, V.7, 1 18), 27 91

17 I.Ya. Immreev where W 1 = Π 1 t)dt, W 21) = Π 21) t)dt, W 22) = τ τ Π 22) t)dt an energy density flw f the radar τ prbing signal in the pint f target and energy density flws f signals btained in the reeiving pint frm the first refletr at the mment t 1 and frm the send refletr at the mment t 2. Quite bviusly, in this ase f the EDS f the sendary radiatr, the EDS f suh refletr will be determined frm whih the energy flw has me in at the greatest density value Π 2 t). The energy flw arriving in the reeiving pint frm the smaller refletr appears t miss being used, whih an be regarded as a lss. With an inreasing number f refletrs, thse lsses will inrease, as well. In rder t avid these lsses and btain the maximum EDS value f target during its illuminatin with UWB signal, it is neessary t gather tgether, ver ne time interval, all f the energy reeived frm different target refletrs ver different time intervals. It an be dne at the nditin that radar shuld emply the abve ptimal signal pressing. Let us assume, as befre, that the grup sendary radiatr refletrs shuld be equal. By substituting in 12) eah tw refleted pulses in eah perid the index dentes the number f refletr), we shall btain: U utput = + u 2 1t)dt + u 2 1t + T r )dt u 2 2t)dt u 1 t)u 2 t)dt u 2 2t + T r )dt u 1 t + T r )u 2 t + T r )dt u 1 t)u 2 t + T r )dt u 2 t)u 1 t + T r )dt u 1 t)u 1 t + T r )dt + 2 u 2 t)u 2 t + T r )dt. 16) The first fur integrals determine the energy f the first and send pulses f signal in the first and send repetitin perids. The subsequent six integrals determine the mutual energy f different pairs f the pulses. The first fur integrals ut f thse six desribe the mutual energy f pulses that d nt verlap ver time, and whih are zer anyway. The last tw integrals determine the mutual energy f tw verlapping after the delay by T Π ) pairs f the pulses. In this way, the ttal energy f reeived signal, whih is numerially equal t the vltage at the utput f the pressr, will be as fllws the first index in parentheses dentes the perid number, the send ne the refletr number): W 2 = + u 2 1t)dt + u 2 2t)dt u 2 1t + T r )dt u 2 2t + T r )dt u 1 t)u 1 t + T r )dt u 2 t)u 2 t + T r )dt = W 21,1) + W 21,2) + W 22,1) + W 22,2) + 2W 21,1 2,1) + 2W 21,2 2,2). If the energy f radar prbing signal in the pint f target is equal t W 1, then by substituting the btained energy values in 14), we shall btain the fllwing: σ Σ2 = 4πr 2 W 21,1) + W 21,2) + W 22,1) + W 22,2) + 2W 21,1 2,1) + 2W 21,2 2,2) )/W 1 = σ 1 + σ 1 + σ 2 + σ 2 + 2σ σ 2 1. With the equality σ 1 = σ 2 = σ 1 2 = σ 2 1 = σ, we shall prdue σ Σ2 = 8σ. This EDS value has been btained taking int aunt the target-refleted energy in tw perids f prbing. In ne perid f prbing the rati f energy in the reeiving pint t that in the pint f target mes ut with the EDS value σ Σ2 = 4σ. Respetively, with N sendary radiatrs that have the same EDS σ, the ttal EDS f the grup radiatr will be as fllws: σ ΣN = N 2 σ. 17) While mparing the EDS values btained after illuminatin f ne and the same target nsisting f N similar refletrs with UWB 17) and narrwband 15) signals ding the mathed pressing f thse signals in the reeiving pint), we an nw see that the fllwing inequality is fulfilled σ ΣN σ ΣN, that is σ uwb σ nb. In the general ase, with arbitrary EDS values f individual target refletrs the ttal target EDS value 92 Электромагнитные Явления, Т.7, 1 18), 27 г.

18 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Naitwband Radar UWB Radar Fig. 24. Pulse vlume f narrwband and UWB radars. Fig. 25. Signal-t-nise rati at utput f twfld SAPC system. σ Σ will be determined via signal amplitude at the mathed pressing system utput. Sine the mathed pressing llets in ne time interval all energy f the signal returned frm target, we shall refer, frm nw n, t the value σ Σ as energy EDS. 9. Passive Interferene Immunity In UWB radar, immunity t natural and manmade passive interferene has peuliar features f its wn. We shall nw nsider thse features by prviding an example f emplyment in this kind f radar f a system f alternating-perid mpensatin SAPC) that takes measurements f variatins f the phase differene f sillatins refleted frm mving target and frm lutter ver ne r several) repetitin perid [29]. The shrt UWB impulse reates a very small impulse vlume f radar beam ver distane, whih drastially redues the EDS interferene and simplifies target surveillane against its bakgrund Fig. 24). Hwever, the redutin f the radar impulse vlume ver distane des mre than simply t derease the pwer f interferene. As a rule, a lutter prduing the interferene is mvable luds, grund vegetatin, artifiial aersls). Owing t the mtin f the lutter inside the impulse vlume during the repetitin perid, a part f this interferene reahes utside this vlume, while a part f new lutter mes in thse parts f interferene are shwn tentatively in Figure 24 as dark belts n the fringes f impulse vlume). These hanges at t disrupt the rrelatin f signals refleted frm the lutter and reeived in ntiguus repetitin perids. The resulting vilatin f interpulse rrelatin ats t redue the interferene suppressin fatr in the SAPC system and wrsens its effiieny. When the radar impulse vlume is large enugh fr example, at τ = 1 mirsend, its reah ver distane is 3 m), the shifting part f the lutter nstitutes a small prtin ut f the entire impulse vlume and des nt exerise a nsiderable influene n the vilatin f inter-pulse rrelatin f the lutter. Hwever, when the impulse vlume bemes small at τ = 1 ns its reah ver distane is 3 m), this part f the lutter an nstitute a nsiderable prtin f the entire impulse vlume, wrsening substantially the inter-pulse rrelatin f signals returned frm the lutter and dereasing the SNR at the utput f the SAPC system. Figure 25 presents the plts f SNR Q relatinships at the utput f twfld SAPC SAPC-2) vs.uwb wavefrm duratin t, nrmalized t the average signal spetrum frequeny perid T av, at different values f the repetitin perid T r. The plts shw tw extremums, the first f whih maximum) inides with the impulse duratin t =.5 av. Upn variatin f the impulse duratin frm t = av t t =.5 av the effiieny f the SAPC inreases due t the redutin f impulse vlume f the radar. At τ <.5 av an intensive lutter derrelatin influene begins, with the SAPC effiieny ging dwn. With further dereasing f t the SAPC eases t exert any influene n nise immunity n aunt f the ttal de-rrelatin f the lutter and nly the first fatr remains there, i.e. the impulse vlume redutin. The nise level mes dwn again and Q inreases. In this way, the psitin f the send extremum minimum) rrespnds t the ttal lutter de-rrelatin and absene f velity seletin. Nte that, with an inreasing impulse repetitin Eletrmagneti Phenmena, V.7, 1 18), 27 93

19 I.Ya. Immreev 15 P*** GWatt dbm ,5ns 1ns 2ns 3ns -5 Band f GPS R, km Fig. 26. Dependene f UWB radar impulse pwer n detetin range. perid, the psitin f the send extremum shifts t the left in the diretin f the shrter duratins τ. This means that, with a dereasing impulse repetitin rate, the ttal lutter de-rrelatin mes abut with shrter signal duratins. Within the limits f nnflutuating passive interferene, the impulse duratin redutin des nt affet SAPC. Thus, the use f SAPC in UWB radar is the mre effiient, the lesser is the lutter de-rrelatin and the higher is the repetitin rate. 1. Range Equatin. Partiulars f Appliatins Cnventinally, the range equatin nnets the narrwband signal pwer ming t the input f reeiver threshld devie and the pwer f this signal emitted by transmitter. The signal energy determining the harateristis f radar detetin is nt, as a rule, inluded expliitly in the range equatin. In UWB radar, the wavefrm variatin during radar surveillane des nt permit t emply suh parameter as signal pwer. Fr this reasn, the radar range determinatin R is made using the energy parameters: WD R = 4 T σ Σ D R 4π) 2, ρqn where: W an emitted signal energy; D T the energy DG f transmitting antenna; D R the energy DG f reeiving antenna; σ Σ the energy EDS f target; ρ lsses in all radar systems; q the threshld SNR; N a nise pwer spetral density. The high-reslutin data ntent f UWB radars is ahieved via emplying the impulses f nan- and pisend duratins. If plain shrt wavefrms are emitted, similar t thse shwn in Figure 5, then the GH Fig. 27. Allwable levels f UWB systems radiatins fr HF UWB systems. energy needed fr target detetin an be prdued nly due t a high peak inident pwer P peak. Let us assess the rder f this pwer in a speifi example. Cnsidering that W = P peak τ, we shall determine the value f P peak using the range equatin parameters: P reak = 4π)2 ρqn R 4 D T σ Σ D R τ. The results f mputatins f the peak UWB generatr pwer vs. radar range fr several values f the impulse duratin τ are given in Figure 26. The fllwing numeri values were used in the mputatins: the energy DG f the antennas D T = D R 1 irular muth 3 meters in diameter), σ Σ =.1 m 2, the prbabilities f true detetin P D =.9 and false alarm P F = 1 6. The abve example indiates that the use f plain UWB wavefrms fr target detetin and disriminatin ver lng ranges requires the emplyment f generatrs f nansend impulses at the peak pwer f several t tens giga-watts. These generatrs are unique devies warranting inrpratin f elements with high eletri strength, nt being envirnmentally friendly bth due t parasiti x-ray radiatin and diret eletrmagneti radiatin. A dereasing f the peak pwer in high-pwer UWB radars an be ahieved in the nventinal way: transitin t mplex, large-base signals and their subsequent mathed filtratin. In rder t frm and press these UWB wavefrms with high rrelatin prperties, the pisend auray is required t exerise ntrl ver tempral psitin f the ded impulses. Aquiring f the neessary ptential in these radars withut invlving the use f giga-watt generatrs an als be dne, using ative pulsed 94 Электромагнитные Явления, Т.7, 1 18), 27 г.

20 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Fig. 28. A simplified blk sheme f UWB radar. antenna arrays. Yet, in this ase as well, a high tempral stability f the system is needed fr preise ntrl ver the array sillatrs. Hwever, the use in UWB radars f mplex ded UWB wavefrms with their subsequent mathed pressing and/r f ative pulsed antenna arrays slts thse radars in the ategry f sphistiated and stly systems, the tehnlgy f whih is immature t date. Fr all that, nt even the mplexity f engineering slutins is the main hindrane t reatin f relatively high-pwer UWB radars. The high-reslutin data ntent f UWB systems mandates the use f brad prtins f the bandwidth. On this aunt, the UWB radars may interfere with many ther radi systems sharing the same prtins f the spetrum, inluding suh vitally imprtant systems as the satellite navigatinal systems GPS, GLONASS, Galile), satellite mayday systems, airtraffi ntrl systems ATC), et. Fr that matter, the eletrmagneti mpatibility f the UWB radars with ther radi systems is f ruial imprtane fr their prspetive develpment. Cnerning lw-pwer UWB radars, fr the first time in the histry f radi engineering, a nrmative dument has been mpiled permitting the simultaneus peratin f UWB and narrwband radi systems arss the same frequeny range. This nerns the Regulatins f US Federal Cmmuniatins Cmmissin FCC) that went int effet in April f 22, with supplements effeted as f 23 and 24 [3,31]. This dument represents a result f wrkut relative t UWB radiative radiatin systems) f Part 15, Artile 47 f US Federal Regulatins Cde [32]. It frmulates restritins fr UWB radiatin levels in different frequeny ranges, the s-alled masks an instane f this mask is given in Figure 27). Meeting thse requirements, as well as bserving sme ther restritins, peratin f UWB systems is authrized withut liensing. At present, this dument is used as referene in many untries all ver the wrld. In the meantime, the eletrmagneti mpatibility f UWB radars ver lng peratin ranges, fr example, fr satellite-brne radars, with ther radi systems perating in the same prtins f the frequeny spetrum, shuld, in all evidene, be very prblemati. All tld, the mst realisti way f using UWB tehnlgies in radilatin at present wuld be prdutin f relatively lw-pwer radars fr peratin ver distanes f several t tens f meters. Thse radars are finding their appliatins in diverse areas f human ativities and, as a nsequene, have immense marketing prspets. 11. Sme f Examples f UWB Radars Created by the Russian UWB Grup f Msw Aviatin Institute A simplified blk sheme mst f the radars examples shwn belw is represented at fig. 28. The sillatr with ntrlled pulse repetitin frequeny prdues retangular pulses with frequeny f.5 3 MHz. The transmitter nsists f the shrt pulse shaper. The pulses frm shaper utput are delivered t transmitting antenna and make shk exitatin f it. Transmitting antenna radiates shrt RF pulses. The eletrmagneti field s pulses radiated are refleted frm mving bjet. Here the mdulatin f pulse repetitin frequeny arises. The mdulatin perentage depends f the velity and amplitude f target s mtin. The radar wrks in nditins f high level f passive nise the signals, refleted frm statinary bjets, whih will have large amplitude and will disguise useful signal. Time slts, pening the reeiver at the mment f input f signal refleted frm bjet at distane defined are frmed in reeiving path t eliminate interfering pulses. This task in radar design is exeuted Eletrmagneti Phenmena, V.7, 1 18), 27 95

21 I.Ya. Immreev a) b) Fig. 29. The appearane f the first example f the UWB radar U, v U, v a) b) Fig. 3. Time diagrams f heart and respiratry beats. t, s t, s by time disriminatr, being gated. It nsists f fast-ating eletrni swithes. The swithing time is in rder f 2 3 pisends. The swithes nnet reeiving antenna t UWB amplifier at the mments f signals input. These mments are defined by delay magnitude f ntrl signal at sftwarentrlled delay line. All the rest time the reeiver is shut. The signals reeived at time slts are deteted and amplified in integrating amplifier and the signal, arrying data f target mtin is seleted at its utput. The gating unit is nsists f sftware-ntrlled delay line and the shaper f shrt pulse. Time delay set by mirpressr-ntrlled unit defines the distane t bjet. Time nstant f integratin f integrating amplifier is hsen in dependene f the bandwidth f desired signal dynami harateristis f mtin f bjet examined). Fr example under measuring f parameters f persn vital ativity the bandwidth f desired signal is near 4 5 Hz, that rrespnds t aumulatin f 1 3 thusands f pulses apprximately. The aumulatin permits t derease average radiated pwer f transmitter and inrease signal-t-nise rati at the input f amplifier. The seleted and amplified lw-frequeny signal enters t analg-digital nverter ADC). The mirpressr-ntrlled unit direts the wrk f radar n given algrithms, mnitrs the state f majr units and mdules and prvides data utput fr further digital pressing in mputer. The seletin f mving targets, fast Furier transfrm and digital filtratin are sftware-prgrammable at the mputer. Physially all radars are built as mdular hardware. All mdules are implemented in shields, eliminated interferene f eah ther. Antennas nnetin is arried ut diretly t utput nnetrs f radar s reeiver and transmitter. All examples f radars are reated and tested with respet t priniples pinted. First example Figure 29 demnstrates external and internal printed iruit bard) views f this UWB radar example. The majr speifiatins f example are given belw: Range.1 3 m; Pulse pwer.4 W; Average pwer 24 µw; Repetitin frequeny 2 MHz; Duratin f radiated radi pulses 4 ns. First example is intended fr medial researhes. Figures 3 demnstrates the results f remte measuring physilgial parameters. At the Figure 3a) we demnstrate the time diagrams f summarized signals rrespnding heart and respiratry beats, whih were deteted by the UWB radar. The amplitude f radar utput signals is diretly prprtinal t the amplitude f thrax and heat beats. At the Figure 3b) shwn time diagram 96 Электромагнитные Явления, Т.7, 1 18), 27 г.

22 Ultra-Wideband Radi Systems. Their Peuliarities and Capabilities Fig. 31. Variability f ardia rhythm. Fig. 34. Third example f the radar ms Fig. 32. Send example f the radar. Cartid Artery Radial Artery U, v t, Se Fig. 35. The utput data f the third example f the radar. -1 t, s Fig. 33. The utput data f the send example f the radar. rrespnding nly heat beat signals deteted by the radar when a patient hlds his breathing. On tp f Figures 3a) and 3b) is shwn patient s ntrl eletrardigrams registered at the same time by a medial eletrardigraph. T appreiate the auray f radar measurements and quality f infrmatin nerning patient s heart ativity btained using UWB radar, we mpared data lleted with the radar and a medial ardigraph. The mparisn was led in instantaneus frm beat t beat) variatins f systle perid what is knw as variability f ardia rhythm). Fig. 31 demnstrates the measurement data depending n the number f a beat, whih were btained simultaneusly with using radar red line) and a ardigraph blue line). The effiient f rrelatin between these measurements was alulated. In this experiment, we have a rrelatin effiient.91. Fig. 36. Fifth example n the shunting-yard. Send example Fig. 32 demnstrates views f the send UWB radar example. Send example is intended fr measurements f pulse. At Fig. 33 the utput data f this radar are shwn. Third example Fig. 34 demnstrates views f the third example f the UWB radar in press f the measurement f speed f Eletrmagneti Phenmena, V.7, 1 18), 27 97

23 I.Ya. Immreev Frest Cntrl zne 1 metre 5 metre Fig. 38. Plae f measurements. a pulse s wave. This example nsists f tw radars - sensrs whih measure pulse n different vessels. At fig. 35 we shw the utput data f tw sensrs f the third example. Speed f a pulse s wave is the imprtant diagnsti fatr fr ardia and vasular diseases. Third prttype an simultaneusly measure variability f an ardia rhythm. It is the universal ranilgial tl. Furth example This example f the UWB radar is intended fr measurement f speed and a psitin f railway ars n a shunting-yard. The majr speifiatins f example are given belw: Range 3 m Cntrllable speeds f ars 1.2 m/s Pulse pwer 1 W Average pwer 8.4 mw Reslutin n range 41 m Step f installatin f a strbe f range 3.75 m Fig. 36 demnstrates views f the furth example f the UWB radar n the shunting-yard. At the fig. 37 the example f an arrangement f ars and signals reeived frm radar is shwn. Signals frm many radars lated n twers is transferred t the ntrl entre f the shunting-yard. After pressing this infrmatin is used fr frmatin f the trains. Fifth example The same radar has been used fr detetin f peple in a frest. On fig. 38 we see a plae f measurements and n fig.39 the sheme f measurements. Detetin was made n tw persns mving n distane 5 meters frm edge f a frest. Results f measurements are shwn n fig. 4. Open area Sixth example UWB Radar Fig. 39. Sheme f measurements. The radars desribed abve have been tested fr the detetin f alive peple nealed behind nntransparent barriers. Using the prttype f the UWB radar, we have perfrmed experiments n detetin f mving and mtinless peple nealed behind ptially nntransparent barriers. The radar was lated at a distane f abut 1m at ne side f a brik wall f width.45 m. A persn t be deteted std behind the wall. At the beginning f experiment, a persn was mving arund the rm, and then he beame still and then began mving again. The time diagram f radar utput signal is demnstrated in fig. 41a). One an easily bserve the signals rrespnding persn s mvement large amplitude signals) and signals rrespnding thrax mvements f mtinless persn when respiratin peridial signal in the retangular frame). Fig. 41b) illustrates signal s amplitudefrequeny spetrum. The maximum rrespndene a respiratin frequeny is learly ntieable. 12. Cnlusins The Authr is well aware f the inadequay f his attempt t prvide within the spae f this artile a ertain generalizatin f the peuliar features f peratin and nstrutin f UWB radi systems. He finds his slae in a remark by the funder f this diretin in radi engineering Dr. H. Harmuth made in 1981 [2], whih has nt lst its relevane t 98 Электромагнитные Явления, Т.7, 1 18), 27 г.