AN IMPROVED METHOD FOR RADIO FREQUENCY DIRECTION FINDING USING WIRELESS SENSOR NETWORKS Mickey S. Btson, John C. McEchen, nd Murli Tumml Deprtment of Electricl nd Computer Engineering Nvl Postgrdute School Monterey, Cliforni, USA ABSTRACT We present the design of remotely deployble distributed wireless ntenn system formed from wireless sensor network nodes. Specificlly, the focus is on enhncing the detection rnge of distributed wireless ntenn system. The primry objective is to crete methodology to steer the bem in the desired direction to enhnce rdio frequency (RF direction finding nd follow-on signl reception. The distributed wireless ntenn system uses combintion of time difference of rrivl ( nd dptive bemforming to loclize the trget nd enhnce the reception in the trget direction. The lines-of-bering re clculted using combintion of the Cross-Ambiguity Function to clculte the ctul time difference nd the Newton-Rphson technique to focus the bemforming efforts. A Lest Men Squres (LMS dptive bemforming lgorithm is then used to loclize the trget for further prosecution. Simultions indicte considerble improvement cn be chieved using this combined method. I. INTRODUCTION We present n improved method for identifying the direction of n RF emission using wireless sensor network. The network consists of n interconnected set of wireless sensor motes tht monitor nd collect dt pertining to RF signls of interest. The collected dt hs to be trnsmitted to nother loction for processing nd interprettion. A typicl network node consists of one or more sensors, trnsceiver with n omni-directionl ntenn, n onbord processor nd bttery. An exmple deployment of interest would be lrge number of sensor nodes dropped from n ircrft, Unmnned Aeril Vehicle (UAV or Unmnned Underwter Vehicle (UUV to densely cover n re of interest. Left unttended, these nodes cn then gther dt, collborte mong themselves to form wireless d-hoc network, nd trnsmit the collected dt bck to end-users locted fr from the scene of dnger. A methodology hs been developed using combintion of both nd bemforming in order to enhnce collection in specified direction. It is envisioned tht the individul sensor nodes will hve low-cost omnidirectionl ntenn, but this methodology will tke dvntge of the number of nodes nd hve the sensors working together s coherent ntenn rry. [] Reserch in [] first proposed n rchitecture for using wireless sensor networks to sense the RF environment for the purpose of trget direction finding. Specificlly, they proposed distributed rchitecture consisting of rndomly distributed collection of wireless sensor motes in communiction with centrl node, or centrl controller, which performed follow-on processing of individul node signl strengths to computer the rry fctor. The work in [] demonstrted tht rndom selection of subset of ll nodes by the centrl controller could substntilly mitigte the effect of sidelobes, or grting lobes, while nrrowing the bemwidth considerbly. This pper drws from the work in [] nd wireless ntenn foundtions of [3] to develop methodology for identifying nd converging on signl of interest. Specificlly, we explore the use of Time difference of rrivl ( to rpidly converge on qudrnt of interest then use trditionl bemforming pproch to perform fine tuning. A. Time-difference of Arrivl ( tkes dvntge of the fct tht trnsmitted signl will rrive t the different elements t different time instnts, s shown in Fig.. In the distributed wireless ntenn rry ech sensor forms two-node collector pir with the centrl controller. The bsic principle of the two-element liner rry will then be extended to encompss the entire ntenn grid. The sensors within our grid will tke dvntge of the fct tht our grid is densely populted nd tht the sensors re spred over wide re. [4] Defining in terms of the emitter nd ntenn element positions is ccomplished using the vectors r nd r from Fig. where r is the distnce from the centrl controller to the emitter nd r is the distnce from n individul ntenn element to the emitter. [4] Eqution (, illustrtes the difference in the length of the two vectors r =[x e - d/ y e ] T nd r =[x e + d/ y e ] T, divided by the speed of light c, yields the : r r d d xe ye xe y, ( = = + + + e c c where x e nd y e re the respective x-y coordintes of the emitter nd d is the distnce between the two-node collector pir.
where E[ ] is the expecttion opertor. The minimum men-squre error (MMSE is obtined by setting the grdient vector of Eqution (3 with respect to w to zero. Figure. Geometry for collector pir. [4] Multiple mesurements cn be used to estimte emitter position in mnner nlogous to nvigtor performing tringultion. However, since the nodes do not hve good ngulr spred reltive to the trget only line-of-bering is discernble. [4] B. Adptive Bemforming The wireless ntenn sensor nodes re deployed rndomly over n re of interest, resulting in rndom positioning of the sensor nodes. Subsequently, these sensor nodes form clusters nd their loctions re determined using loction discovery techniques. These loctions re then reported bck to the centrl controller. The sensor nodes will mke up n rry ntenn tht performs dptive control of the pttern in order to mximize the rry pttern in the direction of the trget. The pttern of the rry is controlled by dynmiclly vrying the phse nd mplitude of the received signl from ech element. [] Since the sensor grid will require the bility to steer the min lobe n dptive lgorithm will be implemented. The LMS lgorithm recursively computes nd updtes the complex weights. [] The LMS lgorithm requires knowledge of the desired signl, which will be ssumed. The error between the observed nd desired signl is used to clculte the weights required to dptively form the bem in the desired direction. The error is defined to be: ( = α ( ( ( e t t b t where α(t is the reference signl nd b(t is the output of the bemformer. The complex weights re djusted nd pplied to the signl received by the rry elements in n itertive mnner. For ech dt smple, the complex weights re chosen to minimize the men-squre error between the bemformer output b(t nd the reference signl α(t given by [,3,6] E e ( t = E ( α ( t b( t (3 The vlue of the weight vector t time (t+ is updted s follows: [ [ ]] w w t w t E e t ( + = ( + μ (, (4 where μ is the convergence fctor. After obtining the grdient vector ( t the weight vector is updted w E e [ ] by substituting into Eqution (4. Simplifying, we hve: * w( t + = w( t + μ g( t e( t, (5 where * represents complex conjugtion nd the instntneous estimtes given by [α(tg(t] nd [g(tg H (t] hve been used insted of E[α(tg(t] nd E[g(tg H (t], respectively. The term E[g(tg H (t] is commonly known s the rry correltion mtrix R gg nd denotes the correltion between the signls received by the vrious rry elements. [, 3, 6] II. ANALYSIS OF METHODS AND BEAMSCANNING METHODS A. Anlysis When the complex envelopes of n emitter signl re collected by the two sensors then s were determined directly by clculting the cross-mbiguity function (CAF. A frequency difference of (FDOA cn lso be determined from clculting the CAF, which could be very useful if prosecuting mobile trget. [4, 5] However, our trget is ssumed sttionry or slow moving. The complex envelopes of the two signls will be denoted by s (t-τ nd s (t, where t is the time of the first smple, nd τ is the time dely between the two. The CAF is defined s T jπ ft (, τ = ( τ ( (6 CAF f s t s t e dt 0 where f is frequency, T is the integrtion time, nd denotes the complex conjugte. Since the function peks when τ = nd f = FDOA, it is often used s mens to determine these two quntities simultneously. [4, 5] The solution is determined by locting the pek of the CAF, CAF(f,τ. [4, 5] It is worth noting tht when the sensors or the emitter re not in motion tht the crossmbiguity function is simply the utocorreltion function. In Fig., the of the sensor locted the frthest from the centrl controller is depicted. The frequency difference of rrivl is zero which is expected. Once the s were determined the Newton- Rphson technique ws used to determine line-ofbering. The Newton-Rphson lgorithm is bsed on estimtion theory nd uses n over-determined set of liner equtions of the form m= f z, t, (7 (
where m is k-vector representing the mesurements nd z is the loction of the emitter. Figure. Mx distnce 3D. Figure 3. 4 Sensors. 5 Estimtes per Two-node Collector pir. The time difference of rrivl ws clculted using the cross-mbiguity function discussed erlier. This would be the k observtions referred to s the m vector. The m i vector is the mesurements for the current estimted position s shown in Eqution (8. δ m= m m i (8 By iterting through this process the current solution is used s the next estimted emitter loction until the solution flls below some predetermined smll threshold. A lest squres estimtion is pplied to yield n emitter position estimte. In Fig. 3, the trget emitter ws locted t 45 from the centrl controller in the first qudrnt. Three frequencies 57 MHz, 800 MHz nd.4 GHz were simulted nd ll produced similr results. Only the 57 MHz frequency is illustrted in this pper. Severl simultions were conducted with the figure shown being representtive of the results. Since the wireless ntenn grid is not moving nd the emitter is t the sme reltive bering to ll the two-node collector pirs geoloction ws unobtinble. However, s seen in Fig. 3 nice lineof-bering to the trget cn be clculted. A method for computing s nd then subsequent lines-of-bering hs been presented. As ws shown the CAF nd Newton-Rphson methods were ble to determine line-of-bering to the trget. Now n illustrtion of bemscnning will be presented. B. Bemscnning Method Two described in [] is used for our sensor grid. The centrl controller selects the number of rry elements needed to form the desired bem. The centrl controller in effect cretes n rry, which is merely subset of the totl rry. For exmple, consider sensor grid tht contins K elements rndomly spred over totl re, A. The centrl controller will select, Λ nodes within n re, A, where A A nd Λ K. The centrl controller will crete P node subset from the Λ nodes where P<<Λ. This subset will form the bsis for the rry fctor. The following is n nlysis of the LMS dptive bemforming lgorithm. ( ( ( ( ( ( π j, * x sin θ *cos + y e sin θ sin λ θ = (9 where λ is the wvelength of the signl in meters. x nd y re the loction of the individul ntenn elements in meters. θ is the elevtion ngle nd is the zimuth ngle. The centrl controller then clcultes the rry weights w by summing ech element over ll possible vlues of θ nd. ( θ, M N m= n= * mn π j ( xmn sin( θ cos( + ymn sin( θ sin( λ = w e (0 where P=MxN is the totl number of nodes in the subset nd w mn is the complex weight π j ( x sin( 0 cos( 0 sin( 0 sin * mn θ + ymn θ ( 0 λ w mn = Wmne ( pplied to the (m,n th element. The mximum vlue of ( θ, occurs t ( θ, = ( θ0, 0, nd the min lobe θ,. points towrds ( 0 0 Ech dt smple of the signls collected from the chosen nodes itertively updtes the corresponding rry weights. The mgnitude nd ngle of ( θ0, 0 re stored. This completes n itertion of the dptive bemforming solution. Now the centrl controller tkes nother 500 dt smples from ech node within new subset of P nodes. Then the process described erlier is repeted nd the finl result is dded to the previously stored result. This process is shown in Eqution (. L Totl ( θ, = i ( θ, ( where L equls the totl number of subsets creted. Substituting Eqution (0 into the bove eqution results in the following: L M N π j ( x sin( cos( sin( sin * mn θ + ymn θ ( ii ii λ Totl ( θ, = w min e i m n (3
where P=MxN is the totl number of nodes in ech subset. This mgnitude is then plotted in db ginst ll possible vlues of zimuth nd elevtion. This process is repeted until desired solution hs been found. Method Two in reference [] ws shown to hve n energy cost per sensor of δ joules/trnsmission. Reference [] demonstrted tht this energy cost per sensor did not increse even though the totl number of trnsmissions within the network my increse. III. BEAMWIDTH CONTROL With the desire to enhnce RF collection in specified direction it is importnt to understnd how to control the bemwidth of the bem. When in locliztion mode wider bem would be preferred. After the signl hs been loclized it would be preferble to nrrow the bem in order to enhnce collection. As cn be seen in Fig. 4-5, the min bem bemwidth hs continued to get nrrower s the centrl controller chose nodes tht re further wy from its own loction. In ffect, the centrl controller is reducing the node density of the ntenn rry. Unfortuntely, there re limits to how wide the initil serch bem my become. As the number of rry elements re incresed, unless the overll size of the rry is incresed, n upper limit on the bemwidth is reched. This cn be seen through nlysis of both plnr rry bemwidth nd the rndom rry discussed in the previous section. The bemwidth for plnr rry is determined by using Equtions (4 nd (5. In order to determine the respective bemwidth the rry is seprted into x nd y liner rrys. These equtions for the respective scn ngles for both elevtion nd zimuth re shown in Eqution (6 []. uniform liner rry. Now shown below for the zimuth []. x0 y0 0 ( L d + 0 ( L+ d = cos cos 0.443, = + cos cos 0.443, (7 where d = L/ N, L is the length of the uniform liner rry nd N is the number of nodes long the length of the uniform liner rry. Exmining equtions (6 nd (7 it cn be seen tht s the number of elements increses for specific re, i.e. the node density increses, the bemwidth reches n upper-bound for given wvelength []. Figure 4 illustrtes for both the uniform liner rry nd the rndomly dispersed rry tht when the number of sensors is incresed, but the size of the rry is held constnt, i.e., the node density increses, the bemwidth increses resulting in loss of gin, up to limit. Consequently, centrl controller my find the direction of trget emitter by scnning with lrge bemwidth, but the number of scns required to do this will hve some lower bound due to the limit on the size of the bemwidth. Thus if we cn find wy to reduce the initil scn re, we cn improve the minimum time to find the direction to trget. Θ = elevtion cos ( [ ( ( ] cos, (4 θ θ + θ sin x 0 y 0 Θ = zimuth [ ( ( ] sin θ + θ cos x 0 y 0, (5 where 0 is the desired zimuth scn ngle nd θ is the desired elevtion ngle. It cn be seen how the bemwidth in the zimuth nd elevtion directions impcts the gin of the bem. [] θ θ x y θ ( L d + θ ( L+ d = cos cos 0.443, = + cos cos 0.443, (6 where d = L/ N, L is the length of the uniform liner rry nd N is the number of nodes long the length of the Figure 4. Bemwidth versus Node Density where the blue sterisks represented vlues from the rndomly dispersed rry of eqution (3 nd red vlues represent clculted vlues from equtions (6 nd (7. Reference [] demonstrted how the centrl controller cn control the bemwidth of the minbem through the node selection process. As cn be seen from Fig. 5-6, the frequency of the SOI nd the size of the distribution re of the subset
round the centrl controller, hve the gretest effect on bemwidth. The subset cretion will be used to trnsition the bem from signl locliztion mode to either pssive or ctive signl prosecution mode. Wht is significnt bout the results from reference [] is tht no dditionl trnsmission burden hs been plced on the individul sensor nodes, therefore giving cpbility to control the bemwidth without incresing the overll energy consumption of the rry. IV. DIRECTION FINDING METHODOLOGY The proposed methodology for enhncing collection in distributed wireless ntenn system is described s follows. A two-tiered hierrchicl clustering sensor network rchitecture is ssumed. A primry node (i.e. UAV, UUV, etc. is tsked with mintining frequency, phse nd dt synchroniztion mong the remining nodes (or secondry nodes within the cluster. The network is comprised of K sensors spred over nd re, A. Figure 5. Arry Pttern. 57 MHz (outer pttern-red, 800 MHz (middle pttern-blue & 400 MHz (inner ptterngreen. Nodes within 5 sq. m. grid of the bemcontroller. Figure 6. Arry Pttern. 57 MHz (outer-red, 800 MHz (middle-blue & 400 MHz (inner pttern-green. Nodes within 500 sq. m. grid of the bemcontroller. -- Step. The centrl controller cts s reference ntenn by gining initil intercept nd frequency-ofinterest (FOI determintion. -- Step. The centrl controller will then determine the collected from the Υ sensors furthest from its loction. Ech sensor forms two-node collector pir with the centrl controller. The centrl controller will utilize the cross-mbiguity function presented erlier to clculte the s between ech of these Υ sensors nd the centrl controller. -- Step 3. The centrl controller will then use the modified Newton-Rphson technique to loclize the signl-of-interest to two specific lines-of-bering. -- Step 4. The centrl controller will then begin the bemforming process. From the re, A, the centrl controller will crete rndom P i node subset from the Λ nodes contined within given re, A. Following the lgorithm stted bove the centrl controller will crete L subsets to crete the pproprite bem for given ( θ0, 0. -- Step 5. Bsed on the results of this locliztion the bemcontroller cn rndomly choose sensors tht re dispersed within lrger re to further nrrow the bem into the trget direction in order to mximize reception. V. COST ANALYSIS For the computtion of steps nd 3 bove, the totl trnsmissions re defined s T = Ωϒ, (8 where Ω is the totl number of two-node collectors nd ϒ is the totl number of received dt smples sent bck
to the centrl controller per two-node collector pir. These received dt smples re then used by the Centrl Controller to determine the line of bering. If the cost per trnsmission is δ joules/trnsmission, χ joules is the energy expended when the receiver is on, but witing to trnsmit nd ssumes the worst cse. χ joules is the energy required to fully energize trnsmitter tht hs been in sleep mode nd lso ssumes the worst cse. The totl energy cost to clculte line of bering is then defined s Γ = δt + ( Ω ϒ χ+ωχ, (9 = δωϒ+ ( Ω ϒ ( 0.δ +Ω( 0.5δ where Γ is in units of joules. The first term in Eqution (9 is the energy expend the dt. The second term in Eqution (9, is the totl energy expended witing to trnsmit. This term ssumes tht node wits for ll other nodes to trnsmit before it cn trnsmit. χ is defined in terms of frction of the energy expended to trnsmit the dt. The third term is the energy expended to bring ll of the prticipting nodes out of sleep mode, which ssumes tht ll prticipting nodes were in sleep mode. χ is lso defined s frction of the energy to trnsmit the dt. The energy cost per sensor is ϒ( 0.δ Ξ = δϒ+ϒ( 0.δ + ( 0.5δ, (0 Ω where Ξ is mesured in units of joules/sensor. The determintion process would tke totl of t seconds. t =Ωςϒ+Ω ε +Ωϒ t+ω t, ( where Ω is the number of nodes, ς is the cost per estimte to perform the CAF, ϒ is the number of estimtes per two-node collector pir nd ε is the time required to clculte the line of bering using the NRT. The time node tkes to trnsmit is t. This term ssumes TDMA type medium ccess, in which node hs time slot nd wits for ll other nodes to trnsmit before it cn trnsmit. The time required to wke the nodes is t nd ssumes the worse cse, tht ll nodes selected re in sleep mode. Now the totl time required to do combintion nd bemforming cn be defined s follows: t = / t + tbf, ( where t is the time to required to loclize the trget nd t BF is the time required to form one bem. After substituting Eqution ( into Eqution ( nd combining like terms the totl time required cn be rewritten s t/ =Ωςϒ+Ω ε +Ω t+ω t + t +Λ t+λ t. (3 Eqution (3 ssumes the worst cse tht ll the nodes need to be brought out of sleep mode. In ddition, it ssumes tht the nodes used in the clcultions re not used in the bemforming clcultions. The totl energy to enhnce collection using combintion of nd bemforming is defined s Γ / =Γ +Γ BF, (4 where gin Γ is defined in Eqution (9 s the energy required for nd Γ BF is drwn from [] s the energy required to form one bem using the multiple rndom selections method. After substitution, Eqution (4 cn be rewritten s follows: L Γ / =Ωδϒ+ ( Ω ϒ χ+ω χ + δ + ( Λ χ+λχ / δ ( ( 0.δ ( 0.5δ δ ( ( 0.δ ( 0.5δ (5 Γ =Ω ϒ+ Ω ϒ +Ω + + Λ +Λ VI. COST COMPARISON The energy cost using the combintion of nd bemforming will lwys be less thn the bemscnning only method s long s the following criteri is met: Γ/ Γbs L Ωϒ+Ω δ ( ϒ ( 0.δ +Ω ( 0.5δ + δ +Λ ( ( 0.δ +Λ( 0.5δ L ηδ + η ( Λ ( 0.δ +Λ( 0.5δ L Ωϒ + Ωϒ( 0.δ ϒ ( 0.δ + Ω( 0.5δ ( η + ( Λ ( η ( 0.δ T +Ωϒ( 0.δ ϒ ( 0.δ +Ω( 0.5δ ( η T + ( Λ ( η ( 0.δ (6 Upon close inspection of Eqution (6, it cn clerly be seen tht the our proposed method will lwys use less energy thn [] s long s the number of trnsmissions to perform the plus the dditionl fctor ssocited with the energy spent witing to trnsmit nd the energy required to bring sensor out of sleep cycle is less thn the number of trnsmissions required to conduct the 360 bemscn minus the trget bem. The trget bem will be formed in both cses. Additionlly, the combintion of nd bemforming will lwys be fster s long s the following criteri is met: t/ tbs Ωςϒ+Ω ε +Ωϒ t +Ω t + t +Λ t +Λt ηt + ηλ t +Λt Ωςϒ+Ω ε +Ωϒ t+ωt ( η t +Λ( η t t +Ωϒ t +Ωt η t +Λ η t ( ( (7 Eqution (7 shows tht this new method will be fster thn [] s long s the time required to form the bems, less the trget bem, plus the mount of time spent L
witing to trnsmit nd the time required to bring sensor out of sleep mode is greter thn the time to determine the trget line-of-bering. In prctice, the combintion of nd bemforming will lwys be fster thn bemscnning only. Focusing on the 45 bems from Figure 5, it cn be observed tht 360 scn could be conducted t 5 increments with sufficient overlp to not leve gps in coverge. This cn be ccomplished with η = 4 bems. Using the bemwidth from Figure 5 nd the method in [] it would require 6850 time units ( time unit being relted to processor cycles to scn 360. The energy nd time cost re dependent on the number of bems tht need to be formed for bemscnning only. As stted erlier, the number of bems required would be bsed on the solid ngle of the bem nd the desired overlp of the bems. Tble depicts the energy cost nd times for vrious η. The tictoc commnd in MATLAB ws used to determine tht t = 5 time units were required to crete bem, ε ws determined to be equl to 0. time units nd ς ws determined to be time units per CAF estimte for ech two-node collector pir. These times would vry bsed on hrdwre nd softwre implementtion. Additionlly, it is expected tht these times would be much lower in rel world implementtion. From [], the energy to form one bem is 399.9δ joules. From Eqution (9, the totl energy to do is 45δ joules, where Ω = 4 sensors. ACKNOWLEDGEMENTS This work is supported in prt by the lnd nd UAV component of the U.S. Specil Opertions Commnd. REFERENCES [] Blnis, C. A., Antenn Theory Anlysis nd Design, nd edition, Wiley, New York, 997. [] Btson, M. S., McEchen, J., Tumml, M., Enhnced Collection Methodology for Distributed Wireless Antenn Systems, IEEE Conference on Systems of Systems, Sn Antonio, Texs, April 007. [3] Litv, J. nd Lo, T., Digitl Bemforming in Wireless Communictions, Artech House, Norwood, MA, 996. [4] Loomis, H. H., Geoloction of Electromgnetic Emitters, NPS- EC-00-003, Nvl Postgrdute School, Monterey, CA, Revised October 003. [5] Steinberg, Bernrd, Principles of Aperture nd Arry System Design, John Wiley & Sons, Inc., 976. [6] Hrry L. Vn Trees, Optimum Arry Processing, Prt IV of Detection, Estimtion, nd Modultion Theory, John Wiley & Sons, New York, 00. # of bems, η Γ bs, (joules Γ /, (joules t bs, t /, 0 874δ 445δ 3000 6 4 67.6δ 445δ 6850 6 30 837δ 445δ 8500 6 Tble. Energy nd Time Cost comprison between bemforming method of [] vs. the combined bemforming method of this pper. It cn be seen from the results shown in Tble tht the combintion of nd bemforming in most prcticl cses will lwys be fster nd more energy efficient thn the bemscnning only method. VII. SUMMARY In summry, methodology for enhncing direction finding nd reception in distributed wireless ntenn system hs been presented. This methodology demonstrted how to focus energy in specified direction using combintion of nd dptive bemforming techniques. It ws shown tht the combintion of nd dptive bemforming provides rpid locliztion of the trget. In ddition the energy burden cn be distributed throughout the entire network creting significnt energy svings. This process is not only more ccurte, but is lso less computtionl burdensome to the centrl controller.