Impacts of Signals Cross-Correlation Characteristics on Matched Filtering Performance for MIMO Radar

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1 22 4th Intenational Confeene on Signal Poessing Systems (ICSPS 22) IPCSIT vol. 58 (22) (22) IACSIT Pess Singapoe DOI:.7763/IPCSIT.22.V58.8 Impats of Signals Coss-Coelation Chaateistis on athed Filteing Pefomane fo IO Rada Qing Wang + Huai-tie Xiao and Hao-wen Chen ATR Key Lab National Univesity of Defense Tehnology Changsha 473 China Abstat. Consideing that ompletely othogonal signals annot be found in eality the impats of oelation haateisti of IO ada signals on the pefomane of mathed filteing output at the eeive ae disussed in this pape. Fistly the outputs of mathed filtes ae peisely modeled by autooelation funtions and oss-oelation funtions of multiple signals. And an impat fato is also defined to evaluate the degee that the oelations an affet the filte outputs unde diffeent onditions. The impat fato funtion ontains the influene of senso spaing the efletion oeffiient of diffeent tanst signals and taget azimuth angle simultaneously. Then we qualitatively analyze the elationship between the oelation effet on mathed filteing and those thee paametes and obtain some useful esults. Finally some numeial examples ae pesented to demonstate the onlusions. Theoetial analysis and expeiments both show that the outputs of mathed filtes may be obviously influened by the oelation of signals and the effet vaies unde diffeent onditions patiulaly enomous in some situation. Consequently IO ada system with multiple signals equies moe highly on the othogonality of tanst wavefoms. Keywods: IO ada mathed filteing othogonal signals.. Intodution IO ada [] is a new bon onept that has been poposed fo a few yeas of whih both system ahitetue and signal design ae vey flexible and its pefomanes in taget detetion paamete estimation and high esolution ae elatively extaodinay ompaed to onventional adas. Theefoe it is paid muh attention to by many eseahes and institutions. Sine its naissane in 24 a lage numbe of lettes have ome foth advaning it into ealization by theoetial suppots. Fo example in [2] J. Li and the othe authos summaized some new onlusions in eent yeas deeply intepeted the idea of IO ada and polaimed its potentials. The authos in [3] and [4] studied on the detetion pefomane and paamete estimation apability of the new ada espetively. any othe papes alike the pevious also demonstated the geat supeioity of IO ada fom diffeent pespetives. Howeve as a fesh new idea the studies on IO ada ae fa fom in-depth. Its onept needs to be undestood moe peisely and numeous poblems in theoy and implementation demand settlements. Essentially the advantages of IO ada ae obtained fom divesity tehniques suh as spatial divesity wavefom divesity and so on. In othe wods IO ada an impove taget infomation aquisition apabilities by optizing aay and wavefom design. Usually the multiple wavefoms used in IO ada need to be othogonal to eah othe so that mathed filtes an be employed at the eeive to sepaate all the tanst signals in ode to ahieve the effets of wavefom divesity. Afte that we an ay out the signal poessing poedues like beam fong and paamete estimation subsequently [5-6]. The othogonality of tanst wavefoms is theeby the basis fo IO ada signal poessing. Cuently many + Coesponding autho. addess: qwang_87@63.om. 6

2 eseahes have been making thei effots to find othogonal wavefoms and some of thei appoahes ae designed to ahieve good oelation pefomane [7] taken as an example. Howeve in patie ompletely othogonal wavefoms do not exist even if small oss-oelation value is diffiult to ealize. When tanst wavefoms ae not ompletely othogonal they may not be able to be sepaated by passing eeived signals though mathed filtes and the follow-up poessing will inevitably be affeted. Hene the mathed filteing of inomplete othogonal o quasi-othogonal signals used in the sene of IO ada is studied in this pape and some impotant onlusions ae dawn. Fist the output of quasi-othogonal IO ada wavefoms passed though mathed filtes is modeled. The model involves in the efletion oeffiients of diffeent tanst wavefoms senso positions and taget azimuth that may impat on the output of filtes. Then an impat fato funtion is poposed to indiate the degee of influene aused by signal oheene in filte output. Finally we pesent some numeial esults to illustate this effet. 2. athed Filteing odel As shown in Fig. assume that thee is a naow-band monostati IO ada system of whih both tanstte and eeive ae linea aays with and N elements espetively. All of the elements at d tanstte and eeive ae omnidietional antennas loated at known loations given by tm d n and. The tanst signals aie fequeny is f and thei omplex envelopes ae diffeent fom eah othe epesented by s () m t. The azimuth of the fixed point taget is θ and the distanes fom tanst and eeive aay elements to the point taget is tm and n sepaately. t θ t N s ( t ) s (t) N Fig. : IO ada system model. Eah tanst signal popagates though diffeent path and aives at the eeive with a delay equal to tm / + n / so we an expess the eeived signal at the nth eeive as x () t s ( t ) e n () t () tm n tm n j2 π f ( t ) n = αm m + n m= whee αm is the efletion oeffiient of the mth tanst signal nn () t is zeo mean omplex Gaussian noise and assumed ielevant to all the tanst signals (hee the popagation powe loss is otted so as to simplify the fomula). If the tanst signals ae ompletely othogonal to eah othe whih means they an satisfy the following ondition: * δτ ( ) k = l sk() t sl ( t τ ) dt = (2) k l whee is pulse width τ τ is time delay and δτ ( ) is an impulse funtion. Then the mathed filte an be used to isolate the eho of diffeent tanst signals fom the eeived signals. The mathed filte stutue of IO is usually the fom shown in Fig. 2. 7

3 Fig. 2.athed filte stutue of IO ada. The at of a mathed filte is the same as a oss oelato whih suggests that we only need to oelate the eeived signal with tanst signals espetively to ahieve the pupose of tanst signal sepaation. Howeve (2) atually an not be met in patie that is when the kth tanst signal pass though the lth oelato the output will be as below: ( ) * kk τ k = l sk() t sl ( t τ ) dt = (3) kl ( τ ) k l whee τ τ is the time delay of the mathed filte and satisfies () kk τ is the autooelation funtion of the kth tanst signal kl() τ is the oss-oelation of the kth and the lth signal. Though wavefom optization algoithms suh as the law in [7] we an design some wavefoms that have elatively small oss-oelation values. But we should note that the eeived signal at the eeive is some kind of supeposition of multiple tanst signals. Theeby the oveall effet annot be just negleted. Futhemoe mathed filteing is a sliding oelation poess. While filteing diffeent signals ossoelation output will ause sidelobes whih may podue false taget o mask off the eal taget [8]. Fom hee on we will stat to ahieve a peise model of the mathed filte output. In ode to make the model moe onise some paamete substitutions ae pesented ahead. Fist let ti j t' = t (4) ti / + j/ This step is atually to move the oigin of time axis to whih is the delay of the signal fom the ith tanst element to the jth eeive element. By substituting (4) into (2) we an get the output of the jth eeive as bellow ti j tm j j(') = αm m(' + + ) m= ti j tm j j2 π f ( t' + + ) ie + nj (') t ti tm j2 f ( t' ) ti π + tm = αm m + + j m= x t s t s (' t ) e n (') t (5) [8] When tanst signals ae not ompletely othogonal the output of the ith mathed filte an be given by y x t s t e dt * j2 π ft' ji ( τ) = j ( ') i ( ' τ) ' ti tm ti tm j2 π f ( ) = αiii( τ) + αm( τ + ) e (6) Fo a fa field point taget ti tm ( dtm dti )sinθ d sinθ = = (7) Then we have 8

4 θ y e 2 θ j π f ji ( τ) = αi ii ( τ) + αm ( τ + ) (8) Now we have obtained the output by passing the jth eeive signal though the ith mathed filte. And the output fomula is simply omposed of shifted oelation funtions weighted by efletion oeffiients and exponential fatos. As an be seen fom the above equation the effet of signal oelation funtion between signals is mainly efleted in the seond tem whih is also affeted by aay element spaings taget loation and efletion oeffiients. Theefoe in ode to evaluate the effet on the pefomane of mathed filteing when the paametes ae diffeent we define an impat fato: F ( θ) = max i sin 2 θ d j f θ π αm( τ + ) e α d (9) α () i ii whee α is the taget efletion oeffiient veto whih is made up of all the efletion oeffiients of diffeent signals d is tanst aay element position veto and θ is taget azimuth. When the numbe and fom of the tanstted signals ae all known the signals oelation funtions ae detenate and F( α d θ) is only elated to the thee paametes α d and θ. The impat fato is atually the maximum magnitude of the oss-oelation pat nomalized by autooelation peak in all the hannels. It epesents the geatest impat of signal oelation haateisti on the pefomane of mathed filteing. Smalle impat fato suggests that oss-oelation has less effet on mathed filteing while the lage fato may indiate that false peak would be aused and even the eal taget signal would pobably be offset. 3. Impat with Diffeent Paametes It an be seen fom (8) that when the tanst signals ae not ompletely othogonal the output of mathed filte is the supeposition of signal autooelation and oss-oelation funtions and affeted by tanst aay element position taget efletion oeffiients and taget azimuth. Sepaately we qualitatively disuss as follows: 3.. Impat of tanst aay The distanes between tanst aay elements will indue time delay of omplex envelope of tanst signals esulting in oss-oelation funtion shift. Unde nomal iumstanes the magnitude of ossoelation funtion geneally deease as time delay gows whih is shown in Fig. 3 as an example. Theefoe when the taget loation is fixed with the aay element spaing ineases the oelation effet on the mathed filte output will gadually deeases. In patiula when 2 θ the tanst T signals have a time inteval of two times of p and the two signals outputs though the mathed filte do not ovelap. So at this time the impat of oelation is nized. Coss-oelation Coss-oelation x -7 x -7 Fig. 3. Coss-oelation of tanst signals Impat of efletion oeffiients 9

5 The size of efletion oeffiients affet the powe of eah impinged signal at the eeive so will it hange the magnitude of autooelation and oss-oelation funtion in the output of eah mathed filte. Espeially weak taget that has small efletion oeffiient is moe vulneable to be influened by ossoelation pat (the seond tem in (8)) so that the eal signal is vey likely to be masked off Impat of taget azimuth Sila to the impat of aay element spaing when the aay element spaing is lage the hanges in azimuth will affet the delay of signal envelope and also the phase of the oelation funtion weight e 2 θ j π f. Espeially when aay element spaing is lage a small azimuth hange will esult in signifiant phase vaiety. In addition while tanst aay apetue is small (an be ompaable with the aie wavelength) the popagation delay has little effet on signal envelope so the mathed filte output an be appoximated by: 2 θ j π f y () τ = α () τ + α () τ e () ji i ii m Then the aay element spaing and taget position pimaily impat on the phase of oelation funtions. 4. Numeial Results The tanst wavefoms used in ou expeiments ae poly-phase othogonal ode wavefoms given by [7]. The numbe of the ode sequenes is 4 length 4 and phase numbe 4. The pulse width is μs and aie wavelength is. m. eanwhile in ode to moe auately haateize the oelation between signals omplex oelation funtion is employed hee [9]. 4.. Aay element spaings In onsideing the influene of aay element spaings on the output of mathed filte all efletion oeffiients ae set to so as to elinate thei impats. And the azimuth of the fixed taget is 2. Then we foe the distibution of aay elements to be unifom and obseve the impat fato vaying with the aay apetue ineases. The esult is illustated in Fig Impat fato Apetue/m Fig. 4. Impat of element spaing on mathed filteing. As expeted while the aay apetue ineases the spaing between aay elements gows aodingly so the impat fato gadually deeases. Besides when all aay element spaings meet 2 θ that is when the aay apetue is geate than 278 m the impat fato hanges to Refletion oeffiients Assung that the efletion oeffiients of the fou tanst signals ae.7 and.6 espetively tanst aay position veto is d = [ 2 3] in units of m taget azimuth is θ = 2. The outputs of the fou mathed filtes ae shown in Fig. 5.

6 Channel4 Channel3 Channel2 Channel x x x x -6 Fig. 5. Impat of Refletion oeffiients. It an be seen that in hannels and 4 in addition to the peaks at τ= the positions identified by the dotted lines also have lage peaks esulting in false tagets. Theefoe if the taget efletion oeffiient of the signal is smalle the eal signal would be onealed in the sidelobes Taget azimuth The impat of azimuth hange is bound by aay element spaings so we fistly assume a unifom linea aay ase with an apetue of 3m. The esult is plotted in Fig. 6 whih illustates the hange of impat fato in azimuth fom π /2 to π /2. Apetue=3m.55.5 Impat fato θ/adian Fig. 6. Azimuth impat when apetue is 3 m. It an be seen that as the taget azimuth ineases the impat fato funtion shows damati hanges in the ups and downs. And on some loations thee ae vey high peaks indiating that the mathed filte output will be even wose at these angles. Then suppose that the aay apetue is 3m whih is 3 times the aie wavelength and the poess same to the fome is epeated. We obtain a uve dawn in Fig. 7. Clealy when the aay element spaings ae small the impat fato uve flutuates moe smoothly but thee ae still some high peaks emege at etain angles. Apetue=3m.55.5 Impat fato θ/adian Fig. 7. Azimuth impat when apetue is 3m.

7 5. Conlusions In this pape we studied the impats of tanst signal oss-oelation on mathed filte output when using quasi-othogonal multiple signals in IO ada. By moe auately modeling the poess of mathed filteing the pefomane of mathed filte output unde diffeent onditions is analyzed. Theoetial analysis and expeiments show that in the inomplete othogonal tanst signal ase the influene on mathed filte output pefomane is subjet to diffeent degees. These impats ae not only elated to autooelation and oss-oelation pefomane of the signals themselves but also the distibution of tanst aay taget efletion oeffiient of eah signal and the taget azimuth angle. Theefoe the multiple signal system of IO ada equies moe pefet othogonal tanst signals. Although we still have lage oom in designing signals it is an indisputable fat that the signals an not be ompletely othogonal. oe ational as it is we may be able to utilize the oss-oelation haateistis of the tanst signals so as to enhane the pefomanes of some othe aspets of IO ada. Theefoe it is also the signifiane of this pape to stimulate moe ealisti and novel ideas and onepts to pomote the implementation of IO ada system. 6. Refeenes [] E. Fishle A. Haimovih R. Blum L. Cini D. Chizhik and R. Valenzuela IO ada: An idea whose time has ome in Po.of the IEEE Int. Conf. on Rada. Philadelphia PA Apil 24. [2] J. Li and P. Stoia IO Rada Signal Poessing New Yok: Wiley & Sons 28. [3] E. Fishle A. Haimovih R. S. Blum L. J. Cini D. Chizhik and R.A. Valenzuela Spatial divesity in adasmodels and detetion pefomane IEEE Tans. Signal Poess. vol 54 pp [4] L.Z. Xu J. Li and P. Stoia Taget detetion and paamete estimation fo IO ada systems IEEE Tans Aeospae and Eletoni Systems vol. 44 no. 3 July 28 [5] C.Y. Chen and P.P. Vaidyanathan inimum edundany IO adas in Po. ISCAS 28 pp [6]. Jin G.S. Liao and J. Li Joint DOD and DOA estimation fo bistati IO ada Signal Poess. vol. 89 pp [7] B. Liu Z. S. He J. K. Zeng and B. Y. Liu Polyphase Othogonal Code Design fo IO Rada Systems poeeding of IEEE 26. [8] G. Rihad Cuy Rada System Pefomane odeling 2nd ed. London: Ateh House 25. [9] S.C. Joseph R.S. Yahya.A. Jensen and G.J. Pottie Evaluation of Pesonal Communiations Dual-Antenna Handset Divesity Pefomane IEEE Tans. Vehiula Tehnology 47(3): August